Take Profit Stop Loss Probability Calculator

Key takeaways

With no edge, the chance your take profit is hit first is SL ÷ (TP + SL): 50% at 1:1, 33.3% at 2:1, 25% at 3:1. It depends only on the two distances in points, not on the price level.
A wider take profit is hit less often but pays more. Before costs, the two effects cancel out exactly.
Round-trip costs c raise the win rate you need to (SL + c) ÷ (TP + SL): 34.5% instead of 33.3% for a 20-point target, a 10-point stop and 0.34 points of costs.
A trend moves the odds less than most traders expect: an assumed 5-point-a-day trend in your favour with 50 points of daily volatility lifts 33.3% only to 34.7%.
A time limit adds a third outcome, the time-out, and lowers the chance of both orders being hit. Checking prices only at bar closes nudges the odds toward 50%.
Only a real edge, measured over many of your own trades, makes the average trade positive. Losing streaks are normal even with an edge.

F1

The no-edge odds: SL ÷ (TP + SL)

With no edge, the chance your take profit is hit before your stop loss equals your stop distance divided by the two distances added together. A 20-point take profit and a 10-point stop give 10 ÷ 30 = 33.3%, so about one trade in three reaches the take profit first.

Formula F1: chance the take profit is hit first, no edge

P = \frac{SL}{TP + SL}

What each letter means

Letter	What it means	Unit	Example
P	Chance the take profit is hit before the stop loss	0 to 1 (or 0% to 100%)	0.333
TP	Take profit distance: how far your target is from your entry	points	20
SL	Stop loss distance: how far your stop is from your entry	points	10

In plain English

F1 says the nearer order is hit more often, in exact proportion to the distances. Price has to travel twice as far to reach a take profit that is twice as far away, so with no edge it gets there first only one time in three. The formula has no volatility in it: a fast market reaches one of your orders sooner, but it does not change which one.

Analogy: you play a fair coin-flip game for 1 point a flip and stop when you are 20 points ahead or 10 points behind. You reach +20 first about one time in three, because the losing wall is twice as close. That is a 2:1 bracket. The same holds for someone walking at random down a hallway: they bump into the nearer wall more often.

When F1 applies

Your entries have no edge: price is as likely to go up as down from your entry.
Both orders rest at the broker or exchange, so every touch counts.
No time limit: the trade stays open until one order fills.
Moves are small compared with your distances, so price cannot jump far past an order.

When it does not

The market trends during your trade: use F2.
You close trades after a set time: use F4.
Your strategy checks only at bar closes: use F5.
You want the win rate that pays your costs: use F3.
Big gaps (news, the weekly open) can jump past a stop; that shows up as slippage.

F1 at common brackets, before costs. With no edge the average trade is zero in every row.
Take profit : stop	Chance TP is hit first	About how many wins in 100
1 : 1	50.0%	50
1.5 : 1	40.0%	40
2 : 1	33.3%	33
3 : 1	25.0%	25
4 : 1	20.0%	20

Worked example

Take profit 20 points, stop loss 10 points, no edge.

Write the formula
$P = \frac{SL}{TP + SL}$
Put in your distances (points)
$P = \frac{10}{20 + 10}$
Add the bottom
$P = \frac{10}{30}$
Divide
$P = 0.3333 = 33.3%$

Try F1 with your numbers

Turn on JavaScript to use this calculator. The worked example above shows every step.

Your numbers, step by step

–chance the take profit is hit first, no edge

CFTC RULE 4.41 HYPOTHETICAL PERFORMANCE DISCLOSUREThese results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under-or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.

Source.

Grinstead, C. M. and Snell, J. L. (2003). Introduction to Probability, 2nd edition, American Mathematical Society. Section 12.2, "Gambler's Ruin": for a fair game the chance of reaching M before 0 from z is z/M. Free edition: math.dartmouth.edu/~prob/prob/prob.pdf. Set z = SL and M = TP + SL to get F1.
Ross, S. M. (1997). Introduction to Probability Models, 6th edition, Academic Press, ISBN 0-12-598470-7. Chapter 10, "Brownian Motion and Stationary Processes", derives P(up A before down B) = B/(A + B) as the limit of the gambler's ruin.

F2

With a trend: adding drift to the odds

If the market drifts steadily in one direction, the odds tilt toward the order on that side. F2 adds the drift μ and the volatility σ to F1. With a 20-point take profit, a 10-point stop, an assumed trend of 5 points a day in your favour and 50 points of daily volatility, F2 gives 34.7%, only 1.3 percentage points above F1's 33.3%.

Formula F2: chance the take profit is hit first, with drift (A = TP distance, B = SL distance)

P = \frac{1 - e^{2 μ B / σ^{2}}}{e^{- 2 μ A / σ^{2}} - e^{2 μ B / σ^{2}}}

The same formula, easier to read, with k standing for 2μ ÷ σ²:

k = \frac{2 μ}{σ^{2}}, P = \frac{1 - e^{k B}}{e^{- k A} - e^{k B}}

What each letter means

Letter	What it means	Unit	Example
P	Chance the take profit is hit before the stop loss	0 to 1	0.347
A	Take profit distance (the same as TP in F1)	points	20
B	Stop loss distance (the same as SL in F1)	points	10
μ	Drift in your favour: the average move per day toward your take profit. The calculator asks for the market's trend and sets μ from it (see the sign rule below). How to find the trend.	points per day	5
σ	Volatility: the typical size (standard deviation) of one day's price change. How to find σ.	points per √day	50
k	Shorthand for 2μ ÷ σ², the trend's strength measured against the noise	1 per point	0.004
e	The number 2.71828…, the base of natural powers (the e^x key on a calculator)	none	2.718

Sign rule used on this page. The calculators ask for the market's trend the way you see it on a chart: positive when price is rising, negative when it is falling. For a long, μ is that trend. For a short, the calculator flips the sign (μ = −trend), because a falling market moves a short toward its take profit. So a long in a +5 market and a short in a −5 market get the same odds. μ and σ must use the same time unit; per day is used here, but any unit works if both match, because only 2μ ÷ σ² enters the formula.

In plain English

F2 is F1 on a tilted floor. The tilt is the trend, and the noise is the volatility. What matters is the tilt compared with the noise, which is why the formula only uses 2μ ÷ σ². A small trend in a noisy market barely moves the odds; the same trend in a quiet market moves them more. Over the few hours most trades last, even a strong daily trend is small next to the day's noise.

Analogy: the random walker from F1 is now on a moving walkway that runs gently toward one wall. They still stumble about at random, but the walkway carries them a little toward that wall, so they hit it a little more often.

When F2 applies

You have a real, steady estimate of the trend for the length of the trade.
μ and σ are in the same time unit and stay about the same while the trade is open.
No time limit and continuous checking, as in F1.

When it does not

You do not really know the trend. Estimating drift from a chart is very noisy, and a guess can make F2 look precise when it is not.
The trend or volatility changes during the trade.
You also have a time limit: F4 assumes no trend, so the two are not combined here.

Show that F2 becomes F1 when there is no trend (μ → 0)

When a number x is tiny, e^x is almost exactly 1 + x. With μ close to 0, k is tiny, so e^kB ≈ 1 + kB and e^−kA ≈ 1 − kA. Put those into F2:

P \approx \frac{1 - (1 + k B)}{(1 - k A) - (1 + k B)} = \frac{- k B}{- k (A + B)} = \frac{B}{A + B}

That is F1, with A = TP and B = SL. The calculator below shows the F1 value next to F2 so you can see the gap the trend makes. It computes F2 in a rearranged but identical form so very strong trends do not overflow.

Worked example

A long trade. Take profit A = 20 points, stop B = 10 points. Assumed market trend +5 points a day and volatility σ = 50 points per √day. These are illustrative assumptions, not a forecast.

You are long, so a rising market is in your favour: keep the sign of the trend
$μ_{fav} = μ = 5$
$= 5$
Work out k = 2μ / σ²
$k = \frac{2 \times 5}{50^{2}}$
$= 0.004$
Top power: e to the kB
$e^{k B} = e^{0.004 \times 10}$
$= e^{0.04} = 1.04081$
Bottom power: e to the −kA
$e^{- k A} = e^{- 0.08}$
$= 0.923116$
Put them in the formula
$P = \frac{1 - 1.04081}{0.923116 - 1.04081}$
$= \frac{- 0.0408108}{- 0.117694}$
Divide
$P = 0.3468 = 34.7%$
Compare with F1 (no trend). The difference is in percentage points.
$P_{F1} = 33.3%$
$P - P_{F1} = +1.34$

Try F2 with your numbers

Turn on JavaScript to use this calculator. The worked example above shows every step.

Your numbers, step by step

–chance the take profit is hit first, with your trend

F2, with your trend

–

F1, no trend

–

Difference

–

CFTC RULE 4.41 HYPOTHETICAL PERFORMANCE DISCLOSUREThese results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under-or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.

Where do these two numbers come from?

The F2 calculator asks for a market trend and a volatility σ. You can get both from a daily chart or a spreadsheet with simple sums. This part shows how, explains why σ is measured "per √day", and works through a full example. The helper below can do the sums for you.

Trend μ: the average daily change

The trend is how far price moved, on average, each day over the last N trading days. Take today's close, subtract the close from N days ago, and divide by N.

μ = \frac{C_{today} - C_{N days ago}}{N}

Example: 20 trading days ago ES closed at 5,000. Today it closed at 5,100. (C means a daily closing price.)

Trend: the average daily change over the last N days
$μ = \frac{C_{today} - C_{N days ago}}{N}$
$= \frac{5,100 - 5,000}{20} = \frac{100}{20} = +5$

A falling market gives a negative number. From 5,100 down to 5,000 in 20 days is −5 points a day.

Be honest about the trend. A past trend is a weak guide to the next few hours. Markets reverse often, and a 20-day average says little about the next 30 minutes. For most intraday trades, enter 0, which gives the no-edge odds of F1, unless you have a real, tested reason to expect a drift. A small trend barely moves the odds anyway: with a trend of 1.5 points a day, σ = 50, a 20-point take profit and a 10-point stop, F2 gives 33.7%, against 33.3% for F1.

Volatility σ: the typical size of one day's move

σ is the standard deviation of the daily price change, in points. In F2's random-walk model, about two days in three move less than σ from close to close. Here are three ways to estimate it, easiest first. They will not agree exactly. If two of them come out close, you have a sensible number.

From the daily ATR

$σ \approx \frac{ATR}{\sqrt{8 / π}} \approx \frac{ATR}{1.6}$

Add ATR with a length of 14 to a daily chart and read its value. For a random walk, the average high-to-low range of a day is √(8/π) ≈ 1.596 times σ (Parkinson, 1980), so divide ATR by about 1.6. The helper uses the exact 1.59577. Example: an ATR of 80 points gives 80 ÷ 1.596 = 50.1, so σ ≈ 50 points.

This is a rough estimate. ATR's "true range" also counts any gap from the previous close, and real prices have calm and wild spells that a pure random walk does not. Check it against way 2 if you can.

From daily closes

d = C_{day} - C_{day before}, σ = \sqrt{\frac{\sum {(d - \bar{d})}^{2}}{K - 1}}

Take the last 20 or so daily closes. Work out each day's change d (close minus the previous close), then take the standard deviation of those K changes. The bar over d means their average. This is exactly what σ measures, so it is the most direct way. In a spreadsheet, with 21 closes in cells C2 to C22, oldest first:

Where	Formula for σ
Any spreadsheet (helper column)	In D3 type `=C3-C2` and fill it down to D22. Then `=STDEV.S(D3:D22)`
Excel for Microsoft 365, or Excel 2021 and later	`=STDEV.S(C3:C22-C2:C21)`
Older Excel	The same formula, but press Ctrl+Shift+Enter instead of Enter. With plain Enter it shows #VALUE!
Google Sheets	`=ARRAYFORMULA(STDEV.S(C3:C22-C2:C21))`

With the helper column, =AVERAGE(D3:D22) gives the trend μ from the same data. It equals (C22 − C2) ÷ 20.

From implied volatility

$σ \approx \frac{Price \times IV}{\sqrt{252}}$

Implied volatility (IV) is the yearly volatility that option prices expect. For ES and MES, the VIX is the one to use: it is the implied volatility of S&P 500 options over the next 30 days. For other contracts, use the IV shown on that contract's options. Enter IV as a decimal in the formula (16% is 0.16) and divide by √252 ≈ 15.87, because a year has about 252 trading days. Example: ES at 5,000 with the VIX at 16 gives 5,000 × 0.16 ÷ 15.87 = 50.4, so σ ≈ 50 points a day.

Why 252 and not 365? Cboe measures the VIX over a 365-day calendar year, and its own articles divide by √365 ≈ 19.1 to get the expected move per calendar day (41.9 points here). Weekends and holidays are quiet, so almost all of a year's movement happens on about 252 trading days. Dividing by √252 gives σ per trading day, the same unit as your daily bars and ATR. Cboe's shortcut that a VIX of 16 means about 1% a day is the same idea: dividing by 16 is dividing by √256, close to √252. Remember that IV is what option traders expect, not a promise.

Why σ is "per √day"

Random moves partly cancel out, so they grow with the square root of time, not in a straight line. If one day's typical move is σ, the typical move over 4 days is σ × √4 = 2σ, not 4σ. A trend is different: it adds up in a straight line, so 4 days of a 5-point trend is 20 points. To change to a shorter unit, such as an hour, with h trading hours in the day:

σ_{hour} = \frac{σ_{day}}{\sqrt{h}}, μ_{hour} = \frac{μ_{day}}{h}

Example: ES trades about 23 hours a day, so with σ = 50 the typical hourly move is 50 ÷ √23 ≈ 10.4 points. If you count only the 6.5-hour cash session, it is 50 ÷ √6.5 ≈ 19.6 points. Volatility is not spread evenly through the day (the cash session is usually busier than the night), so treat any hourly figure as an average.

You do not have to convert anything for F2, as long as μ and σ use the same time unit. F2 only uses k = 2μ ÷ σ². Changing from days to hours divides μ by h and also divides σ² by h, so h cancels out:

k_{hour} = \frac{2 (μ_{day} / h)}{σ_{day}^{2} / h} = \frac{2 μ_{day}}{σ_{day}^{2}} = k_{day}

So enter both numbers per day, as the calculator asks, or both per hour, and you get the same odds. Mixing units, such as a trend per day with a σ per hour, gives wrong odds.

A full example: a short in a falling market

You are short, with a 20-point take profit and a 10-point stop. The market trend is −5 points a day and σ is 30 points per √day. These are the example values in the F2 calculator above. A falling market helps a short, so the page flips the sign: the drift in your favour is +5.

Short, take profit A = 20 points, stop B = 10 points, market trend −5 points a day, σ = 30 points per √day. Illustrative assumptions, not a forecast.

You are short, so a falling market is in your favour: flip the sign of the trend
$μ_{fav} = - μ = - (- 5)$
$= 5$
Work out k = 2μ / σ²
$k = \frac{2 \times 5}{30^{2}}$
$= 0.0111111$
Top power: e to the kB
$e^{k B} = e^{0.0111111 \times 10}$
$= e^{0.111111} = 1.11752$
Bottom power: e to the −kA
$e^{- k A} = e^{- 0.222222}$
$= 0.800737$
Put them in the formula
$P = \frac{1 - 1.11752}{0.800737 - 1.11752}$
$= \frac{- 0.117519}{- 0.316782}$
Divide
$P = 0.3710 = 37.1%$
Compare with F1 (no trend). The difference is in percentage points.
$P_{F1} = 33.3%$
$P - P_{F1} = +3.76$

Here is the same trade with more volatility. The same trend matters less when the market is noisier, because k divides the trend by σ².

Short trade, 20-point take profit, 10-point stop, market trend −5 points a day. Hypothetical odds from F2's random-walk model, not a forecast.
Volatility σ (points per √day)	k = 2μ ÷ σ²	F2: take profit first	F1: no trend	Difference (percentage points)
30	0.01111	37.1%	33.3%	+3.76
50	0.004	34.7%	33.3%	+1.34

CFTC RULE 4.41 HYPOTHETICAL PERFORMANCE DISCLOSUREThese results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under-or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.

Estimate my inputs

Type in numbers from your own chart. The helper works out a trend and a volatility, shows every step, and can copy them into the F2 calculator. Nothing is looked up or sent anywhere: it only uses what you type.

Turn on JavaScript to use the helper. The examples above show every step by hand.

Your numbers, step by step

Trend μ (points per day)

–

Volatility σ (points per √day)

–

Estimates only, not a forecast. They describe the past prices you typed. The next day can be calmer or wilder, and the trend can reverse.

Source.

Ross, S. M. (1997). Introduction to Probability Models, 6th edition, Academic Press, ISBN 0-12-598470-7. Chapter 10, exercises 8 and 22: the chance that Brownian motion with drift μ and variance σ² goes up A before going down B, derived from the gambler's ruin and from the martingale stopping theorem.
Grinstead, C. M. and Snell, J. L. (2003). Introduction to Probability, 2nd edition, AMS, section 12.2: the gambler's ruin with an unfair coin (p ≠ q), the step-by-step version of F2. Free edition.
Parkinson, M. (1980). The Extreme Value Method for Estimating the Variance of the Rate of Return. The Journal of Business 53(1), 61–65. doi:10.1086/296071. The average high-to-low range of a random walk over one period is √(8/π) ≈ 1.596 times σ; used for σ from ATR. Parkinson works with log prices; in points the rule is the same for moves that are small next to the price.
Cboe Global Indices (2026). Cboe Volatility Index Mathematics Methodology, version 5.0, last revised 26 February 2026. cdn.cboe.com. Time to expiry is counted in minutes of a 365-day year (525,600 minutes).
Doar, S. (2023). What the VIX and VIX1D Indices Attempt to Measure and How They Differ. Cboe Insights, 24 April 2023: the VIX is a 30-day, annualised expectation of the S&P 500's standard deviation, and a VIX of 16 means a daily range of about ±1%.
Bauer, S. (2022). Inside Volatility Trading: Breaking Down the VIX Index and its Correlation to the S&P 500 Index. Cboe Insights, 21 June 2022: daily expected volatility is the VIX divided by √365 (a VIX of 28 implies about 1.46% a day).

F3

The win rate you need after costs

Your break-even win rate is (SL + c) ÷ (TP + SL), where c is your round-trip cost in points. With a 20-point take profit, a 10-point stop and 0.34 points of costs, you need 34.5% winners just to break even. The average result per trade (expected value) is p·TP − (1 − p)·SL − c.

Formula F3: break-even win rate, and expected value per trade

p^{*} = \frac{SL + c}{TP + SL}

EV = p \cdot TP - (1 - p) \cdot SL - c

What each letter means

Letter	What it means	Unit	Example
p*	Break-even win rate: the share of trades that must hit TP for the average trade to be zero after costs	0 to 1	0.345
p	Your win rate: the share of trades that actually hit TP (from your journal)	0 to 1	0.40
TP	Take profit distance	points	20
SL	Stop loss distance	points	10
c	Round-trip cost per trade: commission and fees plus the slippage you expect, turned into points	points	0.34
EV	Expected value: the average result per trade if you repeated this trade many times	points	+1.66

How to get c in points. Divide your round-trip fees by the dollar value of one point, then add the slippage you expect in points. On ES (one point = $50), $4.50 of fees is 4.50 ÷ 50 = 0.09 points, and one tick of slippage is 0.25 points, so c = 0.34 points. This page charges c on every trade. If your slippage only happens when the stop fills, that is slightly conservative.

In plain English

Every trade pays c, win or lose. A win nets TP − c and a loss costs SL + c. The break-even win rate is the point where the wins exactly pay for the losses. Without costs (c = 0), F3 gives the same number as F1: with no edge you exactly break even before costs, and costs are what push the average below zero.

Analogy: a toll road. Every trip pays the same toll, whether the trip was worth it or not. The shorter the trip (the tighter your bracket), the bigger the toll is compared with what the trip earns, so you need more good trips to come out ahead.

When F3 applies

Every trade ends at your take profit or your stop, at the same distances every time.
c is your real average cost per round trip, in points.
p is measured over many trades with this same bracket.

When it does not

You scale out, move your stop or close trades early: the win and loss sizes change.
Trades time out and close at market (see F4).
Slippage in fast markets is much bigger than your average.

Show that the expected value is exactly zero at p*

Put p = p* into the expected value. Multiplying out, p*·TP − (1 − p*)·SL = p*·(TP + SL) − SL, and p*·(TP + SL) is just SL + c by the definition of p*:

p^{*} (TP + SL) - SL - c = (SL + c) - SL - c = 0

Worked example

Take profit 20 points, stop 10 points, costs c = 0.34 points (ES: $4.50 of fees plus one tick of slippage), and a hypothetical win rate of p = 40%.

Break-even win rate: put in your numbers
$p^{*} = \frac{SL + c}{TP + SL}$
$= \frac{10 + 0.34}{20 + 10} = \frac{10.34}{30}$
Divide
$p^{*} = 0.3447 = 34.5%$
Expected value at your win rate p = 40.0%
$EV = p \cdot TP - (1 - p) \cdot SL - c$
$= 0.4 \times 20 - 0.6 \times 10 - 0.34$
Multiply, then subtract (points per trade)
$EV = 8 - 6 - 0.34$
$= +1.66$
Check: at exactly p*, EV is zero
$p^{*} \cdot TP - (1 - p^{*}) \cdot SL - c$
$= 0$

On ES, +1.66 points is +$83.00 per contract per trade, if that 40% win rate held. Hypothetical: see the disclosure below the calculator.

Try F3 with your numbers

Turn on JavaScript to use this calculator. The worked example above shows every step.

Your numbers, step by step

Break-even win rate p*After your costs: –
Average per trade with no edgeHypothetical; at the F1 win rate, costs are all that is left: –
Average per trade at your win rateHypothetical; every trade ends at TP or SL: –

–

CFTC RULE 4.41 HYPOTHETICAL PERFORMANCE DISCLOSUREThese results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under-or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.

Source.

López de Prado, M. (2018). Advances in Financial Machine Learning. Wiley, ISBN 978-1-119-48208-6. Chapter 15, "Understanding Strategy Risk", Snippet 15.3 "Computing the implied precision": the minimum win rate for a target Sharpe ratio given a profit-taking and a stop-loss threshold. With a target of zero it reduces to SL ÷ (TP + SL); F3 is the same with costs taken out of each outcome.
Grinstead, C. M. and Snell, J. L. (2003). Introduction to Probability, 2nd edition, AMS, chapter 6, "Expected Value and Variance". Free edition.

F4

With a time limit: take profit, stop or time-out

If you close any trade that has not hit either order within N bars, some trades end in a time-out. With a 20-point take profit, a 10-point stop, an ATR of 10 points and a 10-bar limit, the no-edge split is 26.9% take profit, 60.3% stop loss and 12.8% time-out.

Formula F4: chance each outcome happens within the time limit, no edge (L = A + B)

P (TP) = \frac{B}{L} + \sum_{n = 1}^{\infty} c_{n} \sin (\frac{n π B}{L}) e^{- n^{2} x}

P (SL) = \frac{A}{L} + \sum_{n = 1}^{\infty} c_{n} \sin (\frac{n π A}{L}) e^{- n^{2} x}

c_{n} = \frac{2 {(- 1)}^{n}}{n π}, x = \frac{π^{2} σ_{T}^{2}}{2 L^{2}}

σ_{T} = \frac{ATR}{\sqrt{8 / π}} \cdot \sqrt{N}, L = A + B

P (time-out) = 1 - P (TP) - P (SL)

What each letter means

Letter	What it means	Unit	Example
A, B	Take profit and stop loss distances	points	20, 10
L	The whole gap between your two orders, A + B	points	30
N	Time limit: how many bars you hold before closing at market	bars	10
ATR	Average true range of one bar on the chart you count bars on	points	10
σ_T	Volatility over the whole holding time. A random-walk bar's average range is √(8/π) ≈ 1.596 times its standard deviation, and volatility grows with the square root of time.	points	19.82
x	Decay number: how much time the trade has, compared with the size of the bracket	none	2.153
n, c_n	n counts the terms of the sum (1, 2, 3 and so on); c_n is each term's size factor, 2(−1)ⁿ ÷ (nπ)	none	1, 2, …
sin, π, e	The sine function, 3.14159… and 2.71828…	none

In plain English

The first part of each line, B ÷ L and A ÷ L, is F1: the odds if the trade had all the time in the world. Each term of the sum takes away the trades that would have reached that order after your time limit. The terms shrink very fast (e^−n²x), so only the first two or three matter unless your time limit is very short. The more time you allow, the bigger x gets, the smaller the terms, and the closer F4 gets to F1.

Analogy: the random walker from F1 now has a timer. When it rings, they stop wherever they are. Walkers who were slowly heading for the far wall (your take profit) are the ones most often stopped by the timer, so a time limit cuts the take-profit share more than the stop-loss share.

When F4 applies

No edge and no trend.
Both orders are checked continuously and you exit at market when the time is up.
Your ATR reflects ordinary bar-to-bar movement.

When it does not

You have a trend: F4 assumes none, and this page does not combine F2 with F4.
Real ATR also includes gaps between bars, so treat the time-out split as a rough guide.
Volatility changes a lot over the holding time (for example across the market open).

The origin of the series

Think of the chance of reaching the take profit by time t as a temperature along a rod from the stop (0) to the take profit (L). It obeys the heat equation, is 0 at the stop and 1 at the take profit, and starts at 0 everywhere inside. The steady answer is a straight line, B ÷ L, which is F1. The gap between the start and the steady answer is written as a sum of sine waves, each fading at its own rate e^−n²x. Working out each wave's size gives the 2(−1)ⁿ ÷ (nπ) factors. The stop-loss line is the same problem seen from the other end. The calculator adds terms until they are smaller than 10⁻¹⁶.

Quant researchers label trades the same way, by which of three barriers is touched first (profit-taking, stop-loss or a time limit). This is the "triple-barrier method" of López de Prado (2018), chapter 3.

Worked example

Take profit A = 20 points, stop B = 10 points, ATR = 10 points per bar, time limit N = 10 bars, no edge.

Volatility of one bar from your ATR
$σ_{bar} = \frac{ATR}{\sqrt{8 / π}}$
$= \frac{10}{1.59577} = 6.2666$
Volatility over the whole holding time
$σ_{T} = σ_{bar} \times \sqrt{N}$
$= 6.2666 \times \sqrt{10} = 19.8166$
The decay number x (L = TP + SL)
$x = \frac{π^{2} {σ_{T}}^{2}}{2 L^{2}}$
$= \frac{9.8696 \times {19.8166}^{2}}{2 \times 30^{2}}$
$= 2.1532$
Take profit: B/L plus the series terms (n = 1, 2 shown; the page adds all 4 that matter)
$P (TP) = 0.33333 - 0.06402$
$+ 0.00005$
$+ 2 more terms$
$= 26.9%$
Stop loss: A/L plus the same kind of terms
$P (SL) = 0.66667 - 0.06402$
$- 0.00005$
$+ 2 more terms$
$= 60.3%$
Whatever is left times out: P(time-out) = 1 − P(TP) − P(SL)
$1 - 0.2694 - 0.6026$
$= 12.8%$

Try F4 with your numbers

Turn on JavaScript to use this calculator. The worked example above shows every step.

Your numbers, step by step

–take profit within the time limit

TPTime-outSL

CFTC RULE 4.41 HYPOTHETICAL PERFORMANCE DISCLOSUREThese results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under-or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.

Source.

Redner, S. (2001). A Guide to First-Passage Processes. Cambridge University Press. Chapter 2, "First Passage in an Interval": diffusion between two absorbing ends solved as a sine series. doi:10.1017/CBO9780511606014
López de Prado, M. (2018). Advances in Financial Machine Learning. Wiley, ISBN 978-1-119-48208-6. Chapter 3, the triple-barrier labeling method (Snippet 3.2): profit-taking, stop-loss and a time limit.

F5

Checking only at bar closes

A strategy or backtest that checks for a hit only at each bar's close misses touches between checks, which acts like moving both orders a little further away. Broadie, Glasserman and Kou (1997) put that shift at about 0.5826 × σ × √Δt. With a 1-minute ATR of 4 points, a 20-point take profit and a 10-point stop, the no-edge odds rise from 33.3% to about 34.8%.

Formula F5: approximate odds when hits are checked only once per bar

s = β σ \sqrt{Δ t} \approx 0.5826 \cdot σ_{bar}

P_{bars} \approx \frac{B + s}{A + B + 2 s}

What each letter means

Letter	What it means	Unit	Example
s	The shift: how much further away each order effectively sits	points	1.46
β	A constant, −ζ(1/2) ÷ √(2π) ≈ 0.5826, from the paper	none	0.5826
σ√Δt = σ_bar	Volatility of one bar: the typical move between two checks. From ATR: σ_bar = ATR ÷ 1.596.	points	2.51
A, B	Take profit and stop loss distances	points	20, 10
P_bars	Chance the take profit is hit first when checked only at bar closes	0 to 1	0.348

In plain English

Between two checks, price can poke through an order and come back. A check at the close never sees it, so the trade carries on as if the order were a little further away. Moving both orders out by the same amount matters more for the nearer one, which pushes the odds toward 50%.

Analogy: a guard who looks at the door once a minute misses anyone who steps out and back in between looks. A guard who watches all the time sees everyone.

When F5 applies

A backtest, script or alert that only checks for a hit at each bar's close.
The shift is small compared with each distance (a bar is short next to your bracket).

When it does not

Bracket orders held by your broker or the exchange react to every trade, so they are monitored continuously: use F1.
The paper's result is for one barrier; applying it to both orders is an approximation that is good when the shift is small.
Bars that are long compared with your bracket.

Worked example

Take profit A = 20 points, stop B = 10 points, checked at each 1-minute close, with a 1-minute ATR of 4 points (an example value).

Volatility of one bar from your ATR
$σ_{bar} = \frac{4}{1.59577} = 2.5066$
The shift
$s = 0.5826 \times 2.5066 = 1.4604$
Move both orders out by s and use F1
$P_{bars} \approx \frac{10 + 1.4604}{20 + 10 + 2 \times 1.4604}$
$= \frac{11.4604}{32.9207} = 34.8%$
Compare with F1 (checked continuously)
$P_{F1} = 33.3%$

Try F5 with your numbers

Turn on JavaScript to use this calculator. The worked example above shows every step.

Your numbers, step by step

Checked at bar closes (F5)

–

Resting broker orders (F1)

–

CFTC RULE 4.41 HYPOTHETICAL PERFORMANCE DISCLOSUREThese results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under-or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.

Source.

Broadie, M., Glasserman, P. and Kou, S. (1997). A Continuity Correction for Discrete Barrier Options. Mathematical Finance 7(4), 325–349. doi:10.1111/1467-9965.00035. The abstract gives the shift as a factor exp(βσ√Δt) with β ≈ 0.5826 on log prices; in points, the same shift is added to each distance.

All-in-one

All-in-one TP/SL calculator

This calculator puts F1 to F4 together for one trade. It uses F1 by default, F2 if you add a trend, and F4 if you add a time limit, then applies F3 for your costs and win rate. Distances are in the units chosen at the top of the page. Example values are filled in; replace them with your own.

The calculator needs JavaScript. For the example trade (20-point take profit, 10-point stop, 0.34 points of costs, no edge) the results are 33.3% take profit first and a 34.5% break-even win rate.

Your bracket

Side

Long (buy) Short (sell)

Side only matters when you add a trend (F2).

Take profit distance (points)

Stop loss distance (points)

Costs and size

Round-trip cost c (points)

Fees ÷ dollars per point, plus expected slippage. 0.34 is ES with $4.50 fees and 1 tick.

Optional: a trend (F2) Add a market trend

Optional: a time limit (F4) Close the trade if neither order is hit within a set number of bars

Optional: your own track record

Your historical win rate (%)

Example value. From your trading journal: trades that hit TP ÷ all trades with this bracket. Leave empty to skip.

Inputs look right.

Chance take profit is hit first, with no edge (F1)

33.3%about 1 trade in 3

TP first 33.3%SL first 66.7%

Reward : riskTake profit distance ÷ stop distance: 2.00 : 1
Amount at risk per tradeStop + costs (SL + c): –
Result if take profit is hitAfter costs (TP − c): –
Win rate you need to break even (F3)(SL + c) ÷ (TP + SL): –
Average result per trade, no edgeHypothetical: –
Average result per trade at your win rateHypothetical; assumes every trade ends at TP or SL: –

–

All figures are hypothetical. "No edge" means your entries are no better than random. Your real results depend on fills, gaps, liquidity and your own trading.

CFTC RULE 4.41 HYPOTHETICAL PERFORMANCE DISCLOSUREThese results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under-or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.

Simulation

Watch 100 random trades

This simulation sends 100 random price paths from your entry, using the all-in-one calculator's settings, and counts which order each one hits first. It then runs 20,000 more and puts the result next to the formula, as a check you can see: the two should agree to within random noise.

The simulation needs JavaScript.

HYPOTHETICAL SIMULATION

Path reached take profitPath reached stop lossTime-out (only with a time limit)

Take profit first

– of 100

Stop loss first

– of 100

Time-out

– of 100

Formula F1 says (TP first)

–

Simulation of 20,000 trades got

–

Gap, and normal random noise

–

Check

Waiting

Running 20,000 more simulated trades in the background…

Idealised uses smooth, bell-curve price steps, which is exactly what F1, F2 and F4 assume, so the two numbers should match within the noise band. Realistic uses occasional big jumps (fat tails) and calm and wild spells (volatility clustering), as real markets have. The formula does not model those, yet the no-edge odds barely change: jumps change how the ride feels, not the baseline. Paths are checked between steps the way a resting order at the exchange would be.

CFTC RULE 4.41 HYPOTHETICAL PERFORMANCE DISCLOSUREThese results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under-or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.

Simulation

What a run of trades can look like

Win rate is an average, and averages hide streaks. This chart replays the all-in-one bracket hundreds of times at the win rate you choose. The shaded band shows where 90% of the simulated accounts ended up after each trade, the dark line is the middle result, and the blue line is one example account.

The simulation needs JavaScript.

HYPOTHETICAL SIMULATION

Middle 90% of accountsMiddle result (median)One example account

Accounts that ended in a loss

–

Typical worst drop from a peak

–

Bad-case drop (1 in 20)

–

Longest losing streak

–

Each account starts at zero and adds or subtracts the after-cost result of each trade.

Show the chart as a table

After trade	5th percentile	Median	95th percentile
Run the simulation to fill this table.

CFTC RULE 4.41 HYPOTHETICAL PERFORMANCE DISCLOSUREThese results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under-or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.

Ratio

Why a wider take profit is hit less often but pays more

Moving your take profit further away lowers the chance it is hit first, but each win pays more. With no edge these two effects cancel exactly: a 3:1 bracket wins about 25% of the time and a 1:1 bracket about 50%, yet both average zero per trade before costs. A wider target is not better or worse by itself.

Take a 10-point stop. A 10-point target wins about half the time. A 30-point target wins about a quarter of the time, but each win is three times bigger. Over many trades both come out even before costs.

What changes is how the ride feels. Low win rates mean longer losing streaks, and many traders abandon a sound plan in the middle of one. Pick the ratio you can stick with, then check that your measured win rate beats the break-even rate for that ratio (F3).

Costs

Why costs matter more on tight brackets

Commissions, exchange fees and slippage are roughly fixed per trade, so they take a bigger bite when your stop is small. In the example below, F3 says a 2:1 bracket needs a 34.5% win rate with a 10-point stop, but 39.0% with a 2-point stop. Tight brackets need more edge just to break even.

Example only: 2:1 brackets with c = 0.34 points of round-trip costs (on ES, $4.50 of commission and fees plus one 0.25-point tick of slippage). Dollar figures are per ES contract. Your costs may differ.
Stop distance	Amount at risk (SL + c)	Costs as % of the stop	Win rate needed (F3)	No-edge result per trade
2 points (8 ES ticks)	2.34 points ($117.00)	17.0%	39.0%	−0.34 points (−$17.00)
4 points (16 ES ticks)	4.34 points ($217.00)	8.5%	36.2%	−0.34 points (−$17.00)
10 points (40 ES ticks)	10.34 points ($517.00)	3.4%	34.5%	−0.34 points (−$17.00)
20 points (80 ES ticks)	20.34 points ($1,017.00)	1.7%	33.9%	−0.34 points (−$17.00)

The drag with no edge is the same in every row: c = 0.34 points per trade. Against a 2-point stop that is 17% of the stop; against a 20-point stop, only 1.7%.

AI

Can AI or chart reading tell you the odds?

No tool can look at a chart and tell you the true odds of one trade. In an April 2026 study, seven vision AI models looked at candlestick charts and guessed whether HS300 stocks would be up or down 30 days later. They were right 49.4% to 53.5% of the time, close to a coin flip.

The study is Hu et al., "Do VLMs Truly 'Read' Candlesticks?" (arXiv 2604.12659). Its authors found the models did well only in strong, steady uptrends or downtrends and poorly in ordinary markets. A simple model given the raw numbers (XGBoost) scored 50.9% on the same HS300 test.

Real-money trading tells a similar story. In Alpha Arena Season 1 (October to November 2025), six AI language models each traded $10,000 of crypto perpetual futures. They read prices and indicators as numbers, not chart images. Four of the six finished below $10,000, down 31% to 63% (Protos reports the same balances). The organiser itself warned that one short run can reflect luck.

Neither result proves AI can never help a trader. Both show that a confident-sounding prediction is not the same thing as a measured edge. Use F1 and F3 as the bar any method has to beat, over many trades.

Edge

What actually improves your odds

Your odds improve only when your entries have a real edge that you have measured over many trades. Keep a journal, count how often your take profit is hit first, compare that with the break-even win rate after costs, and keep costs low. Position size does not change the odds, but it decides whether you survive the losing streaks.

Measure, then trust. Log every trade with the same bracket. After 100 trades, a 40% win rate is still uncertain by roughly ±10 percentage points either way, so keep counting.
Compare with break-even, not with 50%. A 38% win rate is good at 2:1 and poor at 1:1.
Cut costs where you can. Lower fees, fewer stop-outs from over-tight stops, and limit entries where they suit your plan.
Size for the streak. Risk a small, fixed share of your account per trade so a run of 8 to 10 losses is survivable.
Keep the bracket you tested. Moving a stop mid-trade changes the ratio and makes your journal numbers meaningless.

PickMyTrade

How to use this with PickMyTrade

PickMyTrade does not predict trades. It takes the TradingView alert you already built and sends it to your broker or prop-firm account. If your alert JSON includes a take profit and a stop loss, PickMyTrade sends them with your entry, so the bracket you checked here is the bracket your broker receives.

Check the ratio, your costs and your break-even win rate here first. Then put the same take profit and stop loss distances in your alert, in the units your alert field uses. Test on a demo account before going live.

Read the JSON alert guide · See how PickMyTrade works

{
  "symbol": "NQ",
  "data": "buy",
  "quantity": 1,
  "price": "{{close}}",
  "tp": 0,
  "dollar_tp": 10,
  "sl": 0,
  "dollar_sl": 5,
  "token": "your_token_here"
}

Excerpt adapted from the indicator example in PickMyTrade's JSON alert guide, where the take profit is set to twice the stop (a 2:1 bracket). Fields such as tp, percentage_tp and dollar_tp use different units; check the guide for the one you use.

Glossary

Definitions

Take profit (TP): A resting order that closes your trade at a set profit. On this page, its distance from your entry in points.
Stop loss (SL): An order that closes your trade at a set loss. Most stops become market orders when triggered, so they can fill a little worse (slippage).
Point: One whole unit of the quoted price. A move from 6000.00 to 6001.00 is one point. Distances in points work the same at any price level.
Tick and tick value: The smallest price step a contract can move, and what one step is worth in dollars per contract. On ES one tick is 0.25 points and $12.50.
Bracket order: An entry sent together with its take profit and stop loss. When one exit fills, the other is cancelled.
Reward-to-risk ratio (R:R): Take profit distance divided by stop distance. A 20-point target with a 10-point stop is 2:1.
No edge: Entries that are no better than random. Price is equally likely to go either way from your entry.
Drift (μ) and volatility (σ): Drift is the average move per unit of time (the trend). Volatility is the typical size of the random part of the move. F2 uses both.
Standard deviation: A measure of how spread out a set of numbers is: roughly the typical distance of each number from their average. On this page, σ is the standard deviation of one day's price change, in points.
Implied volatility (IV): The volatility that option prices expect for the future, quoted as a yearly percentage. The VIX is the implied volatility of S&P 500 options over the next 30 days.
Round-trip cost (c): Commission, exchange fees and expected slippage for one complete trade, entry and exit, turned into points.
Break-even win rate: The share of trades that must hit TP for the average trade to be zero after costs (F3).
Expected value (EV): The average result per trade if you repeated the same trade many times.
ATR (average true range): The average size of one bar's range on your chart, in points. F4 and F5 turn it into volatility.
Time-out: Closing a trade at market because neither the take profit nor the stop was hit within your time limit.
Drawdown: How far an account falls from its highest point before it recovers.

FAQ

Frequently asked questions

What win rate do I need with a 2:1 risk reward?

You need a win rate above 33.3% to break even with a 2:1 reward-to-risk ratio before costs. After costs you need a little more. With a 20-point take profit, a 10-point stop and 0.34 points of round-trip costs (about $4.50 of fees plus 1 tick of slippage on ES), the break-even win rate is (10 + 0.34) ÷ 30 = 34.5%. Tighter stops need even higher win rates.

How do I calculate the probability of hitting take profit before stop loss?

With no edge, divide your stop distance by the sum of both distances: SL ÷ (TP + SL). A 10-point stop and a 20-point take profit give 10 ÷ 30 = 33.3%. This is the classic gambler's ruin result for a fair random walk, and it works in points, ticks or dollars.

Why does this calculator use points instead of prices?

Because the odds depend only on how far each order is from your entry, not on the price level. A 20-point take profit and a 10-point stop give the same 33.3% no-edge odds whether the market is at 4,000 or 6,000. Points work for any market; pick an instrument only if you also want ticks and dollars.

Is a 1:3 risk reward better?

Not by itself. Risking 1 to make 3 means your take profit is hit first only about 25% of the time with no edge, so before costs the average trade is still zero. A 1:3 setup is better only if your measured win rate stays above about 25%, plus a bit extra to cover costs.

Does a tighter stop loss improve my win rate?

No. With the same take profit, a tighter stop lowers the chance your take profit is hit first, because the stop is now closer to price. It also makes fixed costs a bigger share of each loss. A tighter stop can still make sense for sizing, but it does not raise your odds.

Does stop loss slippage matter?

Yes. Slippage makes every losing trade a bit bigger, which raises your break-even win rate. On ES, 1 tick of slippage is 0.25 points, or $12.50 per contract. On a 2-point stop that is more than 10% of the amount at risk. Fast markets and news can cause several ticks of slippage or more.

Why do I lose money with a 50% win rate?

A 50% win rate loses money when your average loss is bigger than your average win. That happens if your take profit is closer than your stop, or if costs and slippage eat into a 1:1 bracket. At exactly 1:1, you need slightly more than 50% wins to cover costs.

Does a trend change the chance of hitting take profit first?

Yes, but usually less than traders expect. With an assumed trend of 5 points a day in your favour and 50 points of daily volatility, a 20-point take profit and 10-point stop go from 33.3% to 34.7%. The effect depends on the trend divided by the volatility squared, so the same trend matters more in a quiet market.

Does market volatility change the chance of hitting take profit first?

Not the no-edge odds. With no edge, the chance of hitting take profit first depends only on the two distances, not on how fast the market moves. Volatility changes how quickly one of them is hit, how often a time limit runs out first, how much a trend matters, and how much your stop slips.

How do I find the volatility (σ) to use?

Use a daily chart. The quickest way is to divide the 14-day ATR by about 1.6: an ATR of 80 points gives σ ≈ 50. You can also take the standard deviation of the last 20 or so daily changes (each close minus the one before), or multiply the price by the implied volatility and divide by √252 ≈ 15.87. ES at 5,000 with the VIX at 16 gives about 50 points a day.

Should I enter a trend for intraday trades?

Usually not. A past trend is a weak guide to the next few hours, so for most intraday trades enter 0, which gives the no-edge F1 odds. A small trend barely changes the answer anyway: 1.5 points a day with 50 points of daily volatility moves a 20-point take profit and 10-point stop from 33.3% to 33.7%.

Why does a backtest that checks bar closes show different odds?

Checking only at bar closes misses touches between checks, which acts like moving both orders a little further away. Broadie, Glasserman and Kou (1997) put the shift at about 0.5826 times the volatility of one bar. With a 1-minute ATR of 4 points, a 20-point take profit and a 10-point stop go from 33.3% to about 34.8%. Bracket orders resting at your broker are checked continuously, so 33.3% applies to them.

Can AI predict if my trade will hit take profit?

There is no good evidence that it can do so reliably. In an April 2026 study (arXiv 2604.12659), seven vision AI models guessed the 30-day direction of HS300 stocks from candlestick charts and were right 49.4% to 53.5% of the time. In Alpha Arena Season 1, four of six AI models that traded real money finished with losses.

How many trades do I need to know my real win rate?

More than most traders expect. After 100 trades, a measured 40% win rate could plausibly be anywhere from about 30% to 50%. After 400 trades the range narrows to about 35% to 45%. Keep journaling the same setup before deciding you have an edge.

Is this calculator financial advice?

No. This is an educational tool. It does not know your situation, does not recommend any trade or instrument, and shows hypothetical results only. PickMyTrade is not a registered commodity trading advisor or investment adviser. Talk to a qualified professional before making trading decisions.

For the curious: models, contract specs and references

What all five formulas assume

F1 to F4 treat price as Brownian motion: a random walk with no jumps, watched continuously. F1 holds for any fair process that cannot jump over an order (a martingale), which is why volatility does not appear in it. F2 adds a constant drift. F4 adds a time limit to F1. F5 corrects F1 for checking only at bar closes.

Fat tails, jumps and fills

Real returns have fatter tails and calm and wild spells (Mandelbrot, 1963; Cont, 2001). The "realistic" simulation mode uses Student-t steps with 4 degrees of freedom and GARCH(1,1) volatility with α = 0.08 and β = 0.90 (Bollerslev, 1986). Gaps can jump straight past a stop, which shows up as slippage. A take-profit limit order can also be touched without filling if you are late in the queue, which trims real TP odds slightly.

Contract specs used by this calculator

Outright minimum price moves and dollar values per contract, from CME Group's contract specification pages (linked), checked on 2026-09-23. They are used only to turn points into ticks and dollars. Calendar spreads use finer ticks; for example, silver spreads and settlements move in 0.001 ($5.00).

Symbol	Contract	Tick size (points)	Tick value	Value of 1.00 point
ES	E-mini S&P 500	0.25	$12.50	$50
MES	Micro E-mini S&P 500	0.25	$1.25	$5
NQ	E-mini Nasdaq-100	0.25	$5.00	$20
MNQ	Micro E-mini Nasdaq-100	0.25	$0.50	$2
YM	E-mini Dow ($5)	1	$5.00	$5
MYM	Micro E-mini Dow	1	$0.50	$0.50
RTY	E-mini Russell 2000	0.10	$5.00	$50
M2K	Micro E-mini Russell 2000	0.10	$0.50	$5
CL	Crude oil (WTI), 1,000 barrels	0.01	$10.00	$1,000
MCL	Micro WTI crude oil, 100 barrels	0.01	$1.00	$100
GC	Gold, 100 troy oz	0.10	$10.00	$100
MGC	Micro gold, 10 troy oz	0.10	$1.00	$10
SI	Silver, 5,000 troy oz	0.005	$25.00	$5,000
6E	Euro FX, €125,000	0.00005	$6.25	$125,000
ZN	10-Year T-Note, $100,000 face	1/2 of 1/32 (0.015625)	$15.625	$1,000

References

Grinstead, C. M. and Snell, J. L. (2003). Introduction to Probability, 2nd edition. American Mathematical Society. Section 12.2, "Gambler's Ruin"; chapter 6, "Expected Value and Variance". Free edition (Dartmouth). Used for F1, F2 and F3.
Ross, S. M. (1997). Introduction to Probability Models, 6th edition. Academic Press. ISBN 0-12-598470-7. Chapter 10, "Brownian Motion and Stationary Processes". Used for F1 and F2.
López de Prado, M. (2018). Advances in Financial Machine Learning. Wiley. ISBN 978-1-119-48208-6. Chapter 3 (triple-barrier method, Snippet 3.2) and chapter 15 (implied precision, Snippet 15.3). Used for F3 and F4.
Redner, S. (2001). A Guide to First-Passage Processes. Cambridge University Press. Chapter 2, "First Passage in an Interval". doi:10.1017/CBO9780511606014. Used for F4.
Broadie, M., Glasserman, P. and Kou, S. (1997). A Continuity Correction for Discrete Barrier Options. Mathematical Finance 7(4), 325–349. doi:10.1111/1467-9965.00035. Used for F5.
Parkinson, M. (1980). The Extreme Value Method for Estimating the Variance of the Rate of Return. The Journal of Business 53(1), 61–65. doi:10.1086/296071. Used for σ from a daily ATR (F2's inputs).
Cboe Global Indices (2026). Cboe Volatility Index Mathematics Methodology, version 5.0, last revised 26 February 2026 (PDF), with Cboe Insights articles by Doar (2023) and Bauer (2022). Used for σ from implied volatility.
Hu, K., Xiao, L., Xu, S., Tang, Z. and Liu, M. (2026). Do VLMs Truly "Read" Candlesticks? A Multi-Scale Benchmark for Visual Stock Price Forecasting. arXiv:2604.12659. Accuracy figures are from Table 4 (HS300 dataset).
Nof1 (2025). Exploring the Limits of Large Language Models as Quant Traders. Archived copy. Final balances: organiser's post and Protos.
Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance 1(2), 223–236. doi:10.1080/713665670
Mandelbrot, B. (1963). The Variation of Certain Speculative Prices. The Journal of Business 36(4), 394–419. doi:10.1086/294632
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31(3), 307–327. doi:10.1016/0304-4076(86)90063-1
CME Group contract specifications for ES, MES, NQ, MNQ, YM, MYM, RTY, M2K, CL, MCL, GC, MGC, SI, 6E and ZN (linked in the table above), checked 2026-09-23.
17 CFR § 4.41, Advertising by commodity pool operators, commodity trading advisors, and the principals thereof. Cornell LII.

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Important disclaimers

Educational use only

This calculator and everything on this page are for education only. They are not investment, trading or financial advice, and nothing here is a recommendation to buy or sell any futures contract, security or other instrument. PickMyTrade is not registered as a commodity trading advisor (CTA) or investment adviser. The tool does not know your finances, goals, experience or risk tolerance.

Futures risk

Trading futures involves substantial risk of loss and is not suitable for all investors. You can lose more than your initial investment. Only use risk capital. Past performance is not indicative of future results.

What the model ignores

All results on this page are hypothetical and come from simple mathematical models you control. The formulas assume a random walk with the drift and volatility you enter; real markets change their trend and volatility, and nobody knows the true drift in advance. They ignore price gaps, liquidity, queue position, partial fills, rejected or delayed orders, data errors and platform or broker outages, any of which can change real outcomes. Contract specifications are provided for convenience; confirm them with the exchange and your broker before trading.

About PickMyTrade

PickMyTrade automates the alerts you create; it does not choose trades for you. This page makes no claim about the win rate or profitability of PickMyTrade users, and PickMyTrade does not offer a feature that predicts whether a trade will reach its take profit.

Hypothetical performance (CFTC Rule 4.41)

These results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under-or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.

What are the chances my take profit is hit before my stop loss?

Key takeaways

Units for every calculator on this page

The no-edge odds: SL ÷ (TP + SL)

What each letter means

In plain English

When F1 applies

When it does not

Worked example

Try F1 with your numbers

With a trend: adding drift to the odds

What each letter means

In plain English

When F2 applies

When it does not

Worked example

Try F2 with your numbers

Where do these two numbers come from?

Trend μ: the average daily change

Volatility σ: the typical size of one day's move

From the daily ATR

From daily closes

From implied volatility

Why σ is "per √day"

A full example: a short in a falling market

Estimate my inputs

The win rate you need after costs

What each letter means

In plain English

When F3 applies

When it does not

Worked example

Try F3 with your numbers

With a time limit: take profit, stop or time-out

What each letter means

In plain English

When F4 applies

When it does not

Worked example

Try F4 with your numbers

Checking only at bar closes

What each letter means

In plain English

When F5 applies

When it does not

Worked example

Try F5 with your numbers

All-in-one TP/SL calculator

Watch 100 random trades

What a run of trades can look like

Why a wider take profit is hit less often but pays more

Why costs matter more on tight brackets

Can AI or chart reading tell you the odds?

What actually improves your odds

How to use this with PickMyTrade

Definitions

Frequently asked questions

What all five formulas assume

Fat tails, jumps and fills

Contract specs used by this calculator

References

Important disclaimers

Educational use only

Futures risk

What the model ignores

About PickMyTrade

Hypothetical performance (CFTC Rule 4.41)

Send the bracket you checked to your broker