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Options Probability Calculator

Probability of touching a target, probability of expiring ITM, probability of profit. Black-Scholes-based math for any contract.

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Inputs
Target is 1.00% above spot. 1.00% / (14 × √(7/365)) standard deviations.
Probabilities
P(touch $505)
63.6%
P(close > $505)
31.8%
P(close < $505)
68.2%
P(touch) ≈ 2 × P(close at strike) by the reflection principle. Use P(touch) for stop placement and target zones; use P(ITM) for terminal-only payouts like cash-settled SPX or held-to-expiration premium.

How to use these probabilities

P(touch) vs P(ITM)

P(touch) is approximately 2× P(ITM) — touching a price at any point before expiration is roughly twice as likely as finishing there. This matters for stop placement: a 30% P(ITM) at your stop strike means ~60% P(touch).

Long call: P(profit) ≠ P(ITM)

You need price above STRIKE + premium paid to profit, not just above strike. Adjust by computing P(ITM) at the breakeven strike (strike + premium), not the option strike.

Credit spread P(profit)

P(profit) for a credit spread ≈ 1 − P(ITM at short strike). A 0.20-delta short strike has ~20% P(ITM), so the spread has ~80% P(profit) — but max loss is much larger than max win.

The Black-Scholes caveat

These probabilities assume lognormal returns and constant volatility — neither is true in real markets. Reality has fat tails (rare giant moves) and IV smiles (skew). Use these as a baseline, then haircut by 5-10% for fat-tail risk on short-premium trades.

Want probability baked into every AI idea?

OptionsDeck shows P(touch) on every target and stop.

Each AI-generated trade idea includes the implied probability of hitting target before stop — computed live from current IV + DTE. Plus full P/L curves and Greeks via the multi-leg builder.

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