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Probability

Probability

Probability is the engine room of this whole framework. Where most retail education obsesses over direction, the premium-selling approach reframes trading as a numbers game: define the odds before entry, collect a credit that bends those odds in your favor, then place enough small, mechanical trades that realized results converge on the theoretical edge. This section covers the six pillars of that worldview — Probability of Profit (POP), probability of touch, delta as a probability proxy, expected value, the law of large numbers (number of occurrences), and the one-standard-deviation / 16-delta framework that ties them together.

Sourcing note: the bulk of this material lives in video research and recorded segments. Where a support/learn page or named segment backs a claim, it is cited; claims drawn from established options/probability theory rather than a retrieved source page are graded C.

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Probability of Profit (POP) — and how a credit lifts it above 50%

Probability of Profit (POP) is the headline metric for any position. It is defined as the probability that a position makes at least $0.01 at expiration — i.e., the chance the trade is a winner by even a penny.

The reason POP matters so much to a premium seller is mechanical. When you sell an option (or spread) you receive a credit of extrinsic value up front, and that credit pushes your breakeven past the short strike by exactly the credit amount. Because the breakeven now sits farther out-of-the-money (OTM) than the strike itself, the position can be profitable even if price moves slightly against you — so its probability of finishing profitable is higher than the probability of the short strike simply expiring OTM.

Worked intuition for a single short option:

So for a short OTM option, POP ≈ (1 − delta) + the cushion from the credit, which is why selling a 30-delta option typically yields a POP in the low-to-mid 70s rather than exactly 70%.

This is the structural reason the premium-selling approach favors selling premium and high-POP trades: a credit is the cheapest way to move the breakeven and buy a probability edge above the 50/50 coin flip.

POP vs. ePOP

The platform distinguishes POP (a theoretical, model-based number) from ePOP — "expected POP" — which incorporates the actual bid/ask credit you could realistically transact, giving a more execution-aware estimate.

Nuance / limitation: A high POP is not high expected value. A naked short option can show a 90%+ POP while risking a loss many times the credit collected. POP tells you how often you win, not how much — the two must be read together (see Expected Value below).

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Probability of touch ≈ 2× probability of finishing ITM

For an OTM option, the probability that price will touch that strike at some point during the trade is roughly twice the probability that the option finishes in-the-money at expiration. A 30-delta strike (≈30% chance of expiring ITM) therefore has roughly a ~60% chance of being touched at least once before expiration.

The intuition: finishing ITM requires price beyond the strike on one specific day (expiration); touching only requires price to reach the strike on any day along the path — a far easier condition. The reflection-principle result from probability theory gives the clean ~2× rule.

Why this matters operationally:

Practitioners have noted that touch probability is computed from exotic-option (barrier) pricing models and is "not well understood or readily available" to most retail traders — part of why the platform surfaces it.

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Delta as a proxy for probability of finishing ITM

The single most useful shortcut on the options chain: an option's delta approximates its probability of expiring in-the-money. A 0.30-delta option has roughly a 30% chance of finishing ITM; a 0.16-delta option, roughly 16%. As the platform's own learn material puts it, delta "acts as a proxy of the option's probability of expiring ITM, also available on the platform as 'ITM %' when viewing the options chain in Table mode."

Practical uses traders make of this:

Caveats stated honestly. (1) Delta is a rough proxy, not the exact risk-neutral ITM probability — they diverge because of volatility skew, the dividend/carry term, and the fact that strict ITM probability uses the d₂ term in Black-Scholes while delta uses d₁. The platform's ITM % is the more precise figure. (2) Delta drifts as the underlying, time, and IV change, so the probability read is a snapshot, not a constant.

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Expected value: win rate vs. magnitude

POP answers how often you win. Expected value (EV) answers whether the strategy makes money over time, and it forces you to weigh win frequency against win/loss magnitude:

EV = (P(win) × average win) − (P(loss) × average loss)

A recurring lesson in the premium-selling literature is that short-premium strategies deliberately trade a high win rate of small wins against an occasional larger loss — and that this can still be strongly positive EV. In one illustration, a position with a 90% win rate, an average win of ~$90 and an average loss of ~$475 produced a positive expected P/L of ~+$335 over 10 trades, because the frequent small wins outweighed the rare large loss.

The flip side — and the reason position sizing is inseparable from EV:

The honest tension: the edge here is not a huge expected value per trade — it is a small, repeatable, positive EV (anchored in the volatility risk premium) that only compounds into real money across many occurrences. That is the bridge to the next pillar.

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The law of large numbers — "number of occurrences"

A positive expected value is a theoretical average. You only realize it by repeating the trade enough times for the law of large numbers to take hold. This framework calls it "number of occurrences," and it is one of the most-repeated ideas in the literature: "The greater the number of occurrences, the greater the chance that the probabilities will be closer to our expectations."

The canonical example:

How the canon operationalizes it:

Limitation worth stating: the law of large numbers assumes occurrences are roughly independent and identically distributed. Real portfolios are not — positions across SPY, QQQ, and tech names are correlated, so 50 simultaneous index-correlated trades are not 50 truly independent occurrences. A market shock can turn many "independent" winners into simultaneous losers. Diversification and uncorrelated underlyings partially restore the assumption.

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One standard deviation, the 16-delta, and ~68%

The framework that unifies everything above is the standard-deviation view of an option chain. Under the lognormal (Black-Scholes) model, price has roughly a 68% chance of finishing within ±1 standard deviation of its current level over the period — the familiar empirical "68–95–99.7" rule.

The bridge to the chain: the ~16-delta strike sits at approximately one standard deviation away from the underlying. Why 16? Because if ~68% of outcomes land inside ±1 SD, then ~32% land outside, split between the two tails — ~16% in each tail. A 16-delta option (≈16% chance ITM) therefore marks the ~1-SD boundary on each side.

Implications for strangle POP — the flagship application:

The deeper thesis underneath the 1-SD strangle: implied volatility tends to overstate the standard deviation that actually realizes. If the implied 1-SD move is wider than the realized move, selling the 16-delta strangle is selling an overpriced range — the structural source of the edge.

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Key Takeaways

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Common Misconceptions

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Review Questions

1. You sell a 30-delta call and collect a credit. Is your POP higher or lower than 70%, and why does the credit move it? `[answer: higher than 70% — the credit pushes the breakeven beyond the strike, adding a cushion to the ~70% OTM odds]`

2. A short strike has a 20% chance of finishing ITM. Roughly what is its probability of being touched before expiration? `[answer: ~40% — about 2× the ITM probability]`

3. What platform metric is the precise version of "delta as probability of expiring ITM," and where do you find it? `[answer: "ITM %" in the options chain Table mode]`

4. A strategy wins 90% of the time, average win $90, average loss $475. Is its expected value positive, and what single behavior most threatens that EV? `[answer: yes, positive (~+$33.5/trade by the cited example); inconsistent/oversized trade size is the main threat]`

5. Why does the premium-selling approach insist on trading small and frequently rather than placing a few large high-conviction trades? `[answer: the law of large numbers — many occurrences make realized results converge on the theoretical probability; small size makes many occurrences survivable]`

6. The 16-delta strikes correspond to roughly what statistical level, and what is the approximate probability the underlying finishes between the 16Δ put and 16Δ call? `[answer: ~1 standard deviation per side; ~68% inside the range, with POP rising above ~70% once the credit is included]`

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Sources

_Evidence-labeled per the Project Charter. Education only, not financial advice._