Implied Odds

A plain-spoken explainer of implied odds in Texas Hold'em, in a country voice, with the arithmetic left in and a calculator you can poke.

Live: https://nanobotco.github.io/implied-odds/

The whole thing, dirt simple

1. Pot odds is the price the pot lays you right now: what you'd win against what it costs to call.
2. A draw hits some fraction of the time. Count your outs, and that fraction has a number.
3. If the pot pays worse than the draw needs, the naked call loses money.
4. Implied odds count the money you'll pull off the other feller on later streets when you hit.
5. Add that future money and a losing call can turn into a winner — if you actually get paid.
6. Over the long run it's the average that matters, not any one hand.

What's on it

• The example hand — the nut flush draw, drawn as cards.
• A live calculator — pick your draw (flush, straight, gutshot, custom outs), say whether you're on the flop or the turn, set the pot, the bet and the villain's stack, and it computes: the chance you hit (exact, off the real card counts), the pot odds, and whether the call is a call on pot odds alone, a call on implied odds, or a fold — with the arithmetic printed out.
• An outcomes-over-time chart — your chips over 150 plays of the same spot: the expected line plus five runs of pure luck. A dial sets how much you drag off the villain on the river when you hit; turn it and watch the expected line tip from going broke to getting paid.
• The gotchas — you gotta get paid, loud draws pay less, and reverse implied odds.
• The outs cheat-sheet — the common draws, their outs, and the rules of 2 and 4.

The math

• Hit probability. One card to come: outs / 47. Two cards to come: 1 − C(47−outs, 2) / C(47, 2) — the exact chance of missing both, subtracted from one.
• Pot odds. After a bet B into a pot P, you call B to win P + B. Break-even needs p ≥ B / (P + 2B).
• Implied odds. The extra X you need to win on the river to break even solves p · (P + B + X) = (1 − p) · B, so X = (1 − p)·B / p − (P + B).
• Outcomes over time. Per hand, EV = p · (pot + payoff) − (1 − p) · call. The chart plots n · EV against n, with the payoff set by the dial; the luck runs are a seeded coin-flip per hand so they hold still while you turn the dial.

Every figure is computed in the page. Nothing is hard-coded.

Licensing

• Text and the page in docs/ — CC BY 4.0. Credit: "Nan · hongdam.net · CC BY 4.0".
• Code (the calculator and chart script) — MIT.

See NOTICE.txt.