♥ Implied Oddspoker math, dirt simple · Nan · hongdam.net

Implied Odds

Pot odds tell you what's starin' at you on the table. Implied odds count the money you ain't won yet — the pile the other feller pays you when your draw comes in. Here's the whole thing, plain, with the arithmetic left in and a calculator you can poke.

The example hand

what you hold
A♥
K♥
+
the board
Q♥
7♥
2♣

Four hearts. One more heart and you got the nut flush — the best hand possible. Trouble is, you ain't got it yet. It's a draw. The question every hand: is it worth payin' to chase?

♣ Try it — the calculator

Chance you hit
—
Pot odds you're gettin'
—
—

What pot odds are

Pot odds is the price the pot's layin' you, right now, this second. The other feller bets, and you ask one question: what do I stand to win, against what it costs me to call?

Say the pot's $100 and he bets $50. Now there's $150 sittin' out there, and it costs you $50 to see the next card. You're gettin' $150 to win for $50 to call — 150 ÷ 50 = 3, so 3 to 1. Every 4 times you call this spot, you gotta win once just to break even on the money.

Now, how often do you win? Nine hearts fill your flush. With one card to come there's 47 cards you can't see, so 9 ÷ 47 ≈ 19% — about 4 to 1 against. And there's the rub: the pot pays 3 to 1, the draw needs 4 to 1. On pot odds alone, this call loses money. Fold and go fishin'.

What implied odds are

Here's the part that turns a losin' call into a winner. You ain't gotta make all your money from the pot that's out there now. When that heart lands on the river, the other feller can't see your flush comin' — and he'll pay you off. That future money counts too.

So the real question ain't "does the pot pay 4 to 1 today?" It's "will the pot plus the money I squeeze on the river pay 4 to 1?" That's implied odds. Same call, bigger prize, 'cause you're countin' tomorrow's pile.

The arithmetic: to break even at 4 to 1 you need to win about 4 × your call total when you hit. In the $50 spot that's 4 × $50 = $200-ish. The pot's only $150. So you need to drag another ~$60 outta him on the river. He's got a deep stack and no idea what's comin'? He'll pay. Now it's a call.

♠ Grind it out — the same spot, over and over

One call don't mean much. Poker's the long run. Here's your chips over 150 plays of the exact spot in the calculator — the bold line is what you'd expect, the faint ones are luck havin' its way. Turn the dial: that's how much you drag outta him on the river each time you hit. Watch the bold line tip from goin' broke to gettin' paid.

expected chips five runs of pure luck

Where folks get burnt

You gotta actually get paid

Implied odds is money you're countin' on, not money in hand. If he's short-stacked, or he checks it down, or he folds the second a third heart hits the board — that river money's a ghost. No payoff, no implied odds, and your fold-worthy call stays fold-worthy.

Loud draws pay less than sneaky ones

Three hearts on the board and everybody at the table sees the flush comin'. He shuts down; you win nothin' extra. The draws that pay fat are the quiet ones — a gutshot, a set that don't show — 'cause he keeps bettin' into a hand he don't believe you have.

Reverse implied odds — the flip side

Sometimes you hit your draw and you're still beat, and now you're the one payin' off. Chasin' the low end of a straight, or an ace-high flush when he's got the king-high… no, wait — chasin' a weak flush when a bigger one's out there. When hittin' costs you money instead of makin' it, that's reverse implied odds, and it's where bankrolls go to die. The calculator below counts the good kind; keep the bad kind in the back of your mind.

The outs cheat-sheet

Count your outs, then eyeball the odds. Two handy rules of thumb: the rule of 4 (outs × 4 ≈ your % with two cards to come) and the rule of 2 (outs × 2 ≈ your % with one card to come).

DrawOutsFlop → riverTurn → river
Pair → set28%4%
Gutshot straight417%9%
Two pair → full house417%9%
Two overcards624%13%
Open-ended straight832%17%
Flush draw935%19%
Flush + gutshot1245%26%
Flush + open-ended1554%33%

The exact figures come off the real card counts, not the rules of thumb — 9 outs with two cards to come is 1 − (38÷47)(37÷46) = 35.0%, not the rule-of-4's 36%. Close enough at the table; exact in the calculator.

This is math, not gospel. It says nothing about position, about who's got a read on who, or about the fella who calls with everything and pays you off anyway. Count your outs, know your price, and remember the money you're chasin' has to actually show up.