// pot odds · concept

Implied odds, priced

Implied odds: how much more a draw has to win. The derivation first, then the numbers for every common bet size, then where the idea stops being true.

Implied odds are what you expect to win on later streets when your draw comes in. If the direct price is not enough, they are the only reason to call, so it pays to know exactly how much they have to be. With hit chance e, pot P and bet B, and an extra X won only when you hit:

EV(call) = e × (P + B + X) − (1 − e) × B
set to 0:   X = B / e − (P + 2B)

flush draw on the turn vs a pot-sized bet (P = B = 1, e = 9 / 46):
X = 46 / 9 − 3 = 2.111 pots   (25.33 bb in a 12 bb pot)

So calling a pot-sized turn bet with a flush draw needs the bettor to pay off more than twice the original pot on the river when the flush comes in, and to have the stack to do it. Whether they will is a read on the player, not arithmetic; the price of the pot-sized bet is.

Facing a turn bet, one card to come

Extra the draw must win on the river when it hits, in multiples of the pot before the bet. “Priced in” means the direct odds already pay.

Implied odds needed by draw and bet size
Draw1 / 41 / 31 / 22 / 33 / 413 / 223
Gutshot (4)1.382.173.755.336.138.5013.2518.0027.50
Open-ended straight draw (8)priced in0.250.881.501.812.754.636.5010.25
Flush draw (9)priced in0.040.561.071.332.113.675.228.33
Flush draw + gutshot (12)priced inpriced inpriced in0.220.380.831.752.674.50
Flush draw + open-ender (15)priced inpriced inpriced inpriced inpriced in0.070.601.132.20

Facing a flop bet, calling for the turn card only

Same question with 47 unseen cards. This treats the call as buying one card: if you miss and face another bet, that is a new decision with its own price.

Implied odds needed by draw and bet size
Draw1 / 41 / 31 / 22 / 33 / 413 / 223
Gutshot (4)1.442.253.885.506.318.7513.6318.5028.25
Open-ended straight draw (8)priced in0.290.941.581.912.884.816.7510.63
Flush draw (9)priced in0.070.611.151.422.223.835.448.67
Flush draw + gutshot (12)priced inpriced inpriced in0.280.440.921.882.834.75
Flush draw + open-ender (15)priced inpriced inpriced inpriced inpriced in0.130.701.272.40

The model, stated

  • You win X only when you hit, and every hit wins. Clean outs, no ties, no hitting and losing to a better hand (that is reverse implied odds, and it pushes every number up).
  • Missing costs nothing more. You fold the river. If you sometimes bluff when you miss, or call again, those are separate prices.
  • X is capped by the stacks. If the bettor has less than X behind after calling, the call cannot be right on implied odds however often they pay.
  • Draw odds are the counted outs chart: 4, 8, 9, 12, 15 outs. Dirtier draws have fewer real outs; the odds pages show how much a real flush draw or open-ender gains or loses on specific flops.

Every bet size

The ideas behind the numbers

// what is computed and what is assumed
  • The prices are exact. Pot odds, required equity, MDF and the bluff frequencies are arithmetic on the pot and the bet, printed as reduced fractions. Nothing is rounded until it is displayed.
  • Draw odds are counted. The chance of hitting comes from the outs chart, which deals every turn and river. We assume clean outs: every out wins and nothing else does. Real draws are dirtier, and against a stated range the spot check counts the real equity instead.
  • No rake, no future betting unless a page says otherwise. Implied odds are the one place we price a later street, and that page states its model.
  • MDF and the river ratio are a toy game, not a solver output: a bettor with only the nuts or air, a caller with only bluff-catchers. They say what stops the other player profiting automatically. They are not a strategy for any single hand.