Pot odds and implied odds: when the second number changes the call

Pot odds answer one question: does the price in front of me cover the chance that my hand improves? Implied odds answer the next one: if it does not quite cover it, can the rest of the hand make up the difference? We keep the two apart here, because collapsing them is how a marginal call becomes a habit.

The price, exactly

There is £60 in the pot and your opponent bets £20, so the pot is £80 and the call costs £20. You are risking £20 to win the £80 that is already there, which breaks even at 20 divided by 100 — twenty per cent. That is the entire pot-odds calculation, and the only thing to be careful about is the denominator: the bet you are calling goes into the pot you are trying to win, and your own call goes into the money you are risking.

Bet sizes convert to required equity on sight once you have done it a few times.

Bet, as a share of the pot	Equity your hand needs
quarter pot	16.7%
third pot	20.0%
half pot	25.0%
two-thirds pot	28.6%
pot	33.3%

What the draw is actually worth

On the flop you hold two cards and three are face up, so 47 cards are unknown to you. A flush draw has nine of them. Nine over 47 is 19.1 per cent for the turn card — and that, not 35 per cent, is the number that belongs next to a flop bet. The 35 per cent figure is the chance of hitting across turn and river, which is 1 minus 38/47 times 37/46, and it only applies when you are getting both cards for the single price: you are all in, or the stacks are short enough that the rest is a formality.

Draw	Outs	Turn card only	Turn and river
gutshot straight	4	8.5%	16.5%
two overcards	6	12.8%	24.1%
open-ended straight	8	17.0%	31.5%
flush	9	19.1%	35.0%
flush plus gutshot	12	25.5%	45.0%
flush plus open-ender	15	31.9%	54.1%

The shortcut most players use — outs times two for one card, times four for two — is close enough at the table and worth knowing the size of its error. Nine outs: the shortcut says 18 against a true 19.1, so it understates by about a point. Fifteen outs: the shortcut says 60 against a true 54.1, so it overstates by six. The rule is good for small draws and flattering for big ones. Counting the outs correctly in the first place is the harder half, and our older piece on counting outs after the flop is still the clearest statement of the method we have published.

The gap, and what has to fill it

A third-pot bet asks for 20 per cent and the flush draw brings 19.1. The call is 0.9 of a percentage point short — which is where implied odds come in, and the useful move is to price them rather than to invoke them.

Call £20 to win £80 with 19.1 per cent equity. If hitting the flush collects an extra X on the river, the call breaks even when 0.191 times (80 plus X) equals 0.809 times 20. That gives 80 plus X equal to £84.44, so X is £4.44. You need to collect four pounds and change more, on average, across every time you make the hand — which against almost any opponent is already true. The call is fine.

Now change one number. Same £60 pot, but the bet is £45, so you are calling £45 to win £105 and the price demands 30 per cent. Run the same line: 9/47 times (105 plus X) equals 38/47 times 45, so 105 plus X is £190.00 and X is £85.00. You now need to collect eighty-five pounds more on the river, every time the flush comes in, against an opponent who can see the flush come in too. If the effective stacks are £120 that is conceivable; if they are £60 it is arithmetically impossible, and the call is a loser no matter how the hand is described afterwards.

That is the whole discipline. Implied odds are not a reason to call; they are a quantity, and the question is always whether the rest of the stack is big enough to contain it.

The same number pointing the other way

Reverse implied odds are the cases where hitting does not help. The small flush against a player who is drawing to a bigger one. The gutshot to the idiot end of a straight. Two overcards on a board that will pair. In all of them the out is real and the money behind it is negative, so the equity in the table above is an overstatement — sometimes a severe one. The practical test is to ask what the river looks like when you win and what it looks like when you hit and still lose; if the second picture is easy to draw, the draw is worth less than its outs. Our older column on when not to chase a straight or a flush is about exactly those boards, and the vocabulary for all of it — gap hands, gutshots, drawing dead, dead money — is collected in our glossary of odds terms.

What to carry to the table

Two numbers and one sentence. The price, from the bet size. The equity, from the outs and the single card to come. And then: if the price is bigger than the equity, name the amount the rest of the hand has to produce, and check that the stacks can produce it. If you cannot name the amount, you are not using implied odds — you are hoping, with a technical word attached.