Pot Odds

Pot odds are the odds you are getting to call a bet to win the pot. If the bet is small in relation to the pot, then you are getting good pot odds. In general, on the flop and turn people bet around the pot size, which gives a person 2:1 pot odds. Draws in NLHE are not that strong (almost no draws are going to hit 1/3 times getting one card) so for the most part people don’t make those call because of pot odds. Instead NLHE players think more in terms of implied odds – the chances of hitting a hand and winning additional money after making it.

Pot odds are therefore most important on the river where the oppo‐ nent makes a bet and there is no future action. However, pot odds are still relatively not that important even then, as making the cor‐ rect river decision is mainly a matter of hand reading, and then if the decision is close the idea of pot odds can be factored in to sway it one way or the other.

Here is a simple hand to try an equity calculation with. EP min‐ raises to $100 at $25/50 and LP calls with a short‐stack of $3,000. I have A‐Qo on the button. The min‐raise to me says that he has a mediocre hand that he doesn’t want to put a lot of money in with, and doesn’t want to build a pot with – he just wants to see a flop cheaply. So I raise to $500, EP folds and LP calls. The flop comes A‐J‐6 with three spades, he checks, I bet $800 and he goes all‐in for $1,700 more.

So now there is approximately $1,100 in the pot from pre‐flop, then $1,600 more from my bet and his call, which makes $2,700, and he raises $1,700 more so I would put up $1,700 to win $4,400 – so 44:17 or almost 5:2. If he has A‐J, a set, or a flush then I have very little chance of winning. If he has a pair and a flush draw like K‐J with a spade, or maybe 10‐10 with a spade that gives him five or two pair/set outs and nine flush outs, so 12 on average. 12 outs twice is about even money to win the pot. So the equation is:

It’s important to understand how this equation works. X is equal to the percentage of times A‐Q has to be ahead versus a semi‐bluff for our equity to be breakeven in the pot when calling. About 50% of
the time 10‐10 will win so we’ll lose the $1,700 we used to call his bet, and the other 50% of the time we win the entire pot of $4,400. (1‐x) is all the other times when he does NOT have a semi‐bluff – it is the times I’m drawing dead and then I lose the $1,700 call. Note that (1 – x) added to x is equal to 1, i.e. x and (1 – x) account for two different scenarios, which together happen 100% of the time. There are two factors battling each other here – the first is that our pot odds are so good, but second is that he has a lot of equity even when he’s behind. So from the equation we can see that if our hand is good 56% of the time then calling is a break even proposition. Let’s say our hand reading is off and it’s good only 30% of the time. Now we can plug those values in and see how much our mistake cost us:

0.3($4,400*0.5 – $1,700*0.5) – (0.7)($1,700) = –$788

Or let’s say it’s good 70% of the time then it becomes:

0.7($4,400*0.5 – $1,700*0.5) – (0.3)($1,700) = $435

Based on the calculations above if we call when we are ahead 70% of the time then we win $435 from our opponents in Expected Value, and if we call when our hand is only good 30% of the time we lose ourselves almost $800 in EV. You can see that by calling or folding we don’t make decisions that cost us $1,700 or win us $4,400 – they actually win or lose a small fraction of that depending on how good or bad our hand reading was.

Now let’s say he either has A‐10o or one of his huge hands then try running it again:

So if we’re either ahead huge or behind huge (and there is no re‐ drawing) then we only have to be good 27% of the time because our pot odds are so good. Note that this equation is just a long‐hand way of writing out pot odds, which are 4,400:1,700 or 1,700/(4,400 + 1,700) = 0.27.

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