An Example of calculating Probability in Poker:

If you’ve read our strategy guides: About Odds in Poker and Pot Odds & Implied Odds, then it’s now time to put all of this knowledge about probability in poker together.

Let’s look at the following hand:

You are deep in a tournament (a live one, not an MPO Battle Royale), with QQ. You raise to 2,000 and the big blind makes it 5,500. You re-raise to 15,000 and Villain goes all in for another 30,000.

Should you call? What are your chances? What are the odds?

Well, let’s say you judge that Villain is no more than a 5% chance or so to be bluffing.

    • …and that they’d really only do this with AA, KK and AK.
    • You know from our strategy guide, About Odds in Poker, that there are 6 ways they can have AA and KK – so that’s 12 combinations – and 16 ways they can have AK.
    • So, there are just 28 hands they are likely to have.
    • From the same guide, you would know that you are about a 1 in 5 chance against (each of) AA and KK (i.e. of the 12 times they have these hands you can expect to win just 2.4 times.).
    • You are a little better than 50/50 against the AK, so can expect to win a bit over 8 times.
    • So, of the 28 times Villain has these hands, the odds are that you will win a little under 11 times (i.e. 11/28) and lose around 17 times.
    • How much is the pot offering you?
    • Well, with blinds of 400/800 and antes of 100, there was 2,000 in the pot before you bet. After Villain’s final “all-in”, there is now 92,000 in the pot. Your decision is: do you put in another 30,000 to try to win 92,000?

[Refer back to our Pot Odds & Implied Odds strategy guide to see if you can work this out for yourself.]

The Answer:

    • The pot is giving you “pot odds” of 92:30 – that is more than 3:1 (against).
    • Your chances of winning the hand are 11 out of 28 – a bit better than 2.5:1 (against).
    • So, even allowing for the 5% chance that Villain is bluffing…

…you should call.