Mathematics of Poker: Implied Pot Odds

    • craigjo
      Joined: 21.03.2011 Posts: 63
      in example 2 of the above video, once we worked out the pot odds for the flop (2.7:1) and realise we need the odds 4:1 how do we work out the money of a further 1.3:1

      would it be to times the flop bet by 4 to see what the pot would be if we had the correct odds and make the diffrence on the turn
  • 1 reply
    • EuanM
      Joined: 07.05.2011 Posts: 531
      Hey craigjo,

      Thanks for posting!

      I've written some explanation below, I hope this helps you:

      Flop, so after his check-raise:

      You need to call $4 into a pot of $10.85 to continue, so your odds are 2.7:1.

      We can assume he has a strong hand from the check-raise (and is ahead), and we hit our flush about 26% of the time, the other times we lose to his made hand - so we only win 26% of the time - but to make the call profitable we need a certain percentage of pot odds, specifically, it has to be higher than our current equity, which it's not. (2.7:1 is around 36%)


      Pot Odds: 2.8:1 (36%-37%)
      Required Odds: between 4:1 & 5:1 (20%-25%)

      If our opponent bet around $4 on the turn instead of $8, we would have the required odds to continue as it fits in with our equity and thus the call is profitable - otherwise it's not, unless we look at our implied pot odds, which are the chances of stacking our opponent when we do hit, in that case, a tighter opponent is the one we should prefer to call against, as he will comfortably stack-off most times with his set or other holding in his check-raising range - because he is a tight opponent, his range is stronger and so we have a higher chance to get ALL of his money when we hit our hand as well.

      This also means our over-card outs are no good most of the time against the tight player, because his range is stronger than top pair but at the same time against a loose opponent in that spot, our ace or queen would be ahead if we hit on the turn decreasing the pot-odds required to continue against that loose player compared to a tighter player.

      This example comes from the perspective that the tight player has a set, and the loose player would have a top-pair - which is a reasonable assumption to make in most cases on that board after the action post-flop - and what percentage we have of making it to our flush which will beat both the tight and loose players hands.

      We are calling to hit our hand on the turn, and fold everything else at that point - our specific line dictated by the type of player, and the bet-sizing used by him. In cases where the turn bet is smaller, we can call.

      The missing "1.3:1" we need as such isn't there.

      Hopefully this comes from a smaller flop bet when you pick up your nut flush draw :f_biggrin: - which isn't really likely in this scenario if you are playing a competent player. Or it will come from having a more speculative game where stack sizes allow for looser calls. In any case, there are opponents that will not bet a correct size, and give you the odds you need to outdraw them every-time - this example is not one of them, here we have to fold as the river pot odds would force us to call a lot of beat top-pairs for example.

      The Video is telling us that - if we do not pay attention to our implied pot odds and do not make our action in-line with that information, even with all the money we will win with our flush, it will still be less than what we lose making such calls when we don't have correct odds - it's simply a matter of ratio. So then we must get this concept very clear in our minds to maximize our edge against our villain.

      Our implied pot odds increase when:

      Our opponent is showing strength


      Because he will most likely go to showdown with this hand, and we have a good idea from his previous action what the relative strength of his hand is and if we can beat it or not.

      Our hand is less obvious.


      Because we have made it difficult for our opponent to gain information from us, either by playing in position or by mixing it up - in any case, we are disguised and the opponent will have a very difficult time telling if we are strong or not - meaning he is less likely to change his actions in accordance with ours in such spots, because he simply doesn't have the information he needs to make a rational decision.

      If it is harder for our opponent to fold a hand


      Because we can rely on stacking him when we have him beat, and folding when we don't. Not folding often is also the most exploitable leak for new players, and will allow us to play a very straightforward game against them which is still effective nonetheless.

      We need to effectively judge how much money we can get from our opponent and employ this as a dynamic strategy in our game, so in what situations do you think your implied pot odds would decrease?

      I hope this helps, let me know if you have any more questions!