Mathematics of Poker: Implied Pot Odds
Introduction
In this article we will cover...
- why implied pot odds are more exact than pot odds
- why everything depends on your opponents' willingness to pay
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The article "Outs, Odds and Pot Odds" introduced you to the math used to determine the profitability of a draw. You count your outs and determine the likelihood of one of these cards showing up in the community. Then you compare the odds to the pot odds to see whether or not you should stay in the hand.
But this is only the first step. The pot odds only take the money already in the pot into account; it is likely that more money will be invested before the showdown is reached. This is where the implied pot odds come into play. They factor the money still likely to enter the pot into the pot odds equation. Of course, you can't know how much money your opponents will continue to invest in the hand - implied pot odds are not pure mathematics, there is also a fair amount of speculation involved.
What are implied pot odds?
As we already mentioned, implied pot odds are modified pot odds that reflect the additional money you are likely to win should you make your hand.
You already familiar with an example of implied pot odds. The Call20 rule found in the Starting Hands Chart states that you call a raise with a small or mid pair, as long as you and your opponent both have at least 20 times the raise left in your stacks.
You call speculating that you will hit a set on the flop and go on to win a big pot. This will only happen 12% of the time, however. You will miss the flop the other 88% of the time and have to fold your hand.
It is hard to turn a profit when you lose 88% of the time you invest. This can only be profitable if you make more the 12% of the time you hit your set than you lose the 88% of the time you don't.
This is also only possible when your opponent has enough left in his stack to pay you off, which is also only possible when you have to have just as much left, too. As long as this condition is met you will make a profit in the long run, even if your opponent doesn't pay you off every time you hit a set.
This call wouldn't be profitable, however, if you were only to take the pot odds into consideration. The fact that more money is likely to wander into the pot is what can make it profitable to call in this situation. If you make your set you can win a big pot - you have good implied pot odds, but only if your opponent has enough left to lose to you.
A lot of your decisions will depend more heavily on the implied pot odds than the pot odds when you play the Big Stack Strategy, simply because there is no limit to the size of the bets. No Limit Hold'em is a game of implied pot odds. You will ask yourself, "How much will I win if I make my hand?" more often than "How much can I win right now?"
The implied pot odds are therefore: (Pot size + amount likely to enter the pot) : amount required to stay in the hand
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You are the BB
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You have a flush draw and are getting 3:1 pot odds. With 9 outs, you would need 4:1 pot odds to call. You theoretically have to fold.
Here we turn our attention to the implied pot odds. If $.50 more were in the pot, you would have the pot odds necessary to call. Since it is very likely that you will make up this money should you hit your flush on the turn, you can call. Unfortunately this doesn't happen in our example and the opponent continues to bet. The pot odds are now at 2.1:1; you still need 4:1 to call.
The pot would have to be at $7 for you to get 4:1 pot odds. $3.25 are missing. If you call, the pot will grow to $5.50. The problems: 1) It is not certain that you will win on the river, and 2) Your play strongly indicates a draw and your opponent's bet is relatively large in relation to the pot.
If he is a poor player you are certain he will call any bet should you hit the flush on the river, you can consider calling. In general, however, you now longer have the necessary implied pot odds and should give up the hand.
How do you determine the implied pot odds?
Unlike pot odds, which are purely mathematical, implied pot odds are speculative - you have to estimate how much your opponents will continue to invest into the pot.
The most important factors to take into consideration when calculating the implied pot odds are:
- How loose is your opponent?
A loose player likes to see the showdown and has difficulty laying down his hand. The looser your opponent, the higher your implied pot odds.
The opposite is true of players who raise loosely before the flop. The more often a player raises before the flop, the less likely he will be holding a strong hand afterwards. This means the implied pot odds sink, as well, unless he is a maniac who tends to bluff big on the flop.
- How much strength is your opponent signaling?
The stronger your opponents hand is, the more difficult it will be for him to lay it down.
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How well can your opponents read your hand?
The more obvious your hand, the lower the implied pot odds. It's relatively easy to spot a made flush or a draw. A double gutshot, on the other hand, is a lot harder to spot. The community cards and your play provide your opponent with a lot of information.
If you check/call on a suited board and start betting when the turn shows another card of that suit, it will be fairly obvious to your opponents that you have a flush..
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Do you have position?
It's easier to get money out of your opponent when you have position on him. Your implied pot odds are therefore higher when you are in position.
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Are you on the flop or the turn?
The implied pot odds are higher on the flop than on the turn, in general, since you have more chances to entice your opponent to invest with two rounds of betting ahead of you than with one.
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How large are your opponents' stacks?
It's simple logic: The more money your opponents have, the more you can win from them.
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You are on the CO
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You have a flush draw and overcards on the flop. You would have to pay $4 to win $10.85. This gives you 2.7:1 pot odds - you would theoretically need 4:1 pot odds to call. Your opponent bets app. $5.50 on the turn - his check/raise indicates a very strong hand.
Each opponent calls for his own reasons. You can call against a tight opponent; he will probably have something like two pair, overpair, three-of-a-kind etc. Depending on how you discount your outs, you are left with 8. You may not have the strongest draw, but it is likely that you can get an all-in from him if you hit.
If, on the other hand, you have a loose, aggressive opponent, this isn't the case. It isn't likely, however, that he has a very strong hand, so you don't have to discount your overcard outs as heavily. With 12-13 outs you only need 2:1 pot odds to call.
You will usually have to give up your hand if you don't hit the turn, and risk it all if you do. Regardless of your opponent's style, and ace or a queen on the river probably won't give you the best hand. Realistically you only have 7-9 outs. The pot will be at $30.85 and you both will only have about $10 left in your stacks.
If your opponent has any hand at all, he won't be folding. You would be paying $8 on the turn with the chance of winning another $10, should you hit. Your implied pot odds are 4.1:1. It's a close call - you would need something between 4:1 and 5:1 to play your hand profitably.
All in all, you're better off folding in this situation. While you do have the chance at winning an additional $10 if you hit, you also run the risk of losing an additional $10 if your flush card gives your opponent a full house. This risk is the factor the tips the scales in favor of folding in this example.
The decision would be even easier if a three turned up in the turn. The perspective of facing a completed full house on the turn should be enough to keep you from wanting to stay in the hand.
Conclusion
"No Limit" is what makes No Limit Hold'em a game of implied pot odds. Since wagers are not limited and often increase with each round of betting, it is easier to get opponents to make large investments in later rounds of betting than in earlier.
We can conclude with the following summary:
- The more strength your opponent is signaling...
- The harder it is to spot the strength of your hand...
- The harder it is for your opponent to lay down his hand...
...the higher your implied pot odds. They are also higher on the flop than on the turn and when you have position on your opponent.
It is necessary, however, to be realistic when calculating the implied pot odds. Be conservative when estimating how much you will be able to get out of your opponent in the later rounds of betting.
You will have a basic understanding of the mathematics of poker once you've read this article and the one on odds, outs and pot odds. Three other articles in the Big Stack Strategy introductory series focus on play after the flop. The first will cover the most important situation for you as a tight, aggressive player - playing after the flop with initiative.
Go to this article: After the Flop - You Have Initiative
