The Mathematics of Poker: Implied Pot Odds
Introduction
In this article we will cover...
- Why implied pot odds are better than pot odds
- Why everything depends on your opponents' willingness to pay
The article "Outs, Odds and Pot Odds" introduced you to the maths 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.
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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 earn should you make your hand.
You are already familiar with an example of implied pot odds. The Call 20 rule found in the Starting Hands Chart states that you call a raise with a small or middle pair, as long as you and your opponent both have at least 20 times the raise amount 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 however happen only 12% of the time. 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 are losing 88% of the times you invest. This can only be profitable if you make more money the 12% of the time you hit your set, than what 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 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 and 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 your Big Stack Strategy pot odds, 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. In theory you should fold.
Here we turn our attention to the implied pot odds. With $.50 more in the pot, you would have the necessary pot odds 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 and you still need 4:1 to call.
The pot would have to be $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 are: 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 and you are certain that he will call any bet should you hit the flush on the river, you can consider calling. In general however, you no 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. This means you have to estimate how much your opponents will continue to invest in 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 it is for him to be holding a strong hand afterwards. This means the implied pot odds sink too, unless he is a maniac who tends to bluff big on the flop.
- How much hand strength is your opponent signaling?
The stronger your opponent's 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 opponents 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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Are you in position?
It's easier to get money from your opponent when you have the advantage of position. 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 generally higher on the flop than on the turn, since with two rounds of betting ahead of you, you have more chances of enticing your opponents to invest.
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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 theoretically need 4:1 pot odds to call. Your opponent bets approximately $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 and he will probably have something like a two pair, overpair, three-of-a-kind etc. After discounting 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 your opponent if you hit.
If on the other hand you have a loose aggressive opponent, this isn't the case. As it isn't likely that he has a very strong hand, you don't have to discount your overcard outs as heavily. With 12-13 outs, you only need 2:1 pot odds to be able to call.
You will usually have to give up your hand if you don't hit the turn or risk it all if you do hit the turn. Regardless of your opponent's style, an 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 will both only have about $10 left in your stacks.
If your opponent has a hand of any value 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 and 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 of 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 that tips the balance in favour of folding in this instance.
The decision would be even easier if a three turned up on the turn. The possibility of facing a completed full house on the turn should be enough to keep you from wanting to stay in the hand.
Conclusion
Having no limits 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 rather than in earlier rounds.
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...
and the higher your implied pot odds. They are higher on the flop than on the turn and also when you have a position of advantage over your opponent.
It is however necessary, 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 more articles in the Big Stack Strategy introductory series focus on play after the flop. The first of these 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 the initiative
