Pot Odds
Immediate Pot Odds
Knowing the starting hand rankings and the hand improvement odds is not enough to play Hold’em. You must be able to tell if your bets are profitable as well. The hand odds chart show that you will fail to improve your drawing hand most of the time. This means that you must be very careful with your calls to ensure you win enough when you improve your hand to compensate for everything you lose when you don’t. And lose you shall. This brings us to the pot odds:
| Pot Odds: The ratio between the pot and the cost of calling. The pot is always bigger than the cost of calling but the fewer the players chasing the pot, the closer to 1:1 the ratio will be. |
Pot Odds Example
It is currently the flop and the pot is $12. To call the current bet you must add $1 to the pot. The pot odds are 12:1. The call makes up 7.7% of the pot when added to it. Simply divide pot by cost of calling to get the pot odds.
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Pot odds are extremely important when you play cash games. When you play tournaments, on the other hand, there is a discrepancy between the chips and the real money at stake; meaning that you can't use pot odds straight off as basis for decision making. This will be elaborated on later in the school. For now it is enough to know that pot odds are important and that the ability to calculate them on the fly is is what defines a good player.
As long as the pot odds outweigh your hand odds it means the call is profitable in the long run, assuming that you fold every time your hand does not improve on the next community card. Higher pot odds allow for poorer hand odds and better hand odds allow for poorer pot odds. Bear in mind that it is a lot easier to straighten things out when using odds than when using chance and therefore we highly recommend using only odds.
Profitable Cash Game Odds Example
You are on the flop with an OESD which has the odds 4.9:1 against improving on the turn. You should fold if the pot odds are lower than 4.9:1. You should call if the pot odds are higher than 4.9:1.
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Profitable Cash Game Chance Example
You are on the flop with an OESD which has 17% chance of improving on the turn. If your call is more than 17% of the pot size (when added to the pot) you should fold. If your call makes up less than 17% of the pot size (when added to the pot) you should call. So if the pot is $100 and the cost of calling is $20.5 or higher, you should fold. If it is lower than $20.5 you should call. This is because $20.5 is 17% of $120.5 ($100+$20.5).
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Don't forget that you must play a lot of drawing hands to profit from them with any certainty, assuming that the pot odds are on your side in the first place. If the pot odds are not on your side, then you will never profit in the long run no matter how good the hand odds are. You may win every now and then but you will lose more. The balance between hand odds and pot odds can be expressed as the expected value.
►The call has a positive expected value if the pot odds are greater than the hand odds
►The call has a negative expected value if the pot odds are smaller than the hand odds.
► The expected value is zero if the pot odds are equal to the hand odds.
► The expected value is always positive if the chance of winning is over 50% which translates to hand odds higher than 1:1 for winning or lower than 1:1 against winning.
Expected value: (W x pW) – (L x pL)
W=Amount you will win
pW=Probability of winning
L=Amount you will lose
pL=Probability of losing
Or expressed in words:
Expected value: (amount that you will win multiplied by probability of winning) minus (amount that you will lose multiplied by probability of losing). |
Expected Value Example
It is currently the flop and the pot is $100. To call your opponent you must add $25 to the pot. The pot odds are 4:1. You have an ISD with the improvement odds of 10.8:1 against (8.5%) on the turn. The pot odds do not outweigh the hand odds which means that the call has a negative expected value; a negative expectation. The probability to make your hand is 0.085. The probability to not make your hand is 0.915.
Expected value of calling: ($100 x 0.085) - ($25 x 0.915) => $8.5-$22.875 = (-)$14.88
Conclusion: You will lose an average of $14.88 on this call.
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Implied Pot Odds
There are more pot odds to take into consideration than the immediate pot odds. Something many players forget are the implied odds. They should always be considered, whether a call has positive or negative expected value.
| Implied odds: These are the pot odds adjusted for the presumed future bets of your opponents. You simply add their presumed future bets to the current pot size and weigh that against the cost of calling to see the next card. Implied odds are something you consider when you expect to win the maximum when you make your hand and lose the minimum when you don’t make your hand. If you make your hand you assume that you will win the future pot and if you don’t make your hand you simply just fold. The implied odds are fairly easy to project in limit games but in no limit games they are a great deal more complicated. |
Implied Odds Example
You are playing a game of Limit Hold'em. The BB is $5 and the Big Bet is $10. It is currently the flop and the pot is $50. You have an ISD with the odds 10.8:1 against improving on the turn (or 8.5% chance of improving). To call you must add $5 to the pot. The pot odds are 10:1 (9.1%). The call has a negative expected value. However, the implied odds should also be considered.
There is one opponent left in the hand. Your opponent is sitting to your right and has just bet $5. If you call you will end the betting round. You project that your opponent will bet $10 on the turn and if you improve your hand you will raise, otherwise you will fold. You further project that your opponent will call your raise, costing him another $10. You project that your opponent will check on the river and then call the bet you will make after him, costing him another $10.
Projected pot (if you make your hand): $50+$10+$10+$10=$80
Cost for calling: $5
Implied odds: 80:5 = 16:1
The implied odds 16:1 outweigh the hand odds of 10.8:1 making the call profitable.
Implied expected value: 0.085 x $80 – 0.915 x $5 => $6.80-$4.575=$2.23
The call has a positive implied expectation. You will win an average of $2.23 when you make such a call, assuming that your projection is correct.
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Implied odds may be difficult to project for a beginner but as you gain experience you will be able to make more and more accurate forecasts.
Reverse Implied Pot Odds
There are also the reverse implied odds to consider:
| Reverse implied odds: These are the opposite of implied odds. These are odds to consider when you have a made hand and your opponent has a drawing hand that will win if it improves. Your opponent will fold if the hand does not improve. You will lose the maximum if you lose and win the minimum if you win. |
Reversed Implied Odds Example
You are playing a game of Limit Hold'em. The BB is $5 and the Big Bet is $10. It is currently the turn. Your pocket cards are Kh-Kc and the community cards are Kd-2d-7d-6c. You have a set of Kings. The pot is $50. Your opponent has just checked and it is your turn to act. You suspect that your opponent has a FD with the odds 4.1:1 against improving on the river (19.6%). The odds that you will win are 4.1:1 for or 0.24:1 against (80.4%). Your chance of winning is over 50% and from this you can already tell that the expectation is positive. If you bet you give your opponent the pot odds 6:1 for calling which means it is profitable for him to see the river, asuming that he folds if he does not make the flush. In the event that your opponent hits his flush on the river you will only have to call him to see the showdown seeing as he acts before you and there are only the two of you remaining in the hand.
Projected pot* (if your opponent does not make his hand): $50+$10=$60
Projected bets of your own** (if your opponent makes his hand):$10+$10=$20
Reverse implied odds: 60:20=3:1
The reverse implied odds 3:1 clearly outweigh the odd of 0.24:1 against (19.6%) winning the showdown meaning that it is profitable to play your hand.
Reverse implied expected value: 0.804 x $60 – 0.196 x $20 => $48.24-$3.92=$44.32
Seeing the hand through to the showdown has a positive reverse implied expectation. You will win an average of $44.32 on seeing the showdown.
*The current pot size + the amount your opponent pays for calling to see the next card.
**The presumed future bets you will lose if your opponent makes his hand.
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Normally you should only be worried about reversed implied odds if you have a top pair or over pair because those are the only hands your opponent has a considerable chance of improving beyond, assuming he has a weaker hand than you in the first place.
Pot Odds Bottom Line
We have presented you with very basic examples and reality can be much more complicated. Your outs could be dead cards or counterfeits and your legitimate outs could give your opponent a draw that upon improvement would beat your improved hand or the other way around. Your opponent could also be bluffing or simply playing emotionally rather than mathematically. And let us not forget the possibility of having several opponents remaining in the hand. Furthermore, there are huge differences between profitable odds in cash games and profitable odds in tournaments.
What we are trying to say is that Texas Hold'em can be a very complex game. It can, however, also be a very simple game. It all depends on the circumstances. Fortunately you can control some of these circumstances and thereby making the game as simple as you want it to be. You will learn how to control these circumstances as you continue progressing through the school.
Just a few last things about pot odds to help you put things in perspective before we move on:
►Pot odds are simple and precise in so far as the here and now but they don’t look to what the future may bring.
►The implied and reverse implied odds, on the other hand, are far from an exact science. They are more about psychology than mathematics and experience is your best resource when predicting the actions of other players.
►Bear in mind that players with tight passive styles tend to overestimate the strength of their opponent's hands; weighing in pot odds and folding to pressure despite having the best hand.
►Players with aggressive styles, on the other hand, tend to be too optimistic about their number of outs and their implied and reverse implied odds and as a consequence they end up chasing hands that should not be chased.
►To find a balance you need to control yourself and avoid getting carried away by your feelings. Focus on what you do know and assume as little as possible when making your decisions. Knowing your opponent is a great advantage. |
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