Hand Odds and Pot Odds...


After psychology and bluff tactics comes the math. You cannot escape it. If you ever want to move from novice to amateur, online poker’s statistical aspects cannot be ignored. This means learning to calculate pot odds on every hand. Going over the betting and player tells gives you the implied odds of the hand you hold. That is, if the hand you might finish comes through, will it win against all the other finished hands?


Hand odds is a measure of the statistical probability of a particular hand finishing given the number and composition of cards known for certain to have been dealt from the deck and the number of bets in the pot. This figure allows you to supplement your impressions of the hands at the table with quantitative data on your particular hand.


This is a lot less complicated than it sounds, and requires you to use only basic math. There are also a number of odds calculators available online for cheap or free. These can provide in-game assistance as you first learn to calculate and interpret pot odds. Whether or not you use such software assistance or stick with a calculator and pen, with a little practice and constant application the procedure will become almost second nature.


So, how do I calculate the pot odds of a hand? The first step in calculating pot odds is determining the number of outs on your hand. An ‘out’ is any card that might theoretically still be in the deck. In other words, if the card is not in your hand, on the table, or seen in the reflection of your opponents glasses (an impossibility online), then it is still ‘out’ of play.


Of course, not every single card in the deck is of concern to you. In terms of hand odds then, an out is any card theoretically still in the deck and that will serve to complete your hand. For example, you have two diamonds in the pocket. The dealer flops an A and 10 of diamonds and a 4 of spades. This is good news for a flush.


We know for certain that of the 13 diamonds in the deck, 4 are in play. The outs in this instance equal 9, i.e. (13 – 4 = 9). Between our pocket and the flop we know five of the cards in play this hand. This means that theoretically any of the other r47 cards might be drawn on the turn. First divide your outs (9) by 47. This gives you a figure of about .19, which means you can expect to complete this hand on the turn about 20% of the time. 


While this information is itself useful, it can in turn be applied to another calculation. Again, hand odds give you the probability of finishing a hand. The pot odds, however, gives you a measure as to whether or not the risk of investing in this hand, given the number of outs, is worth the amount in the pot. 


Go back to your 9 outs. Now, divide the 47 by 9. Now take this product of 5.2 and subtract 1. This 4.2 represents the number of bets that should be in the pot for the risk of not finishing the flush versus finishing it to be worth the money in the pot. If there are fewer than 4.2 bets on the table, the potential payoff of winning this hand is not worth the 80% chance the hand will not finish in the turn and you will either be forced to fold or pray at the river. Note, the odds for completing the flush in this example on either the turn or river can also be calculated, and is around 35%.


The number of bets in the pot is easy to calculate in limit games. Simply divide the total amount in the pot by the minimum bet. Suppose it is a $1/$2 limit table and the pot is $10, there are then ten bets in the pot. When choosing whether to call at the turn, remember that raises are ubiquitous after the turn. You might then be sucked into risking more than you want to on any one hand. Pot odds should always be considered in combination with implied odds, and never simply followed in a formulaic fashion.



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