The Simple Math
Poker is a game of finite possibilities. There can never be more than 52 cards in a deck, and there can never be more than or less than 13 cards of the same suit. With this in mind, the odds of drawing or catching a winning hand are a constant. The only variable is the risk. Is it worth calling a huge raise if the odds are completely against you? The answer is: it depends on pot odds. In order to determine the best course of action, a player absolutely needs to understand pot odds, and how to calculate them.
Hand Odds and Pot Odds
Sometimes the size of the pot looks very tempting to call in the hopes of catching a draw, but do the odds justify the call? Assuming that your hand will be the winner if the cards fall properly, the scientific method for justifying the risk versus reward factor can be determined by knowing hand odds and pot odds. If you are playing in a hand and have A-Q suited hearts, and the flop gives you a four card flush draw, you must now calculate a reasonable amount to call.
The Hand Odds: Assuming that you have not paired on the board, and that you won’t make a straight, the number of outs to make your flush is 9 (13 hearts – your pocket hearts and the two hearts on the board = 9 possible hearts available). At this point, you have a 35% chance of hitting your flush over the next two cards (turn and river). Assuming that you did not hit your flush on the turn, your odds drop to 19% for making it on the river.
The Pot Odds: On the turn, in this scenario, you have a 19 % chance of making the Ace high flush on the river. In purely mathematical terms, the call to stay in the pot should not be more than 19% of the total value of the pot. If someone makes a $10 raise, then it should be called but if someone makes a $30 raise, the pot odds become greater than the hand odds. For example, if the pot contains $ 90.00 and the bet to call is $10.00, your total obligation is 10% of the value of the pot. The odds of making your flush (and in this example, we assume that your flush will be the best hand), are approximately 20%.
Risk vs Reward
The risk, in this example, is $10.00, or 10% of the pot, but the payout (not counting the bets that would follow if you did hit your flush on the river) is $100.00. Over an extended period of time, based on the law of averages, you can be sure that you will hit your flush roughly 20% of the time (19.14%).
In ten hands of the same scenario, your $10 bet would equal $100 in contributions to pots totaling $1000 . If you are forecast to win 20% of the time, you would win two pots for a total of $200.00, giving you an overall net profit of $100.00. Conversely, if the cost to stay in the same hand is equal to a $30 bet that adds up to a $ 100 pot, you would have contributed $300 in ten hands. Your odds of winning will not change, and therefore if you win 20% of the time, you win $200.00 at a cost of $300.00, for a net loss of $100.00.
Therefore, as you can see, the pot odds play an important factor in your decision to call or fold. While the odds of hitting the winning hand do not change, the risk versus reward factor, or pot odds, fluctuates constantly.
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