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FIGURING THE ODDS A limit poker player can get by with knowing only the approximate odds on a few simple situations. A bigbet poker player needs to know precise information about the odds on a wide range of situations, and how those odds are computed.
Suppose in our flushdraw case the opponent had bet only $500, half the size of the pot. Should we call now? The odds have changed. It will cost us $500 to win $1500. We are getting 31 money odds and are a slightly more than a 41 underdog, so the price is still wrong for a call, if you look at the pot odds. But if we think there is a reasonable chance of making some money if we make the flush, it could be right to call. Even after we know how to compute the math, we still have to use other poker skills to see whether the implied odds justify a call. In this particular situation, because it is a community card type of game, the opponent will see three hearts on the board if we make out hand. He will likely be nervous at the looks of that last card. At limit play the opponent often grits his teeth and calls your bet, because the terrific pot odds he is getting means he cannot afford to fold a possible winner. At potlimit or nolimit play, it is a lot harder to get the opponent to pay us off when we make a hand, especially when it is something as obvious as making a flush. Still, you must think about how the betting has gone to this point, who the opponent is, whether he is stuck in the game, and any other factor that could affect the implied odds. Most decisions at bigbet poker involving the odds will require, in addition to a proper knowledge of the actual odds, good judgment in assessing the implied odds. Some aspects of figuring implied odds were discussed in out chapter titled “Key Potlimit Concepts.”
The math of the situation is there are 47 unknown cards, of which 4 give you a winner and 43 are quite likely to leave you in second place. The odds are nearly 111 against you. Yet the fact of the of the matter is a call in this type of situation is quite a reasonable play and not uncommon at bigbet poker. To see why, let’s look at the deal through your opponent’s eyes. He has probably got an ace with a weak kicker for his bet. With a good kicker, he may well have raised preflop. He could have flopped two pair, but it is more likely he has only one pair. For your call under the gun preflop and a subsequent call of his bet, he will thinks you probably have an ace with a decentsize kicker. His most likely course of action is to check on fourth street if he still has only one pair, and release his hand if you bet. This means your game plan is to call on the flop and take the pot away from him if he checks to you on fourth street. It is a sound plan against many players, even though the odds on actually making the hand are hugely unfavorable. “Bluffing rights” must be taken into consideration when weighing whether to call, if there is the possibility of more betting on the deal. Calculating the odds with two or more cards to come is far more difficult than doing so with only one card to come. For example, after the flop in a hold’em game there are ordinarily 47 unknown cards. (The 52card deck less the two cards in our hand and the three boardcards equals 47.) After fourth street is dealt, there will be 46 unknown cards that could come on the end. Thus the total number of card combinations for the last two cards is 47 times 46, which is 2,162. The only accurate way to calculate the odds on something such as making a flush is to count up all the card combinations that make the hand and compare it with that totalcombination number of 2,162.
We often use shortcuts to give us a ballpark figure that is close enough to the true odds for most poker purposes. For example, if a t hold’em I have pocket aces and my opponent has a set, here is how I would get an approximate idea of my chances of helping with two cards to come. There are 45 unknown cards that could come on fourth street. (My two cards, the opponents two cards, and the three boardcards are known; 52 minus 7 gives us 45.) Of these 45 cards, only 2 help me, and 43 do not. Thus the odds on making the hand on fourth street are 43 to 2 against. That is 21.5 to 1. Since there is yet another card to come, we can take half of 21.5 which is 10.75. The approximate number I get with this method is 10.75 to1 against me making three aces. Here is how the true figure is computed. The number of ways to make the hand on either card is [(2 times 44) plus (43 times2)], which is 174. The total number of possible cardcombinations is 45 times 44, which is 1980. My change of making the hand is thus 174 out of 1980, so 174 cardcombinations make the hand and 1806 do not. The odds on my making the hand are 1806 to 174 against me, which reduces to 10.38 to 1. As you see, in this case we got a reasonable ballpark figure for figuring the odds on making the hand with two cards to come by guessing that they were about twice as good as odds on making the hand with one card to come. In this case the crude figure was 10.75 to1 and the real number was 10.38 to 1. The true odds with two cards to come are microscopically better here for the person drawing than the figure derived by the crude method, but the numbers are so close that the decision of whether to call is not going to be affected by the discrepancy between the methods used. So the simple but crude method to find the chance of hitting with two cards to come is to take the chance of hitting the hand with one card to come and say your chance is about twice as good with two cards to come. Expressed in concrete terms, if you are a 20/1 dog on the next card you will be only about a 10/1 dog with two cards to come. If you are a 6/1 dog on the next card you will be only about a 3/1 dog with two cards to come. The above method worked reasonably accurately because we were figuring the price on a longshot. This method is notoriously inaccurate when the draw is not a longshot. For example, it is obvious that a draw that is even money with one card to come will not be a cinch if there are two cards to come. In other words, a 5 percent draw with one card to come increases to almost 10 percent with two cards to come, but a 50 percent draw with one card to come does not go to anywhere near 100 percent when there are two cards to come. The right way to think about an evenmoney draw is about half the time you hit it on the end you already had made it on fourth street. Thus the chances rise from 50 percent with one card to come to about 75 percent with two cards to come.

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