Mathematics and poker - part 2

matt-matrosThe mathematics of poker are not just for gamers 'nerds': c is for everyone. If you can add, subtract, multiply and divide, you can use mathematics as a weapon to the table. In my last column, j. explained the terms "odds", "combinations", and "outs."

A practical example of the use of mathematics in d a decision of caller one all in.

The mathematics of poker are not just for gamers 'nerds': c is for everyone. If you can add, subtract, multiply and divide, you can use mathematics as a weapon to the table. In my last column, j. explained the terms "odds", "combinations", and "outs."

In this column, I want m tackle the expressions "range of hands", "pot odds", and l 'equity', and demonstrate why these concepts are important. J often hear the following advice: "do not put your opponent on a specific hand, but rather on a range of hand". C is good advice, but this is not enough. Analyze this Board of a mathematical viewpoint, using a poker hypothetical (but realistic) situation. You have revived with a medium pair say 8-8 in part d Hold em without limits, and your opponent has you re-relaunched all in. You "know" that your opponent has either AK or a big pair ladies or better. "Knowing" that you so put your opponent on a range of hands. C is perfect, but now, what should you do? Either you are greatly defavoris (4.5-1 if your opponent has an over-pair), or slightly favorite (about 1.2 1 against AK). Still, that doesn't mean that you need to sleep. You need to go to the next step.

First, you must determine the number of hands against which you are a slightly favourite or greatly defavori. But Matt, hear you say me, I am greatly defavori against three hands the ladies, Kings, and ACEs and a small favorite against one hand, AK, non? No! C is that the combinations come into play.

Hold Em, there are 6 preflop combinations that give you a pair d as: Ac_spade.gif, Ac_club.gif; Ac_spade.gif, Ac_heart.gif; Ac_spade.gif, Ac_diamond.gif; Ac_club.gif, Ac_heart.gif; Ac_club.gif,Ac_diamond.gif; Ac_heart.gif, Ac_diamond.gif. He n is no other way to receive two ACEs. In fact, there are six ways to receive n matter what pair preflop. On the other hand, there are 16 ways to receive a hand other than a pair. Take AK, for example. You can have n matter what as, accompanied by n matter what King. Four times four equal 16. In, going back to our example, there are 18 ways d have a pair better than the ladies (6 ways d have the ladies, 6 ways to have the Kings, and 6 d have as them), and it has 16 ways have AK. So, now that you have counted correctly, it is more likely (by a result of 18 to 16) whether you're against an over-pair whether you're against AK. You are very defavori against an over-pair and slightly favorite against AK. Now you can fold your hand, n is not it? Error! We are missing a part d important information: the size of the pot. If the revival of your opponent is small enough, you should call, even if you have good chance d be greatly defavori. Let me explain why.

Poker, we often need to compare the amount of money than l must call the amount of money as there are in the pot. The ratio between these two amounts is that l is called our pot odds. For example, with blinds of $ 1-2, I raise to $ 6 and my opponent pushes me all in for $ 21. All others fold. You have to call $ 15 (21$-6$) to win $ 30 ($$ + 6 + $2 + $1). My pot odds are therefore 30-15, which is the equivalent of 2-1. Therefore, how often should we win to call this bet when our pot odds are 2 - 1? And well, whenever we win, we triple our $ 15 investment ($15 + $ 30 = $ 45). So if we lose twice affiliate d, but win the third time, our return investment is zero ($0). Therefore, we must win more d once on 3 to make decision d call the correct bet; We must be defavori 2 - 1 or less.

Here's another way to see everything: If you defavori to 2-1 to win the pot, this means that once on 3, or approximately 33% of the time, you win the pot. In such a situation, we, the players of the poker-mathematical type, say while we have a 33% equity. S there are $ 30 in the pot, and we have to call a bet of $ 15, our investment return will be zero if we have 33% d fairness. To prove it, let's say that we call this update. The pot becomes $ 45. 33% of this pot 'ours', which is equivalent to $ 15. C is exactly the same amount of money as we had initially. Now, imagine that the pot was $ 31 and we had to call only $ 14, with this same 33% d fairness. Now, if you referred to, the pot becomes also $ 45, and we "have" always $ 15 this pot. C is a dollar more that the price we pay by calling upgrading, therefore, in the long term, we are $ 1 in calling. We make money, as the sides of the pot were 31-14. We need a fairness of only 31% (14 divided by 45) to make the call profitable and we had a 33% equity. If you compare your equity with l equity you need to call the bet based on the sides of the pot, you can still determine whether or not you should call an all-in raise.

L equity becomes especially useful when we think about the range of hands of l opponent. Back to our pair of eights. If we convert our coasts in percentage (something that we learned in the last column), our equity against an over-pair is approximately 19%, while our equity AK is approximately 54%. C is great, but what is even better is that we can calculate our equity against this range of hand: QQ, KK, AA, AK. We have determined above there were 18 ways that our opponent could have an over-pair and 16 ways qu could have AK. To calculate our total equity, d simply add the equity according to their relative probabilities. There are 34 hand combinations that our opponent can have (16 + 18 = 34). In this case, 18 times 19% for the surpaires, plus 16 times 54% for AK, divided by 34, gives us a total equity d about 35%. (the exact figure is 35.8. I arrived at this result using PokerStove, available for free at

Our 8 pair will win the hand more often as once in three if our opponent can have than the ladies, Kings, ACEs, or AK. So, if we have 2-1 pot odds, with which n we need only 33% d equity, we are supposed to call the bet. In fact, if we receive from sides of pot more 1.8 - 1, should call. Several players from limitless misfit here their pair of eights against an all-in raise, even they receive 2-1 on their money. They thus lose tokens.

C is very rare that the range of our opponent's hand is strong enough to make us sleep when we receive by 2-1 to an all in player. Simply return to our example. The range of our opponent's hand was extremely strong, and c was nevertheless always correct d call the bet with a simple pair of 8. Around d table, little d opponents have a range of hand as strong as that which we have taken in the example above. Of more, when you start to call the reraises all in, your opponents will be less inclined to try to crush you on subsequent hands. Think always in term equity, in terms of value of putting your chips in the pot. Don't you just say "I'm either very late or little in advance, and so I have to lie down.

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