Unlike the slot machines, skill is an important part of winning in poker. It’s not just a matter of luck or chance. The more skilled you are, the more often you can expect to win and the more chips you will win. Using the Math of Poker is an essential part of being skilled.
In high school or college, you may have studied combinations and permutations, and computed the probability of certain events, from which the odds could be calculated. Few if any skilled players rise to this level to determine their poker odds. They do it the easy way, as we will discuss. Knowing the odds, they can then make appropriate decisions: Should I call the bet or should I fold? Should I raise?
Before the flop, many skilled players use starting-hand tables published in books like Lou Krieger’s Hold’em Excellence. Still others rely on the new Hold’em Algorithm in George “The Engineer” Epstein’s Hold’em or Fold’em booklet. So there really is no need to use math before the flop.
After the flop, the math is very important to estimate the card odds and compare these with the pot odds. Most often, you are holding a hand that must improve to be the winner at the showdown. What are the odds against catching one of the cards that will make your hand? I don’t know who deserves the credit for it, but the 4-2 Rule provides the math and does it very well – and it’s easy.
Using 4-2 rule
On the flop, count your outs. How many cards will make your hand, presumably the winning hand. Suppose your hole cards are A-10 suited. The flop brings two more cards of your suit, no pairs. You need one more card of your suit for the nut flush. Without a pair on the board, it is much less likely that an opponent will catch a full-house to beat your nut flush – if you are lucky enough to make it.
There are 9 more unseen cards of your suit remaining in the deck. That’s 9 outs. With both the turn and river cards yet to be dealt out, the chance (probability) of getting another card of your suit is approximately 9 x 4 = 36%. Then, (100 - 36) = 64% is the approximate probability that you will miss. So the card odds are approximately 64-to-36 = 1.8-to-1 against catching the nut flush on the turn or on the river. Meanwhile an opponent has bet on the flop and it’s your turn to act.
Compare these card odds to the pot odds – how many chips you must invest to see the turn, compared to the number of chips already in the pot. You estimate that there is $20 in the pot, including the $4 bet by the player to your right. So your pot odds are $20-to-$4. That’s 5-to-1. And it’s higher than the card odds against you. So you make the call. It’s a “Positive-Expectation” bet. You will come out ahead in the long run.
Shucks! The turn is a brick as far as you are concerned. There’s an $8 bet. You have one more chance to make your nut flush. Should you call to see the river? Now you multiply your outs by 2: 9 x 2 = 18% probability. Round it up to 20%. Thus the card odds are approximately 80-to-20 = 4-to-1 against.
Estimating the pot to contain about $50, you are getting 50-to-8, approximately 6-to-1 pot odds. That’s more than the card odds of 4-to-1 against. Another “Positive-Expectation” bet. Make the bet and hope the poker gods favor you with another of your suit.
In the long run, this skill in using the Math of Poker is bound to make you a winner! Try it. You’ll like it!
“The cards you are dealt is a matter of luck; how you play them is a matter of skill.” – Thomas M. Green; Texas Hold’em Poker Textbook; visit www.PokerTextbook.info
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