Where are the Mistakes?
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The other day a friend of mine was complaining about a bad beat. I normally charge $1.00 to listen to a bad beat, but he caught me off guard while I was online. It seems that someone had called my friend down with an ace and then hit an ace on the river to beat him. What my friend, like most poker players, doesn’t understand is that once the pot is large the so called “fish” are playing as good as the experts.
In The Theory of Poker David Sklansky defines the fundamental theorem of poker as: “Every time you play a hand differently from the way you would have played it if you could see all your opponents’ cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.“ Pages 17-18
With this in mind we can look at an individual hand and see what mistakes were made; the results may be surprising.
Let’s take a look at my friend’s bad beat and see what mistakes we made by the participants along the way. An under the gun players raises; my friend makes it 3 bets with a pair of tens, “hero” in late position” call the 3 bets with A9o and the original raiser folds. So far the under the gun raiser has made the worst play; he put in two bets and then was unwilling to call one more bet getting 9.5:1 on his money (his two bets 3 bets from the other two players and 1.5 bets from the blinds). The “hero” at this point called getting about 2:1 odds. In the hand he can expect to 27.6 % of the time to the TT 72.4% of the time. I will point out that I have converted the ties so these numbers aren’t completely accurate but they represent each player’s equity in the pot (hero can expect to get back 27.6% of the money). So was calling 3 bets with A9o a mistake against TT? The percentages given above show us the A9o is a 2.6:1 underdog to win the hand, so yes he made a mistake calling with the A9, but not that “big” of a mistake.
Next the flop came K 7 2 do three different suits. On the flop my friend bets and “hero” calls. After my friend bets the pot is offering 10:1 (we rounded down to allow for rake) on a call. At his point “hero” can expect to win 12.7% of the money so he is 6.9:1 dog to win, so getting 10:1 on a 6.9:1 shot is offering him a nice overlay. So calling on this flop is clearly not a mistake.
The turn cards comes a 5 and my friend bets and the hero calls. On this call the hero is getting 7.5:1. He can expect to win 6.8% of the time, making him a 13.7:1 dog to win this pot. Here the hero is making a large mistake by calling this bet.
The river came the ace and at this point the has a 100% chance of winning so any money he can put into the pot is in his favor. Could my friend have done anything to win this hand? Could he have played the hand better?
When one is the bettor in a hand they can win in one of two ways; by having the best hand or by having everyone fold. When one is calling the only way to win is to have the best hand. The best position to be in as a bettor is to be betting when the potential caller does not have the correct price to call. In this case you win the pot if he folds and you gain expected value if he calls.
In the real world we do not get to see the opponent’s cards; does this mean we should throw out the fundamental theorem of poker? No, we can use the results of looking at hands to find where hands can be played better. I chose the example above because it is very common for the loose caller to get correct odds to call on the flop. What could my friend do to play better in spots like this? If he does not 3 bet before the flop the pot is smaller making the call on the flop incorrect. If one 3 bets before the flop they should recognize that very few hands will fold for one bet on the flop so a check may very well be in order. When you check on the flop you cut the drawer’s odds in half with the double bet on the turn.
