Poker Behaviors that Change the Odds
Many players understand that probabilities do not change from hand to hand. They know that an unseen card has an equal chance of being any one of the remaining unseen cards. However, they fall into the trap of treating all cards not in their hand as unseen cards. Cards held by your opponents are not unseen cards. Your opponents have seen them and their actions are a source of information. Only one card is out that beats you, but if your opponent acts like he has that one card, don't think that being beaten is unlikely. Many players make the mistake of playing only their cards-and never asking the question: Why are my opponents still in the hand?
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The Improbable Can Happen
On a St. Louis riverboat a number of years ago, the following hand occurred at my table. After the deal, a player in an early position raised pre-flop. Except for one player who called the raise, everyone else folded. The player who initially raised-I will call Player 1- had played a tight game all afternoon. I had observed one other pre-flop raise from him earlier that day and it came on pocket Aces, so I took his raise as a sign of strength. He also appeared to be a regular (the casino employees all knew him by name and greeted him warmly). Players who are regulars at certain cardrooms often play tight, solid games. Otherwise, they can't afford to be regulars. The player who called his raise, Player 2, called without hesitation, so I also put him on a strong hand. The flop came up A, 10, 6. Player 1 bet; Player 2 called. The turn card was an Ace. Player 1 bet and again Player 2 called. The river card fell as a K. Player 1 bet and Player 2 raised. Player 1 countered with a re-raise. In this cardroom, the rule was that if two players went head-to-head on the end, raises were not capped. The rule allowed players to get into a raising war as long as they had money on the table. Player 2 re-raised and the war was on. At this point, it was obvious to me what each player held. Player 1 must have had pocket Aces and Player 2 pocket Kings. Four Aces beats Kings-full but Player 2 seemed oblivious to that possibility. He continued to counter each re-raise with another. Finally, Player 1 decided he had taken enough of Player 2's money, put down a final re-raise and exposed his two Aces. Player 2 showed his two Kings and shook his head in disbelief.
losing with Kings-full to four Aces is a highly improbable bad beat. I'd raise, too, if I hit Kings-full at the river, but with this board, would I completely discount the possibility of my opponent having the remaining two Aces or even one Ace and the remaining King? Player 2 with Kings-full has seen 7 cards, which leaves 45 unseen cards, 2 of which his opponent has. Pick 2 cards from 45 unseen cards and there are 990 possibilities, only three of which (AK, AA, AK) beat Kings-full for this board. However, Player 1's cards are not two random unseen cards from 990 possible combinations. He has seen them and acted in such a way that eliminates from consideration almost all of these 990 possibilities. Player 1 would not be re-raising if he held 2, 5 or J, 7 or 4, 8, so why is he re-raising? It is not correct for Player 2 to assume that the odds of losing are remote (3 in 990), given Player 1's behavior.
Many beginners make the mistake of Player 2 above: They only play their cards and never consider why their opponents are in the hand. As a further example of how behaviors change the probabilities, consider a hand I played in the now-defunct Prince George's County Maryland cardrooms.
I was playing $5-$10 Omaha when a woman joined the game, sitting to my left, whose play immediately changed the dynamics of the table. She played very aggressive poker and rarely called. Her actions were bet, raise, or fold, and she played in most of the hands. She raised pre-flop, regardless of her position, for almost every hand. Since I sat on her right, I knew that any bet I called would be raised, so I tightened my starting requirements for hands, folding hands I ordinarily would call with, calling with my premium hands and letting her put in the raise for me. I was the only player at the table who made this adjustment. Everyone else, seeing that her pre-flop raises conveyed little information, called her raise. Soon almost every player at the table called her pre-flop raise every single hand. With so much money seeding the pot, no one wanted to fold before seeing the flop. The entry of this one player changed the entire table dynamics, causing an extremely loose-aggressive game to develop.
In a loose-aggressive poker game, so-called "bad beats" are actually highly probable. One hand in particular stands out as an example of how the new table dynamics distorted the probabilities. Of my four starting cards, two were Kings. I called, she put in her raise, and every single person at the table (there were eleven including me) called her raise. The three cards that came on the flop were K, A, and 8, all of different suits. I bet my set of Kings. She raised, the man to her immediate left called her raise, and everyone else dropped returning the action back to me. Because two players were up against me after seeing the flop, I thought it likely that each had an Ace and possibly one of them had an Ace, 8, giving them Aces-over. My three Kings had to be the top hand so I re-raised. She called, a first for her that day; he called. The turn card came, a 3 of the only suit not yet on the board (There would be no flush possible). I bet, she called, and he called. Her sudden respect for my bets and his refusal to go away convinced me they both had Aces-over.
The river card was an Ace. Had I been going against one player, I would have checked. But I knew I would not be raised since each of them had to fear the other. I bet my Kings-full (since I knew I had to call with it). If you know you are going to call, and do not fear a raise, take the initiative and bet. Your opponents might not have hit their draw and could fold. In this case, they had hit. Both of them called and each turned over an Ace, 8. As the dealer stacked the chips into two piles in order to split the pot between them, he shook his head in disbelief and said to me: "That was the only card that could beat you."
But how improbable was that last card being the one remaining Ace? My two opponents each have four cards and I "know" they each have an Ace. That means there is only one remaining Ace among the 36 cards that are not part of our three hands or the board. The odds appear to be 1 in 36 or 2.7%. the fact that shocked the dealer.
However, given the behavior of the players at the table, this assessment is not accurate. Think about the table dynamics. Every single person called this woman's pre-flop raise. When an Ace showed on the flop, no one holding an Ace would have dropped. Her raise pre-flop scared no one; neither would her raise after the flop have scared anyone holding an Ace. The man to her left didn't scare, and with 11 pre-flop raises ($110) in the pot, anyone with a chance to win would have stayed. When the other eight people at the table folded a total of 32 cards after the flop, it meant none of those cards was an Ace. When the dealer reached for the river card, only four cards remained in the deck and one of them had to be an Ace. The odds of me being beaten were 1 in 4. As the favorite, my bets and raises were correct, but my 10ss was not a great improbability.
In the previous page, I explained that the distribution of cards to players and the board are completely random events with no memory of the past. However, once the cards are dealt and players have seen them and acted, events cannot be considered random. The probability of a four falling on the board may be the same as an Ace, but an Ace is much more likely to have paired someone than a four. Many players keep any hand containing an Ace, but almost no one keeps every hand that contains a four. To be successful, you need to put your opponents on hands and play accordingly. Do not think only of your cards and the probability that a random unseen hand is better. Always ask yourself: "Why are my opponents acting the way they are?"
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