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Bluffing Against Two or More Opponents
 
It is rarely correct to try to bluff out two or more people when all the cards are out; your chances of success decrease geometrically with each additional player in the pot. Paradoxically you might have a profitable bluffing opportunity against each of two opponents individually, but not against both of them as a group. Suppose, for example, you are heads-up on the end in a $10-$20 games. There is $80 in the pot, and you think you can get away with a bluff one out of three times. Clearly this is an extremely profitable bluffing situation. Once you will win $80, and twice you will lose $20 for a net profit of $40 or an average profit of $13.33 per bet.

Now suppose you are in the identical situation except that you are up against two players instead of one. We'll assume each player has put $40 in the pot to expand it to $120, and you think, as in the former case, that each opponent will fold one time out of three. You are now getting 6-to-1 instead of 4-to-1 from the pot. Nevertheless, an attempt at a bluff is no longer profitable because the probability that both of your opponents will fold is 1/3 X '/2, which equals 1/9. In other words, eight times out of nine one or the other of your opponents will call on average. So you stand to lose $20 eight times for a total of $160 and to win $120 once. Your net loss is $40 or $4.44 per bet. Thus, opposing each individual player by himself results in a profitable bluffing situation, but if they're both in against you, you have gone from a profitable situation to an unprofitable one.

(It should be pointed out that in most bluffing situations against more than one player the probabilities that each player will fold are not independent. The player in the middle will frequently fold a hand that he would call with if he was last, and sometimes the player who is last will call with a hand he would have folded without hesitation had he been in the middle, expecting the player behind him to call. Nevertheless, the general principle still holds that it is usually more profitable to try to bluff one player out of a pot containing 2X dollars than to bluff two players out of a pot containing 3X dollars.)
 
Ace High Flush Draw

 
An Ace high flush draw also gives you a few ways to win. The Ace is key for two reasons: you can win by pairing the Ace and if you make a flush, you'll have an Ace high flush and be less likely to be beaten by some other player's bigger flush. The consideration of having a big flush is an important one in stud. If you make a flush, the distribution of the other cards is such that the likelihood of someone else also making a flush in a different suit increases. If there are two flushes out, you want the best, not the second best. This is a recurring theme in initial hand selection in all forms of poker-don't even get involved when it's likely that the best you can hope for is second best.
 
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