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December 8, 2005
If he holds A-9 or A-7 or 9-7 you're also beaten. On the other Pokerparty hand, he may be betting with A-6 and trying to win the pot right there if no one else holds an ace. While you have some idea about the players in seats eight and nine, you're not certain you have the best hand. However, it's fair to assume that if either seats eight or nine had A-K, A-Q or A-J, they probably would have raised before the flop.
Someone who wins two big bets per hour in a soft, passive game with very little volatility -- almost no preflop raising and reraising -- can expect a lot less variance than a counterpart who plays equally well, but plays in a game with maniacs who make it two and three bets to go almost every hand. A terrific player in a soft Pokerparty game can get by on a much smaller stake; maybe 200 or even 100 big bets will do the trick.
In this case, you'd multiply 4 x 3, or 12, and 2 x 1, or 2. Then set up a division problem, with the product of the universe calculation on top (the numerator, in case you've forgotten) and the product of the choice calculation on the bottom (the denominator). Then divide the numerator by the denominator. The answer, of course, is 12/2, or six. Here's another example.
In the final Partypoker scenario, I used each of these three player profiles to fill in 9 seats at my computerized table. With the Rock player-profile occupying all 9 seats, I asked the computer to play 60,000 hands of $10-$20 Texas hold'em. That's about one year of play, if you figure that a dealer will put out 30 hands per hour and you play 2,000 hours (that's 8 hours per day, five days a week, for fifty weeks) annually.
Checking a very strong Partypoker hand in order to lure your opponents into a trap is the flip side of betting a hopeless hand. Since bluffing only works when used judiciously, you're better off restricting your bluffs to opportunities where you have a couple of ways to win: your bet causes your opponent to release his hand, or he calls and you still have an opportunity to win by catching the card you need to make the best hand.