#12 Scare'em Out Factor
In a flop situation where the chance for winning a pot looks promissing and pot odds are on our side, it is pretty obvious we stay in the game. The key question becomes whether to call or raise and if so to raise for what amount. Let's try to handle that problem analytically.
The flop situation means there are two more cards to come. The deal of those two cards can have several effects for me and another player.
Now End of the game
a) Me > Other Me > Other
b) Me > Other Me < Other
c) Me < Other Me > Other
d) Me < Other Me < Other
(P1 > P2 means P1's hand have better chances of winning with the current community cards than P2's hand)
Situation a) and d) are of lesser interest since my estimate of chances does correctly reflect the chance at the end of a round.
Situation c) is considered blind look for me. But since I assume that I have lost the game, and we actually earn something don't worry :)
However situation b) is very critical and must be avoided. The other guy had worse cards at the flop, but got lucky on river and turn and now has a hand that beats mine. The only thing I can do to prevent him from getting lucky is change the pot odds so the other guy will not take the risk of paying $200 for a pot of $210 with cards that have a chance of nearly nothing.
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Currently I just see another monte carlo approach to tackle that problem. There might me more sophisticated and less time-consuming methods.
Here is the idea (for flop or river situation):
Take my hand cards and at least three community cards as given. Shuffle the rest of the deck and deal two cards to an imaginary player X. Now perform a monte carlo analysis for both players to find out about each one's winning chances.
Then deal the missing amount of community cards and figure out which guy has the better hand. According to the result a), b), c), d) increment a counter and increment the counter for number of simulated games. Maybe also keep in mind how likely it was for the other guy to win before.
Now restart from the beginning and simulate n games (find out what n must be to get a reasonable time/accuracy trade-off).
Compute the ratio of situations c) to all games simulated and find the mean of p(other guy is winning on flop/river) . This will indicate how much you need to raise.
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With a rough assumption about your opponent's cards, the above estimation can be tremendously accelerated.