Is still better to delay your climb to take the first player. (And this, remember, is true even if we assume that there was no money in the pot before). When you’re a 4:1 favorite (80%) against each hand individually, is a different story. This is better to raise on the first street to keep the player and win more money. This move has resulted in a 64% EV of $ 600 less 36% of $300, that is $276. The other way you will have the following: 80% of $400 minus $20 to $300, which is $ 260. Anyway, if the hand were involved in three rivals, instead of two, each of which has an independent probability of earning 20%, the correct play under these simplified conditions would delay your climb. If you do, you’ll earn $ 900 51.2% of the time and lose $ 300 48.8% of the time.
(Do you see why?) This is an EV of $ 314.40. If you wait and take up to two players, you win $ 500 80% of the time and lose $ 300 by 20%. This is an EV of $ 340. Of course this simplified model has a few snags. The most important is that the real players throw does not imply an increase in your chance to win as big as in the model. The probability for each rival is not independent.
This is especially true if your hand is not only the best now, but also is likely to improve. Another problem with this model is the fact that probabilities change from street to street. All these problems mean that you do not need to be as clear favorite as the model suggests to make the right move is to increase the pot from the beginning. Furthermore, the model assumes that there is no money in the pot of previous rounds. If any, would more reason to win the pot at all costs, even if it involves not increase so that it is easier to climb and take players into the next round). What seems to reflect the model is the following. It may well be positive does not raise the pot with hand pretty good boat with several players, if this decision encourages the player to your right to gamble in the next round, which would not do another thing. When to do this exactly is something we will discuss another time. I example in my Hold’em Poker for Advanced Player. For now, suffice it to say that the move is right more times than common sense suggests.