Example of Situation C
Assumptions:
- You have a 25% chance of having the best hand
- If you bet and your opponent has a better hand than yours, he will fold 40% of the time and call 60% of the time.
- If you bet and your opponent has a worse hand than yours, he will fold 100% of the time.
- The pot size is 5 big bets
- Your lone opponent has checked on the River and you are last to act. Expected Value of checking:
The pot size is 5 big bets. If you do not bet, you have a 25% chance of winning the hand and a 75% chance of losing the hand. The expected value of checking in this hand is:
Expected Value of checking = (25% x 5 big bets) + (75% x 0 big bets) = +1.25 big bets
It is important to forget about the chips that you have put in the pot yourself in previous rounds. Those chips are now a sunk cost, it is no longer your chips as it currently belongs to the pot.
Expected Value of betting:
In the assumptions, it states that if you bet and your opponent has a better hand, he will fold 40%
of the time and call 60% of the time, but if he has a worse hand, he will fold 100% of the time.
In the assumptions, it was stated that when you have the best hand (25% of the time in this example), your opponent will not call a bet. When you have the worst hand (75% of the time in this example), your opponent will fold 40% of the time and call 60% of the time.
The expected values individual situations are: You have the best hand = 25% x 5 = 1.25
He has the best hand and he folds when you bet = 75% x 40% x 5 = 1.50 He has the best hand and he calls when you bet = 75% x 60% x -1 = -0.45
Since there is no increased value to betting when you have the best hand (since we have assumed he will fold 100% of the time when he has a worse hand), the only possible extra value that is gained by a bet is due to bluffing, when you bluff him out of a better hand. In this example, we are not sure if we have the best hand or not, so it is unclear if we are actually bluffing.
Expected Value of betting/bluffing = (25% x 5 big bets) + (75% x 40% x 5 big bets) + (75% x 60% x -1 big bet) = +2.3 big bets
When we bet, we have an expected value of +2.30 big bets. In this example, it is clear that betting is better than checking, as an expected value of +2.30 big bets is better than an expected value of +1.25 big bets in checking.
If the numbers were slightly changed, then it could make the bluff an incorrect move. Lets change the assumptions and assume that instead of folding 40% of the time when he has the best hand, your opponent is only going to fold 10% of the time when he has the best hand, and call 90% of the time. Then the expected value equation becomes:
Expected Value of betting/bluffing with adjusted numbers = (25% x 5 big bets) + (75% x 10% x 5 big bets) + (75% x 90% x -1 big bet) = +0.95 big bets
In this case, the expected value of bluffing is +0.95 big bets, which is worse than the expected value of checking +1.25 big bets. So your decision to bluff or not is dependent on how likely your opponent is going to call.
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