First, let's look at TAg #1, who was the original opener in MP:

- TAg #1 Original Raising Range= 15.20% (22+,ATs+,KTs+,QTs+,JTs,ATo+,KJo+,Qjo)
- TAg #1's 4bet calling range= 0.90% (KK+)
- Probability that TAg #1's will call our shove= 5.9% (this is just 4bet calling range divided by original opening range)
- Therefore, probability that TAg #1 will fold to all-in shove= 94.1% (this is just 100% minus the probability that we get called)

- TAg #2 Original ReRaising Range= 5.00% (99+,AQs+,Ako)
- TAg #2's 4bet calling range= 0.90% (KK+)
- Therefore, probability that TAg #2's will call our shove= 18.0%
- Therefore, probability that TAg #2 will fold to all-in shove= 82.0%

- Probability that TAg #1 and TAg #2 will both fold = 77.1% (To calculate this, just multiply the two probabilities that the TAgs will fold together; in this case: 82% x 94.1%)
- Therefore, probability that we get called by at least one TAg = 22.9% (Again, just 100% minus the number in the previous line)

- Amount we're risking when shoving = $1,500
- Amount we win if everyone folds = $195 (dead money in the pot right now)
- Average amount we could win if our shove gets called by one player = $1,590 (this is the calling amount plus the
*average*dead money left in pot)

- Equity of our AK against calling range of one opponent = 18.5%

- 77.1% of the time everyone folds and we win $195
- 22.9% of the time we get called by at least one player:
- 18.5% of the time when we get called by one player our AK wins and we win $1590
- 81.5% of the time when we get called by one player, our AK is beat and we lose $1500

- Our jamming expected value = negative $61.74
- If both opponents call, our EV is even less than this amount
- If I loosen up both of the opponents' calling ranges further to, say, AK+ and QQ+, our EV becomes even more negative (-$103.69)
- Jamming all-in is therefore a mathematically bad play
- QED

-Bug

## No comments:

## Post a Comment