Poker Math That Matters

3. Hero: K♥Q♥
Villain:
Call $20: QT, AJ, QJ, Q7
Bluff raise (you’ll fold): 55
Board: Q♠2♣9♥J♠7♦
The pot is $20. Is a $20 value bet profitable?
193
Answer: Do not be discouraged if you didn’t get this
one. It’s designed to show the impact of villain stealing
from us. Again, QT and AJ give our bet value and total
20 combinations. We lose to QJ and Q7. Those total 12
combinations. We lose to 55 as well, which is 6
combinations. So, the hands that beat us total 18
combinations. We actually have more combinations of
hands we beat, which is more than 50%. So, we may be
thinking we need to bet. However, what we need to
consider is the villain is actually stealing the $20 pot
from us as well as our bet. So, our EV would look like
this.
QT and AJ: 53%
QJ and Q7: 31%
55: 16%
0.53($20) + 0.31(-$20) + 0.16(-$40)
10.6 – 6.2 – 6.40 = (-$2)
So, even though the villain is calling with more than
50% worse hand, we’re still not +EV with our bet
because he’s stealing the pot from us.