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1. Hero: K♥Q♥
Villain:
Call $20: QT, AJ, QJ, J9
Board: Q♠2♣9♥J♠7♦
Is a $20 value bet profitable? If so, what is the EV?
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Answer: In order to have a profitable value-bet, we’ll
need the villain to call with a hand we beat more than
50% of the time. We beat QT and AJ, which total 20
combinations. We lose to QJ and J9, which total 15
combinations. A bet is profitable. What’s the EV? The
hands we beat comprise about 57% of his range (20/35). 0.57($20) + 0.43(-$20) = EV
11.4 – 8.6 = $2.80
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2. Hero: K♥Q♥
Villain:
Call $20: QT, AJ, QJ, J9
Bluff raise (you’ll fold): 55
Board: Q♠2♣9♥J♠7♦
Is a $20 value bet profitable?
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Answer: Again, we need him to call with a worse hand
more than 50% of the time. While we do beat 55, we
have to treat that just like losing since he bluff-raises us
and we fold. We get value from QT and AJ, which total
20 combinations. We lose to QJ and J9, and we have to
add 55 to this group. Those total 21 combinations. We
only get value from about 49% of his range (20/41). A
bet is not profitable.
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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?
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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.
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4. Hero: A♦J♦
Villain has $60 left:
Call up to $20 – A9, AT, AK, AQ, J9, JT, QJ
Call all-in for $60 – AK, J9, JT, QJ
Board: 2♣5♦J♥A♥J♠
Which bet is more profitable?
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Answer: Villain will call the $20 with his entire range,
which contains 44 combinations. We beat all of those.
He will call the larger $60 bet with 20 of those
combinations. That’s 46% of his range. The EV of the
$20 bet is $20 since we get called every time and always
win. The EV of the $60 bet is:
0.46($60) = $27.60
The $60 bet is more profitable.
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5. Hero: A♦J♦
Villain has $60 left:
Call up to $20 – A9, AT, AK, AQ, J9, JT, QJ
Shove $60 as bluff after your $20 bet (you’ll
call) – 78
Call all-in for $60 – AK, J9, JT, QJ
Board: 6♣5♦J♥A♥J♠
Which bet is more profitable
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Answer: The scenario is the same as question four;
however, there’s a little twist. The smaller bet will
induce a bluff shove from your opponent’s missed
OESD. This adds a tremendous amount of value to your
smaller bet. Nothing in his range will fold; however, 16
of the 60 combinations will give you $60. This is our
EV for the $20 bet.
0.73($20) + 0.27($60) = EV
$14.6 + $16.2 = $30.80
Now, let’s examine the EV of the $60 bet.
0.33($60) = $19.80
Obviously the EV of the $20 bet is better and highlights
the power of inducing bluffs. The astute student may
have noticed the EV of the $60 bet is less now than it
was in question four even though the bet size and
number of combinations calling are both the same. If
you're curious, see Appendix A.
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6. Hero is out of position: K♥Q♥
Villain:
If you bet:
Call $20 bet: QT, AJ, QJ, J9
If you check (you’ll call):
Bet $20: QT, QJ, J9, AT
Board: Q♠2♥9♥J♠3♦
Is it better to bet or check/call?
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Answer: With the calling range, there are 20
combinations you beat, and 15 combinations that beat
you. Here’s the EV of betting.
0.57($20) + 0.43(-$20) = EV
$11.4 – $8.60 = $2.80
If we check, his betting range consists of 24
combinations you beat, and 15 combinations that beat
you. Here’s the EV of check/calling.
0.62($20) + 0.38(-$20) = EV
$12.40 - $7.60 = $4.80
Check/calling $20 is superior to betting $20.
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7. Hero is out of position: K♥Q♥
Villain:
If you bet:
Call $20 bet: QT, J9
If you check:
Bet $20: QT, QJ, J9, AQ
Board: Q♠2♣9♥J♠7♦
The pot is $20 before anyone bets. Villain only has $20
left in his stack. What’s the best action to take?
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Answer: If we bet, villain calls with eight hands we beat
and nine hands that beat us. He’s only calling with 47%
worse hands, so betting is –EV.
If we check, villain is betting the pot. We’d need to be
good 33% of the time to call. Of his betting range, we
only beat QT, which is 8 combinations. The rest of his
betting range consists of 25 combinations.
8 / 25 = 0.32
Check/calling is –EV. The best move here is to
check/fold.
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