Let's do a quick exercise to estimate our equity against that
range. We’ll analyze his hand range: 9 combinations of AK, 12
total combinations of 88 and TT, and 3 combinations of 89s.
These hands divide well into two groups.
Group 1: Against 88, TT, and 89s, we have roughly 15 outs with
1 card to come for an estimated 30% equity.
Group 2: Against AK, we only have roughly the 9 flush outs for
a total of 18% equity.
So, the 2 groups are 30% equity and 18% equity. Notice the
30% equity group contains 15 combinations, and the 18% equity
group contains 9 combinations. So, the 30% group "weighs"
quite a bit more than the 18% group. I'd use the MS Method
here to find about 2/3 the way up from 18 to 30. The exact
middle I know is 24, so I'd slide it a bit higher than that and
estimate about 27% equity against this range. If you put this in
Pokerstove, you'll find it gives us 28% equity. We're close, and
close will do just fine.
Remember we needed 23% to call his bet, so we have the
immediate odds to call his turn bet. Against his AK, it's likely
we even make more money on the river as well, so there are
some implied odds to consider. But, we can call without even
considering implied odds.
However, we always need to make sure we consider all our
options. We can fold. The EV of folding is always 0, so we
know that's already worse than calling and out of the question.
We can call, and we already explored that briefly. But, we can
also raise. We can even raise to different amounts. Remember,
only through aggression can we take advantage of fold equity.
I say "roughly" because against some of the TT and 88 hands, he has
a diamond which reduce our flush outs by one.
We can minraise or shove and every amount in between. This
aggression will give us more than one way to win the hand. We
can make the best hand for showdown, or he can fold. Let's look
First, let's make some assumptions about how he'll respond to a
shove with his range. Let's say he'll call with AK and TT, but
will fold 88 and 89s. There are 15 combinations he calls with,
and 9 combinations he folds. So, he folds 37% of the time.
We have about $87 left in our stack, but our stack doesn't matter
here because the big blind has less money than we do. He had
$27 left in his stack on the turn and then bet $12. So, he now has
$15 left. There is currently $39 in the pot. We can move all-in,
which will risk $27 to win the current $39 pot. Going back to
the reward to risk table (See Table 8), we know when risking x
to win about 1.4x, we need to him to fold about 40% of the time.
He's only folding 37% of the time. Does that mean raising is not
good? No. In the bluffing section, we were always looking at a
straight bluff with no chance of improvement. Here we have
showdown equity in the hand to go along with our fold equity.
Let’s look at a detailed way to figure out how often he needs to
fold when we shove. If this look complicated, do not be
concerned. At the end of this section, I’m going to show you a
shortcut to do this at the table.
Fold%(pot won when he folds) + Call%(amount we win/lose
when he calls)
Here we’re going to let x equal the percentage of times he folds.
x($39) + (1-x)(0.24($54) + 0.76(-$27)) > 0
39x + (1-x)($12.96 – $20.52) > 0
39x + (1-x)(-7.56) > 0
39x – 7.56 + 7.56x > 0
46.56x > 7.56
x > 0.1624
He has to fold more than 16% of the time in order for our shove
to be +EV. I often like to test my work to make sure I did it
correctly. Here we can plug in the percentages.
0.1624($39) + 0.8376(0.24($54) + 0.76(-$27)) > 0
$6.33 + 0.8376($12.96 – $20.52) > 0
$6.33 + 0.8376(-$7.56) > 0
$6.33 – $6.33 > 0
Our work checks out. Notice he is folding 37% of the time, and
we only needed him to fold 16%. So, obviously the shove is
+EV. Let’s look at the EV of this shove.
0.37($39) + 0.63(0.24($54) + 0.76(-$27)) = EV
$14.43 + 0.63(-$7.56) = EV
$14.43 – $4.76 = $9.67
Let’s compare this to the EV of the calling.
0.28($39) + 0.72(-$12) = EV
$10.92 – $8.64 = $2.28
So, we can see the power of the semi-bluff here. We often win
the whole pot uncontested, and when we do win on the river if he
calls, we win a bigger pot.
There are three key variables when analyzing whether or not a
semi-bluff shove is a good move.
1. The size of the pot in relation to the money left. The
larger the stack to pot ratio, the more often he must
fold. This is because we're proportionally risking more.
2. How often he folds. Normally the smaller the stack to
pot ratio, the less often he'll fold and vice versa. This is
because our opponent is normally aware of the reward to
risk ratio to some extent.
3. Your showdown equity. The more showdown equity
you have, the less often he'll have to fold.
Now, I promised a shortcut, so here it is. We’re going to look at
our reward to risk ratio in this shortcut.
The pot is currently $39. We have to shove $27. Remember
when we shove, we have equity. So, shoving isn’t risking $27 to
win $39. We have to find out what we’re actually risking. Our
shortcut has three steps.
1. Total pot size times our equity.
2. Subtract the result from step one from our bet.
3. Examine the reward to risk ratio.
Let's examine these three steps from our example.
1. The final pot would be $81. Our equity against his all-in
range is 24%. That would about $20.
Even though they may not know the math, most people will be more
cautious calling a large amount to win a small amount and vice versa.
I would do this quickly by thinking of 80 divided by 4.
$81(0.24) = $19.44
2. Our shove is $27.
$27 - $20 = $7
3. We’re risking $7 to win $39.
7 / 46 = 0.15
We come up with 15%, which is almost exactly what we need.
This shortcut can be done very quickly rounding like this and is
very effective. Let’s look at one more example using this
Let’s say you’re in a hand preflop against an aggressive player.
You’ve been fighting a lot preflop with raises and reraises. You
both start with $100. You have KJo in the big blind. He open
raises on the button to $3. You reraise to $8. He reraises you to
$25. You know he can have a lot of monster hands here, but you
also believe he’s bluffing a lot as well. Calling here isn’t an
attractive play because you miss so often on the flop, do not have
the initiative and are out of position. You’d like to find out how
often he has to fold in order to have a +EV shove. This is a
preflop semi-bluff shove.
The pot is currently $33. You have $92 left in your stack.
Remember if you shove here, you will certainly have showdown
equity. So, shoving isn’t risking $92 to win $33. We have to
find out what we’re actually risking. Let’s use our shortcut. I’m
not going to show the math here and just display how I would
think in the hand.
1. To start this, we need to estimate our equity verses his
all-in range. Let’s assume he’ll call our shove with TT+
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and AQ+. Our equity with KJo against that range is
about 30%. So, when we get all the money in, we’ll
own 30% of that pot. The final all-in pot will be about
$200. And, 30% of $200 is $60.
2. If we subtract that from the amount we have to shove,
which is $92, we get $32.
3. We’re risking $32 to win $33. This is about x to win x,
so we need to have him fold 50% of the time. You can
check the work with the long equation we did before.
We can even take this a step further and find out what percentage
of hands he would have to reraise to make our shove +EV. He is
calling with about 4% of hands. What number times 50% equals
0.50x = 4
x = 8
He would have to reraise with more than 8% of hands to make
our shove +EV.
So, you are now equipped to do a lot of work away from the
table examining semi-bluffs and have a quick way to estimate
how often they need to fold when you’re at the table. As you
work with more of these, you'll get very quick at this.
I would do this quickly by thinking about what 10% of $200 is and
then multiplying that times 3.
(Answers on pg. 188)
Assume villain always has us covered. Use estimations to
answer the following questions.
1. Hero: 3
Pot was $10. We shove $20. How often does villain
have to fold?
Pot was $10. We shove $30. How often does villain
have to fold?
Pot was $10. We shove $24. How often does villain
have to fold?
Fold - 89, 99, TT
Call - AJ, J9, 33
Pot was $10. We shove $25. Is a shove profitable?
Value-betting is one of the most important skills in poker. The
term itself is a little bit tricky because we’re always thinking of
value when we’re betting. The reason we bluff is because we
believe it has more value than not bluffing. However, the term
value-betting is reserved for betting when we believe we have
the best hand. We’re trying to extract as much value as we can
when we actually have the goods.
There are common misconceptions about value-betting I’d like
to address. Often times I hear players say “I want worse hands
to call.” Or they say “I’m trying to not lose my customer.” It’s
important to realize that when we’re betting for value, we’re still
executing the second key to good poker. The goal is to
maximize value. Sometimes we maximize value by getting
small, steady payouts and other times we maximize value by
getting the infrequent, big payoff. Let’s use an extreme example
to see this at work.
Call up to $8 – A9, A2, AJ, AQ, K
Call all-in for $500 - K
We’ll pretend that villain has $500 left on the river. The villain
will never raise any of our bets; he’ll call with his entire range.
However, he’ll only call up to $8 with his entire range. But with
his flush, he’ll put the rest of his money in the pot. So, we’ll say
we can only make either an $8 bet or a $500 bet. Notice the
villain has 29 combinations in his range. His flush hand is only
one combination, which represents about 3.5% of his total range.
His pair hands represent 96.5% of his range. If our goal is to not
lose a customer, it’s obvious which bet size we should make. If
we bet $8, we keep our customer every time. Also, if our goal is
to get worse hands to call, we get them all to call with the $8 bet.
However, let’s examine the EV of both of these bets.
The $8 bet gets called 100% of the time, so, the EV of the $8 bet
$8(1) = $8
The $500 bet only gets called about 3.5% of the time.
$500(.035) = $17.50
The EV of the $500 bet is $17.50. This is more than double the
EV of the $8 bet even though it’s getting called much less often.
So, in this extreme example, we are better off going for that big
Now let’s tweak the example a bit. We’ll give the villain $100
left. Now look at our EV of a $100 bet.
$100(0.035) = $3.50
Here the EV of the $8 bet is more than double the big payoff.
So, when he has $100 left, we’re better off going for the small,
steady payout. But, not every example is this cut and dry.
Much like choosing your bluff sizes, choosing your value bet
sizes can be tricky business. The best way to improve is through
analyzing situations away from the table and getting used to
common situations. That way you can quickly recognize those
situations when you come across them and will know what to do.
Now, let’s say villain will always raise with his flush, but still
will always call with his pairs. His raise will be an all-in raise,
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