Part Two를 병신같이 해석하고 가서 뭔가 찜찜한 기분은 있지만

내능력 밖이라 제외

Post-flop Bet Sizing at a Glance

Although bet sizing is too complex of a concept to confine to a single chapter, we should first make sure to understand the basic mathematics behind it before moving onto postflop play.

베팅 사이징이라는 개념이 한 개의 챕터에 설명하긴 복잡한 개념이지만, 포스트플랖 플레이 챕터로 넘어가기 전에 기초적인 수학적 방법으로서 확실히 이해해야만 한다.

That's because bet sizing is extremely important in no-limit hold'em, and what often separates a great player from merely a good one is how he uses different bet sizes in different situations to manipulate his opponent's range.

NLHE에서 베팅 사이징이라는 것은 굉장히 중요하고,

Specifically, an excellent bet size can force our opponent to make tough decisions and maximizes the expected value of the bettor's hand.
In theory, if a player has a perfectly polarized range which includes hands of either 100
percent equity (the pure nuts) or 0 percent equity (pure air), he will choose his bet sizing
so that he갽s betting an equal fraction of the pot on all three streets and is all in by the
river. A formal proof of the mathematics behind this will not be shown here, but it was
solved for in The Mathematics of Poker by Bill Chen and Jerrod Ankenman. So it갽s
important to understand that a player with a completely polarized range will use this bet
sizing structure to get all the money in by the river to maximize his earnings.
Final pot-size = (Starting pot-size)(Pot growth rate)(Streets Remaining)
Let갽s see how this formula works. Suppose it갽s blind versus blind and we갽ll assume on
the flop that the small blind has a range which includes only hands with either 100
percent or 0 percent equity. For a 3.5 big blind open, the starting pot-size on the flop will
be 7 big blinds, the final pot-size will be 200 big blinds, and there are three streets
remaining. This reduces the following pot growth rate equation
where
7 is the starting pot size,
200 is the final pot size, and
R is the pot growth rate.
This implies that the pot growth rate is 3.06.
Therefore, the pot should increase to 3.06 times its size with each passing street. This
means we must bet 1.03 pot-sized bets on the flop, turn, and river to get all the money in
by the river.
where
SPS is the starting pot size.
And for this example, we should bet 7.2 big blinds on the flop, 22.0 big blinds on the
turn, and 68.1 big blinds on the river to get all the money in.
Since these perfectly polarized ranges do exist, understanding optimal bet sizing for
them is important, but the vast majority of the time a betting range will not be perfectly
polarized. Usually, our opponent will have some hands in his range which either already
beat our value hands or can outdraw us, and likewise, our bluffs will usually be capable
of improving to a strong hand. So when this is the case, betting an equal fraction of the
pot on each street will not usually be ideal.
Stated another way, when our opponent has several hands in his range stronger than some
of our value betting hands, we갽ll only occasionally want to get all the money in by the
river. That갽s because our large bet sizing on each street will encourage our opponent to
fold all but his strongest hands by the river. That is, whenever we value bet each street
only to discover that our opponent has called us down with a better hand, we갽ll lose a
large pot. This is one reason why in single raised pots with 100 big blind stacks, the
majority of the time we will not bet big enough to try to get all the money in by the river.
However, there are other situations we may still want to bet even if our opponent has few
medium strength hands in his range. This will frequently happen if, when in position, we
call one of our opponent갽s bets and he checks to us on a later street that did not improve
any hands in his range. We may want to bet in an attempt to win the hand right there.
To illustrate this concept, suppose our opponent opens in the cutoff and we call on the
button. He continuation bets the
flop and then checks to us when the 2. comes on the turn. While our opponent may have
some marginal hands in his range, such as tens and nines, the majority of his range
should be weak. Therefore, a small bet should prevent him from seeing a free river card
with his weak hands. And because it갽s small, it should also minimize the effectiveness of
any potential check-raise whereas betting large makes a turn check-raise more effective
and allows him to defend less of his turn checking range.
When our strong hands are susceptible to being outdrawn on later streets, we may choose
to use a descending bet sizing structure. That is, by betting bigger on earlier streets, we
make sure our opponent puts more money into the pot when he갽s behind if he wants to
try to outdraw us. Nevertheless, there are still limits on how big our bet sizing can be
since very large bets are punished harshly when our opponent does have a hand which
already is better than ours.
Here갽s an example. We open in the cutoff with the J.T. and only the button calls. The
flop is the T.7.4. and the turn is the 2., Since we have top pair, we may decide to bet a
larger fraction of the pot on the flop than on the turn. Despite our hand not being
especially strong, by betting larger on the flop, we make our opponent fold some
overcard hands with over 25 percent equity. However, his implied odds and equity will
have decreased on a low turn card, and by betting small, on the turn, we hopefully end
the hand here, but if he does call, his range still should not be too strong on the river.
And when we go ahead and bet the river, our bet will often be small (after betting the
turn). Our opponent has no additional implied odds and we갽re not worried about being
outdrawn with his weak hands. In fact, as will be shown in future chapters, when out of
position on the river, there is not much difference between betting small and checking.
So while deciding what bet size is best in a given situation will often be quite difficult,
we should always remember the most important underlying concepts. Large bets, on
average, require our opponent to defend less frequently and put more money into the pot
while small bets require him to defend more. But small bets also require the bettor to be
bluffing less since the defender is getting a better price. Therefore, the choice will often
be between betting small and giving our opponent a good price when he갽ll call with a
wide weak range or betting big so he gets a worse price and calls with a strong range.
A common misconception players have is the belief that they need to have one specific
bet sizing with their entire range in each particular spot. This is not the case. It갽s possible
to have several different bet sizings in the same spot where each range is balanced.
Furthermore, a player who is capable of using multiple bet sizings will have a significant
edge on someone who restricts himself to only a single sizing.
This idea of using multiple bet sizes in the same spot to manipulate our opponent갽s range
is usually theoretically correct and extremely important in many spots. For instance, if,
on the river, the pot is 80 big blinds and we have 100 big blinds remaining, our bet with
one range could be for the whole 100 big blinds, 60 big blinds with another range, and 40
big blinds with a third range. Each of these ranges could be perfectly balanced and
designed to manipulate our opponent갽s calling range in the way that best fits our
purpose.
We should now have a strong enough understanding of the theory behind bet sizing to
proceed to post-flop play. And as bet sizing is discussed in more detail, we갽ll learn how
to recognize when certain bet sizings make sense. Thus, we갽ll be able to exploit weak
opponents who use senseless bet sizings while preventing strong opponent갽s from
exploiting us.
Summary
Although excellent bet sizing is one of the most difficult skills to master, it갽s critical for
success against tough opponents. Specifically, betting the right size manipulates our
opponent갽s calling range to get calls from weaker hands but still make some high equity
hands folds. While we have only scratched the surface of this topic, by understanding
who has the polarized range and what our bets are designed to accomplish, the
foundation has been laid for developing precise bets in future chapters.
Here are some of the important points:
1. Betting equal fractions of the pot on all three streets in order to get all the money in on
the river maximizes our winnings when our range consists of the pure nuts and pure
air.
2. Small bets are often effective against polarized ranges. They prevent our opponent
from getting to see free cards with his weak hands while minimizing the effectiveness
of his raises.
3. A descending bet sizing structure is effective when we likely have the best hand and
do not want to cheaply give our opponent additional cards.
4. Small bets keep our opponent갽s calling range wide and weak, while large bets make
his calling range narrow and strong.
5. It갽s not true that we should only have one bet sizing in a given spot with our entire
range.