Raising as a Means of Cutting Down Opponents' Odds

To illustrate this important point, we'll examine a hand
from five card draw poker. You have a pat flush; the player to your right has
nothing at all, and the player to your left has two pair. For the purposes of
this illustration, we'll assume you know exactly what both opponents have.
We'll also assume the betting limit is a flat $10 but that somehow a $100 pot
has been created before betting gets under way. With the cards out, we'll say
the chances of the two pair improving to a full house are 9-to-1 against. In
other words, the player behind you will improve to the best hand one out of ten
times on average.

With absolutely nothing, the player to your right bets $10 in an attempt to
steal that big pot. You know this player will fold instantly if you raise, and
you are fairly sure the player behind you will fold too. However, if you just
call the $10, the player behind you will also call. Consequently, you may win
$120 plus perhaps another bet at the end if you call, whereas if you raise
you'll most likely have to make do with the $110 already in the pot. Should you
call or raise?

The answer, of course, is you should raise, but let's look at the problem
logically. The opponent with two pair is a 9-to-1 underdog. If you call, there
is $120 in the pot. He would be getting 12-to-1 from the pot for his call when
the odds against his making the best hand are only 9-to-1. Therefore, if you
call and he calls behind you, he is making the correct play, the play with
positive expectation. He will lose $10 in nine hands out of ten on average, for
a total loss of $90, but he will win $120 in one hand out of ten for a net
profit of $30. He gains on the play, and according to the Fundamental Theorem
of Online Poker Games, any time your opponent gains, you are costing yourself
money.

On the other hand, when you raise, making it $20 for the two pair to call, you
are cutting that player's pot odds from $120-to$10, or 12-to-1, to $130-to-$20,
or 6 1/2-to-1. Since the two pair is a 9-to-1 underdog and is now getting only
6 1/2-to-1 from the pot, you have made it correct for the two pair to fold. If
he plays correctly and does fold, you do better, as we shall see presently,
than if you had played incorrectly and allowed him sufficient odds for a call.
However, if the two pair plays incorrectly and calls after you raise, you do
best of all, because when an opponent makes a mistake, you gain. What your
raise did was to reduce correct odds for a call into incorrect odds for a call.
The curious effect of this turnabout is that although you raised to drive the
two pair out, you are rooting for him to call after you raise.

To prove this point, let's see what happend over ten average hands if

1. You call, and the two pair calls behind you.

2. You raise, and the two pair folds.

3. You raise, and the two pair calls your raise.

If you call and the two pair calls, you
will win nine out of ten hands. Assuming you check after the draw and don't pay
your opponent off the one time he makes a full house, you will win $120 (the
$110 already in the pot - not counting your own $10 call - plus the two pair's
$10 call) nine times for a total of $1,080, and you will lose $10 once. Your
net profit is $1,070.

If you raise and the two pair folds, you will win all ten hands, which at $110
per hand comes to $1,100. You win $30 more than you would if you called and the
two pair overcalled.

If you raise and the two pair calls, you win $130 (the $110 already in the pot
plus the two pair's $20 call of a double bet) nine times for a total of $1,170
and lose $20 once for a net profit of $1,150. You win $80 more than you do when
you call and the two pair overcalls and $50 more than when you raise and your
opponent folds.

Taking the $1,100 profit as the norm (since both you and your opponent play
correctly in that case), we can say you lose $30 over ten hands or $3 per hand
when you play incorrectly and only call, and you win $50 over ten hands or $5
per hand when your opponent plays incorrectly and calls your raise. To repeat,
when you raise to drive people out, you are actually raising to cut down their
odds. If they fold, that's fine, but sometimes you have cut their odds to a
point where you are rooting for them to call after you raise. In no-limit games
you can control the odds you are giving your opponents by the amount you bet,
and you frequently find yourself rooting for them to call your raise even
though you would be rooting for them to fold if you had just called.

Of course, it is correct just to call, when you know your opponent will fold if
you raise but would make a mistake by overcalling if he knew what your cards
were. You want to give your opponent every opportunity to make a mistake since
that mistake is your gain even if he happens to get lucky and win an individual
hand because of that mistake. In poker as in any games of skill with an element
of chance, you cannot play results. That is, you cannot judge the value of a
play because of the way it works out in a specific instance. In backgammon, for
example, it's possible for a player to make a mistake or a series of mistakes
that results in a hopeless position from which he can extricate himself only by
rolling double six. The odds against rolling a double six are 35-to1. If the
hapless player happens to roll that double six and go on to victory, you cannot
say he played the games correctly anymore than you can say a person who puts
his money on number 20 on the roulette layout plays correctly when number 20
happens to come up. Both players were just very, very lucky.

To remember, when you raise to drive people out, you are really cutting down
their odds. So you should raise with what you think is the best hand only when opponents
are getting good enough odds to overcall or when you think an opponent will
call a double bet even though he shouldn't even call a single bet.

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