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 happens 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.
