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You have AhAc.
Your opponent flips over 7c2s and raises preflop.
There are 3 small bets ($15 total) in the pot. But there's a catch. It will cost you $20,000 to
play your hand due to some vicious house rules. Should you call? Of course not. It does not
matter that your opponent makes $5 stealing your blind. Even though the opponent would
lose money if you played your pair of Aces (and thus maximizes profit when you fold), it is still
correct for you to fold because the only relevant point is that you lose much, much less
(minimizing your losses) by folding.
Conclusion: Don't worry about the odds of the preflop raiser. Your only concern is whether a
call or raise has positive expectation. We'll use some more examples to crystallize this
argument.
Example 2:
$3/6 heads-up game. Blinds $1/$3.
To steal, the small blind raises $5 to win $4.
Using simple arithmetic, we calculate that the preflop raiser needs to steal the blinds 55% of
the time to make an immediate profit, a considerable increase over the 50% needed in the
$10/20 game. If your goal was only to counter your opponent's strategy, you could call less
since you would only need to defend 45% of the time. Should you therefore play differently?
No. As a big blind, you're facing the exact same situation in both games.
In the $10/20 game, there is $30 in the pot, and you must call $10.
3:1 ratio.
In the $3/6 game, there is $9 in the pot, and you must call $3.
3:1 ratio.
Also note that the small blind is still raising 100% of the time, so his potential holdings have
not changed in frequency.
Example 3:
$10/20 3-handed game.
Blinds $5/10.
Again, we assume no reraising. Our assumptions are helpful to keep the playing field even in
our comparisons of heads-up and 3-handed games. The button is raising 100% of the time,
attempting to steal the blinds ($20 to win $15). Small blind folds. There is $35 in the pot, and
you must call $10. 3.5:1 ratio.
Sklansky and Malmuth suggest that since the small blind is also defending, the big blind needs
to call 70% as often as it would in a heads-up game. This advice is where I differ the most. As
big blind in a 3-handed game, you have better odds to call then you would in a heads-up game,
and with the small blind's cards in the muck, the proper play should clearly include more
calling, not less. Remember, the button is still raising 100% of the time, and even if you
assume the small blind is more likely to fold small cards, the distribution of cards that the
button is raising does not change much.
Calling from the Big Blind
So, how often should you be defending your blinds? To figure that out, we only need to
consider which hands are profitable to call. A reraise will affect how much profit will be won,
not whether the hand should be played. In other words, both raising and calling will have +EV,
but one play makes more profit than the alternative. After a certain point, raising becomes less
profitable than calling. At another point, calling will incur a loss, and the hand should be
folded. Last article, I argued for reraising with approximately the top 17% of all hands,
although that number depends on certain factors. Now, we will examine how many hands
should be called, again assuming that your big blind is raised 100% of the time. We will
examine three circumstances: heads-up, 3-handed, and heads-up when the big blind has
position.
Heads-up (Small blind has position.)
The irony of Sklansky and Malmuth's analysis is that even though the reasoning behind the
recommendation is imperfect, playing 40% of hands in the big blind is close to correct against
an opponent of equal skill. The exact number is impossible to discern, because it depends on
the skill of both you and your opponent. If you are a complete novice, but your opponent is a
novice also, the disadvantage of being out of position is lessened. If you are an expert, but your
opponent is also an expert, the disadvantage of being out of position is magnified.
My recommendation is to tend towards a tighter strategy for several reasons. First, the 40%+
strategy includes many marginal hands such as J8s, 97, 64s, and K3s. While these hands
appear to have sufficient pot odds, they also have two fundamental problems. They will not hit
any of the flop approximately 40-50% of the time and will give up on the flop. Also, when they
hit the flop with a pair, it will often be a very exposed position, susceptible to a well-timed
bluff or semibluff. Since so much of today's opposition relies heavily on bluffs and semibluffs,
hands that are exposed to these moves will pay a significant penalty after the flop.
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