Rob Singer wrote:
Continue doing the math. You toss one kicker. Where's it written
that you won't still get four Aces with a kicker? No one's said
holding AAA w/kicker isn't the mathematically best play. It just
doesn't make sense to hold the 2, 3, or 4 when we don't give that
game our life-long play. And because it's not a positive game, who
plays it all the time anyway?
Rob, I think you know I don't dismiss your strategies out of hand. A
key aspect that has some utility value is that they produce a larger
proportion of winning sessions. As someone who's suffered a
disproportionate amount of losing trips this last year I'm hardly
going to overlook the appeal and satisfaction inherent in that.
However, justifications of a sub-optimal play on the basis of a
"life-long play" requirement hold no water with me. There are two
problems here.
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First, this argument always seems to suggest that in short to medium
term that you bear a very strong likelihood of coming up short in EV
on the play. That's simply not the case.
A longer term play simply involves less certainty that on any given
shot you'll hit. Therefore, it takes longer play than other shots
before you have confidence your results will fall close to the EV of
the play. However, typically you bear nearly the same chance of
exceeding EV in the shorter run as you do of falling short. In other
words, it's a bigger gamble. (OH MY GOD, A GAMBLE??!!) Just as with
any game, if you don't possess the bankroll (or stomach) to bear the
risk of the best hold then you probably shouldn't be playing the game.
Second, the suggestion that "life-long play" is required to come close
to EV is a fallacy in most cases. The TDB quad Aces w/kicker cycle is
tremendously shorter than that of a RF (about 1/3 the length). It
isn't going to take exceedingly long at all before the high cost of
discarding a kicker when dealt trip Aces is very likely to catch up
with you.
Now, granted, because of the volatility of the game there are damn few
players who'll sit down at a machine and bang away for 8 hours or so
trip after trip. But anyone who discards the kicker in this case
probably opts for sub-optimal holds in a number of other games under
the same argument. In aggregate, that adds up to a lot of play and
the probability that a player incurs an overall loss relative to the
best plays becomes very strong.
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Now, I know the "long term play" arguments against optimal play (I
wish people would drop the term perfect play, as if there had been a
suggestion the game is only fit for the gods) aren't going to go away,
so I'd best learn to grin and bear them -- as well as some of the
other discussion that has me gritting my teeth these days.
But I'd dearly love to see a greater focus on the raw fundamentals of
play that have a sound basis in the realities of the game.
- Harry