Somebody (Foolsgold?) asked about the ICM (Independent Chip Model) a
while ago. At some point I want to understand how it works, to see if I
believe in it, but I've been having a play with it, and it got me thinking about
a few things.
Here's what it does:
You tell it the current chip counts in a STT and the prize structure, and it
gives you an estimate of how much each player will win on average. There's
a well-known phenomenon that in a tournament that is not winner-takes-all,
each chip you win is worth less than the last one, so your expected prize
money is not proportional to your chip count, and the ICM tries to give a
quantitative idea of what the effect is.
There are lots of things it doesn't take into account, such as differing
abilities of players, blind levels, rate of increase of blinds, etc.
In a STT with $50/$30/$20 prizes, if there are four players left with an
equal number of chips, then of course it tells you that they'll all win $25
on average.
But if there are three players left, and one has twice as many chips as the
other two, it tells you that the chip leader expects to win $38.33, and the
other two expect to win $30.83.
If these figures are close to accurate, then this has implications for all-in
confrontations. If there are four players left with roughly equal chip counts
and you get into an all-in encounter with another player, then for this to
increase your expected prize money you need to win more than 65% of the
time. If you win 65% of the time, your expected winnings decrease from
$25 to 0.65 * $38.33 = $24.91.
But if he's a muppet calling your all-in bet, then you're presumably better
off with him still in the game than the figures suggest, as they don't take
into account differing abilities. So you probably actually need more than a
2/3 probability of winning: if you go all-in, then you don't want him to call
unless you're
more than a 2-1 favourite. This doesn't mean that he's right
to call if he's a 3-2 underdog, of course. If he does that, it's not him that's
benefitting, it's the other two players at the table.
I knew that you don't want to get into an all-in confrontation in a
tournament unless you're a clear favourite, but I was a bit surprised by
quite how clear a favourite these figures say you have to be.
Maybe this has implications for playing low buy-in STTs against muppets
who'll call with trash? Maybe it means that it's right to try really hard to
avoid confrontations with these people unless you're a very clear favourite?
If anybody wants to play with the ICM, there's a calculator at
http://sharnett.bol.ucla.edu/ICM/ICM.html