Jeff sez:
This limiting case is never the way it is done in any real tournament.
Perhaps that's too bad.
The only rule like this I've ever seen is that you can come in with
all
the starting chips, but only during a limited time window (first hour,
during rebuy period, etc.). Its much harder to argue that this is
unfair.
I disagree. It is easy to argue that this is unfair. In fact, it is
clearly unfair, although the amount of "unfairness" may not be much.
It may be that one hour for many tournament structures isn't a big
deal.
For some it certainly would be, though, and I'd object to some
tournaments
that adopted this format.
If I am allowed to buy in to a tournament and enter the game itself as
late as I want with all my starting stack, then clearly I would choose
to do so at the final table. This is clearly +EV and unfair unless the
tournament is winner-take-all, in which case it's quite fair. While
this
is a reasonable argument in favor of winner-take-all tournaments,
that's
not an argument I want to make here.
As we all know, in a proportional-pay tournament, the average value
of each chip in a small stack is worth more than the average value of
each chip in a large stack. This is because having one chip can win
you
second place money. Moreover, the value of each chip increases the
more
people bust out. In fact, as the chips get unevenly distributed even
if
nobody busts out, the "middle-sized stacks" gain in equity against the
big
and little stacks.
This can be seen most obviously when a proportional-pay tournament gets
3-handed. If the small stack loses a big hand to the big stack (even
if
he doesn't bust out), the total number of chips in play remains the
same, but the chips the short stack lost are each more valuable than
the
chips the large stack won, and the extra equity has to go somewhere, so
it "flows" to the middle-sized stack.
To a much lesser extent, if I can enter a tournament with T100 after
half of the players have dropped to T50 and the other half are sitting
at T150, it is definitely in my advantage to do so, although that
advantage
may not amount to much. My ability to buy-in without giving anything
up at this point net's me EV at a cost to the field, thus it is
*clearly*
unfair. QED
Let's pretend there will be a tournament where I don't think I can
*massively* outplay the field and where every entrant gets T1000 in
chips to start. Let's say I have two opportunities to buy in, once
at the beginning of the tournament, and once later on (say, after the
end of the first two rounds). Let's also say that in either case I
would get to start with T1000 in chips. Given this opportunity, I'm
going to strongly prefer to enter the tournament as late as possible,
even
though that might leave me short stacked. I still gain in equity by
deferring my entry, letting the stack sizes get "choppy", and letting
some other people bust out.
Now, it's quite clear that if my entry into the tournament is deferred
by 1 hand, my added edge is negligible, so allowing this to happen is
really no big deal, and I certainly wouldn't object to this happening.
At some point, and I don't know precisely where, the edge gained by
deferring entry becomes non-fractional percentage point returns on my
equity, and at that point, a late entry is clearly unfair.
Someone may argue that this point doesn't occur until very late in a
tournament, and you might be right. But, before I accept that I'd like
to see the math, as I don't know where this might occur. Until someone
has a good model demonstrating that this point comes quite late in a
tournament, I will prefer it if players can't enter tournaments late
with
their full stacks. If they want to enter late, fine, but blind them
off.
--
Nick Christenson
npc(deleted the rest)