Re: [ba-poker] tournament alternates

[Jeffrey Siegal <jbs(deleted the rest)>]

Nick Christenson wrote:
> > 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.

Okay, it is easy to argue anything, but it isn't so easy to demonstrate 
that your argument is valid in this case.

> 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.

It is true that equity in this case at least usually flows to the middle 
stack (actually, equity can flow to the non-participating stack 
regardless of who wins the confrontation, for example if the small stack 
busts near the money, although the amount of equity shift may vary 
depending on the situation) but that doesn't necessarily mean that chips 
in a middle stack are then worth more than par.

It could be that in a particular chip distribution, all the "extra" 
equity is held by the small stacks, and both big stacks (with a big 
equity deficit) and middle stacks (with a smaller but still positive 
equity deficit) are worth less than par. If this is the case, and if a 
late entrant comes in with a middle stack, then he is doing so at his 
own expense.

In practice I believe the nonlinearity of chip equity early in any real 
tournament (and especially any WSOP tournament, and especially 
especially the WSOP final) to be negligable, and therefore late entries 
are not unfair to any meaningful extent.  That's not a proof, of course. 
 If you want to try to prove my belief incorrect, go right ahead.