Re: [ba-poker] tournament alternates

[Nick Christenson <npc(deleted the rest)>]

> >  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.  
> 
> I don't agree with this. I think that there is no special advantage
> to being middle-sized. 

Here's another way to frame this issue.  Let's imagine there are three
stacks left in a proportional-pay tournament, one has 10 chips, one has 
100 chips, and one has 190 chips.  These have not yet been assigned to 
anyone.  Which would you rather choose, the middle stack or a coin toss
for either the large or small stack.  My statement is that you're better
off choosing the middle stack.  Reasons below.

> The smaller your stack, the greater your
> ratio of equity to stack size.

Yes.

> So I don't see any justification for your claim
> that the middle-sized stacks gain in equity against the big and little
> stacks.

Okay, let's imagine this scenario.  Let's imagine that we have three
players left in a proportional-pay tournament, A, B, and C.  Let us also
assume that right now they all have 10 chips.  If I'm A, let's imagine
a scenario where I get to decide whether B and C would go all-in against
each other or not.  Clearly, I'd choose for them to do so.  Before they
do so, my equity is (1st place + 2nd place + 3rd place)/3.  After, I'm 
assured of 2nd place money and have a chance at first, although I'm a dog 
to the remaining bigger stack.  In fact, my equity is (2nd place + 1st 
place/3).  For a 40%/20%/10% distribution, I've gained 10% in equity.

Now, let's imagine that instead of them being all-in against each other,
I had the option of choosing whether they play for 9 chips (each) against
each other, such that the stacks at the end of the battle would be 10 (for
me), and 19 and 1 for B and C.  Should I elect to have them make this 
contest?  Again, the answer is, "yes".  The 1 chip stack is very weak, 
and will have to play a hand Real Soon Now for everything, such that they're
roughly 50/50 to double up or go bust.  While I don't have 2nd place sewn 
up, I have a strong grasp of it, and I have a *much* better shot at getting 
first from the big stack (10/29 odds) than I do of losing 2nd to the short 
stack (1/11 odds).  I no longer have an increase of 10% of the prize pool,
but I've gained significant equity.

So I want these stacks to become unbalanced like this.  Since that's the
case, this scenario must be good for the middle stack at the expense of
the other two stacks (collectively).  The middle stack has gained equity
as his two opponents have moved their stack sizes to the edge.

-- 
Nick Christenson
npc(deleted the rest)