Minimum R.F.I.

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Minimum R.F.I.

It's quite easy to show that if the utility value of chips is zero, then in games with a big blind the strategy of raising first-in should dominate the strategy of calling first-in.  However, I'm not sure how to derive the minimum raise first-in for each position. 

Can somebody who actually knows what they're doing help me out?

The best argument I have so far is modelling the UTG (for example) as follows:

At a six-handed table, one Orbit is 6 hands.  We are paying 1.5 BBs/Orbit to stay in the game.  Therefore,  we are paying the following quantity per hand to stay in the game:

1.5BB/6 = .25 BB

This is the amount per hand that we would lose if we folded every hand (from each position). 

We are effectively paying an "ante" of .25 BB/hand for a six-handed game, and so if we are playing raise-or-fold (which it seems like we should be), then we must attempt to win the blinds with a raise the following percentage of the time to break-even:

X (1.5)  + (1-X)(-.25) = 0 <==> X = .14285 or 14.285%


With this simplified pre-flop model, we get a minimum R.F.I. of 14.2% from UTG.  Does anybody more well-versed in game theory have a way to improve upon this model?  There seem to be a bunch of ways to tackle this problem, each depending on the assumptions you want to make and the way you want to model it. 

Using this model gives us an increasing R.F.I. as we progress through each position.  It seems reasonable on that front.

The main question I have is whether or not it's reasonable to actually treat the blinds as "antes" in this way.  It seems so, but I could be convinced otherwise. 



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