by **kraada** » Mon Dec 22, 2008 11:22 am

Primo,

There aren't going to be that many instances of this stat if you're playing at full ring. At 6-max it should certainly happen more than 1/1000 hands, but at full ring I'm not so sure.

You're only in the blinds 2/9 of the time. Assume that on average each player from UTG to the HJ raises 10% of his hands (The HJ obviously raises more, but for the simplification of the math, let's start here) . So 10% of the time, UTG raises his hand and we don't have a steal attempt (which leaves us with 90% of hands), UTG+1 raises 10% if UTG folds (leaving us with 81% of hands) continuing this, that only leaves us with 59% of hands that make it to the CO. Let's assume stealing ranges of 30%. So 17.7% of the time overall the CO steals, and 17.7% of the time the button steals.

Now, if you're in the BB and the CO steals the button or sb can play too then you don't have a blind defense opportunity. Let say they play the top 10% of their hands.

So 14.33% of the time we have a blind defense opportunity from the BB, and from the SB you have a blind defense opportunity 15.93% of the time.

So we're already down to just 3.36% of total hands where you have a blind defense opportunity. So our 50k hand player will have about 1679 blind defense opportunities.

Now, of those 1679 blind defense opportunities how many times is he calling? Say it's 15% of his hands (he reraises the top 5% and folds the bottom 80%). So now we see a flop just 252 times. Say hero donkbets sometimes, make it 20%. Now there's just 201 times that the opponent can cbet. If he checks behind sometimes, we could easily expect to see only 175 or so times that he faced a bet in this exact spot even with a 50k hand sample.

That's why some of these stats take so long to converge, the setups are very intricate. Now, I made a whole heck of a lot of assumptions along the way, and it is possible there's something wrong that I don't see. Still, over a 50k hand sample, I'd be surprised to see more than 300 or 400 opportunities for him. Also, this table never limps in EP or MP. If there's an EP/MP limp that removes a chance to steal. That could easily drop the 175 times estimate even further depending on how often people limp. If the limpers take out a little more than 1/3 of the steal opportunities we're down to just 100 opportunities right there . . .