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So there are five loose limpers and you have ATs on the button. Against six random hands (assume the big blind comes along), ATs wins 23.5% of the time (from gocee.com). Your "share" is 1/7 or 14.3%. Thus, ATs wins approximately 23.5 - 14.3 = 9.2% "more than its share." Raising nets you 9.2% of all the post-raise action (in this case, one bet for each player, or seven bets), so failing to raise costs you about 0.092*7 = 0.644 bets or about $1.30 in our $2-$4 game. Now that's obviously just an estimate... real poker isn't played hot and cold. But that $1.30 number is WAY bigger than the numbers we got for the other errors, so we can conclude that failing to raise ATs in that spot is almost certainly a bigger error than the others.
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Your estimates are off by quite a bit here.
1st, you assume using random hands will be close enough, well I checked out my old pokertracker hands from 2-4 to get an idea of what hands we could safely eliminate these hands were 72o 84o KK AK etc. I then ran a simulation(5M hands) ATs vs random hands not including these hands and ATs only won 18% of the time and tied 3.4% (against all random hands I got 22.2% wins and 2.8% ties), so the actually % is closer to 19.7% not 23.5%
2nd, there is a 35% chance there will be a flop that you will not continue with so what % of the time you fold would you have actually won the hand? running simulations I got a rough estimate of 3% so 3% x 35% = 1% of your wins will happen when your hand is mucked. We are now down to 18.7%
3rd, Why are you including your bet when you calculate the value of the raise? I think it should've been 9.2% x 6 opponents
4th, there is that small possibility one of the early limpers has a monster and reraises, its insignificant so I wont include it.
Anyway the actual amount you are losing by not raising in this situation is closer to 18.7% - 14.3% = 4.4%x6 = .264x2 = .528
.528 is quite a ways from 1.30 doesnt seem very important but if you made a mistake like this where the actual value is -.2 and you claim +.572 that would cost a few players a few cents.
On top of all this you lose post flop because your ability to outplay your opponents is lost, its now difficult for a calling station to make a mistake. You also make it really difficult on yourself what if the flop comes 3h4hTc you have AsTs and someone bets a few callers do you call? raise? fold? turn is a Kc how do you continue?
Whats the optimal way to play a game where every hand is capped and every player sees every flop? Is it to play every hand you win your fair share with?
Im sure theres just a very small peice about this in your book if anything at all since its a situation you wont see too often, but I have a feeling your book will have quite a few flaws, this is lees oportunity I hope you 2 can debate some of these topics without it turning into this
http://forumserver.twoplustwo.com/sh...art=1&vc=1
That said im looking forward to reading your book Ive never read a book specifically for small stakes/loose games before.