[Ed Miller]

I don't plan to address (or read) the whole long thread. I did want to discuss this idea, though:

VERY RARE, VERY SLIM +EV SITUATIONS ARE NOT PROFITABLE, BECAUSE OF THE LIKELYHOOD THAT WE WILL NOT SEE THEM ENOUGH TIMES DURING OUR POKER LIFETIMES FOR THE NUMBERS TO NORMALIZE.

This notion is 100% erroneous. How often you are offered a bet does not determine in any way whether it is profitable or not.

To prove this to yourself, you can view any set of bets as a single bet with many possible outcomes. For instance, say you flip a coin three times. For each time it comes heads, you win $1. Each time it comes tails, you lose a $1.

Instead of looking at it as three different bets, you can view it as a single bet with eight possible outcomes. That is, if it comes HHH, you win $3. HHT, and you win $1. Etc. There is no difference in "profitability" whether you view it as a series of N independent "common" bets, or one "rare" bet with 2^N possible outcomes.

Likewise, your bankroll doesn't care what game you are playing, or what situation came up. All it cares is that you made a bet with an EV of +$X/wager with a std. dev. of $Y/wager. It doesn't care if that wager was made at faro or tiddle-e-winks.

Hell, if it were true that "rareness" makes bets unprofitable, then no one would ever win at sports betting. After all, each game is completely unique. You will NEVER have another opportunity to bet on last week's Dolphins game.

Finally, you guys are way too worried in general about the relationship between EV and variance in limit poker. While it is extremely important that you avoid overbetting your bankroll on thin edges in sports, blackjack, or the stock market, you just don't have to worry about it at limit poker (obviously, provided you have a bankroll of a few hundred bets). As has been pointed out, the opportunity to make these super thin wagers just doesn't come up often enough to worry about it. The large majority of you guys will end up doing much better in the long run if you simply IGNORE THE WHOLE THING and make any play if you think it is +EV. Again, this recommendation is only for playing limit poker with a bankroll of several hundred bets. (If you want to learn more about the relationship between EV, variance, and bankroll, google 'Kelly Criterion'.)

If you guys find yourself having negative swings of 400 or more bets it ISN'T because you are "pushing too many thin edges." It's because you don't play that well in general. You are making lots of -EV mistakes.

If you aren't having negative swings that large, then what are you worried about?