Re: Running It Twice and Insurance
running it twice reduces variance. The odds are the same each time, you just smooth out the results a little bit. It is most desirable if you are playing over your head and the suck out would ruin you.
Expand the concept, say you can run it a million times. With pocket kings against AQ, you're going to lose about 28% of the time. If you run it once, you'll either lose the whole pot or win the whole pot. If you run it a million times, you'll win ~72% of the pot, period. Running it twice doesn't get you this close to the average, but it will smooth it out some.
Insurance is a similar concept where you get $X to end the hand right there. In the above example, you know you should average 72% of the pot, but on this particular hand, you could lose the whole thing. Instead, the house pays you 65% of the pot hand and it is over. You are happy because you didn't bust out and got some profit that is close to what you deserved in the hand, whereas the house is happy because they gain 7% equity right there, and can take a high volume of these bets to guarantee themselves profit.
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