[DcifrThs]

[ QUOTE ]
[ QUOTE ]
Yeah it's pretty definitive to say this WILL happen after 8748 hands. What does this mean?

[/ QUOTE ]

That is the number of hands for which being 3 standard deviations below the average win would be the biggest loss in dollars. You could be 3 SDs below average at some time before this number of hands, but since the SD would be smaller, that would be a smaller loss in dollars. You could be 3 SDs below average at some time after this number of hands, and 3 SDs would then be a larger number of dollars, but then your average win would be a larger positive number, so again that would be a smaller loss in dollars. Notice that you can have negative swings much greater than the size of your initial bankroll, but by the time they occur, your bankroll will have grown to a larger value, and you will absorb them without going broke.

The number of hands for which the 3 SD loss is a maximum is found by taking a derivative of your loss and setting it equal to zero. You could be down more dollars than this after some other number of hands, but that would necessarily correspond to a greater number of standard deviations, and hence it is less likely.

The fallacy which many people make, and which is made in GTAOT, is taking the size of this maximum 3 SD loss as the required bankroll for a 3 SD = 0.13% risk of ruin. This is false because it assumes that if you go negative before you get to this magic number of hands, that you will still be able to keep playing until you get to that number of hands, and it then simply looks at the whether or not the bankroll is positive at the end of this period. In a proper risk of ruin analysis, if you go broke before this number of hands, that counts as ruin, and it can be shown that this will always happen at least twice the frequency of the probability of being broke at the end of the period. So if we are using 3 SD = 0.13%, there must be greater than a 0.26% probability that we never reach the magic number of hands, and in fact in this specific case, that probability is actually closer to 1%. You can also go broke after this magic number of hands, and this is also not taken into account by the fallacious analysis. This is why the 5% risk of ruin numbers in GTAOT would actually produce a 26% risk of ruin. The correct bankroll formulas, which I've linked to, are not derived in this simplistic way, but are rather based on a random walk model, so they do not have this problem.

[/ QUOTE ]

DS is a self proclaimed potential nobel laureette (sp?)...wouldn't he proofread the concepts and the formula presented in mason's book?

-Barron