[AleoMagus]

[ QUOTE ]
in general your standard deviation goes down relative to other things if you play more.


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I'm not sure this is really that much of a problem

Consider two players A and B who both play $11 SNGs
A has a 30% ROI and a SD of ~$18.50/t
B has a 3% ROI and a SD of ~$18.50/t

per SNG, if we define this metric as SD/profit:

A would have a value of 6.16
B would have a value of 61.6

this means that compared to one another B would perceive ten times the swings.

After 100 SNGs,

A would have a SD/100t of $185 and a profit/100 of $330
B would have a SD/100t of $185 and a profit/100 of $33

per 100 SNGs then, continuing to define this metric as SD/profit

A would have a value of $185/330 or 0.56
B would have a value of $185/33 or 5.6

So, compared to each other, B still experiences swings ten times as big relative to his bankroll growth. Over 100 SNGs however, they both experience much smaller swings relative to expected growth than they do over a single SNG. This all makes sense to me.

After all, if player A runs badly, he will recover much more quickly, and may even continue to show a profit. If player B runs badly, he will take much longer to recover and will almost certainly show a loss. The reason why the values for 'swings' are much lower in the 100 SNG case is that we are treating a 100 SNG sample as a single unit, and obviously when dealing with these units, swings will be much smaller. When dealing with 100 SNG samples, this metric is lower for the very reasons that you earlier mentioned. SD does not increase linearly, whereas profit does.

As far as wildly different 'swing' values based on differing amounts of games, the solution is just to use the single unit value, much as we do with SD. After all, SD is wildly different as well when we consider differing samples, and we know how to deal with that.

I haven't yet compared this to your suggested metric for takling about swings, so I guess I'll take a closer look at it now, and post again when I can see if there is an advantage to using it. If I am missing something, let me know.

Regards
Brad S

PS - for anyone wondering what these 'swing' values mean, it is just the multiple of your expected profit that you may be up or down from your expectation over the sample.

ie - with a swing value of 61, if you run 1 SD bad, it will on average take you 61 tourneys to recover (return to that expectation). similarly for larger samples