Player A averages $50 a day over a 30 day period. Could be six months or year as well I suppose, it may or may not matter.

Then one day Player A wins $1000.

How many standard deviations above the mean is that? Can you show the math?

Thanks

Not enough info given.

Standard deviation is a measure of the "variability" or "spread" in the underlying data. In your example, the underlying data would be the amount Player A wins each day (positive or negative).

You can imagine an extreme scenario in which Player A wins between $45 and $55 every day. This would be a very "tight" distribution and the standard deviation in this case would be very small. So winning $1,000 in a day would be extremely unlikely and would be many standard deviations from the mean (average).

At the other extreme, you can imagine a scenario in which Player A wins between -$5,000 and +$5,000 every day with the average coming in at $50 a day. In the case the distribution of daily winnings would be very "wide" and the standard deviation in this case would be very large. So winning $1,000 in a day could be fairly likely and could be just a few standard deviations from the mean (average).

Bottom line: standard deviation needs the daily winning figures which were not given in your post.

OK, point taken.

Let's say Player A has average wins between -$100 and +$100 with an average of +$50 a day. Now he has a +$1000 day.

[Or conversely you could say something like: He has average wins of between -$200 and +100 for an average of +$50 a day. In other words, his losing days are larger on average than his winning days, but he wins much more than he loses.]

Is that enough info?

Sounds like the standard deviation is somewhere around $100.

So a $1,000 winning day would be (1,000-50)/100 = 9.5 standard deviations above the daily average winnings.

Thanks, I can work with this.

This doesn't seem right. 9.5 standard deviations is insane. There's no way this type of analysis provides a reasonable likelihood of a $1,000 winning day. It is far more likely that the underlying mechanism generating results has far more variance than what was observed so far.

Way more than a trillion times more likely.

If this is MTT player... If not it is different to what I would wrote under... It basically depends a lot from which perspective you look at your question.

To me, this can sounds like a good MTT player. More losing days than winning days. But he wins more than he loses. The problem with MTT is there is a lot of variance there. For example if everybody is same skilled: there is 100 players: 1 percent for each to win. Even if one person is more skilled than other 99, he does not have a lot bigger chances of winning than I mentioned... And so on...

Anyway, what you describe is "normal winning MTT player" month,year,... Nothing strange actually... This thing basically happens to every serious MTT poker player all the time(and is not important indicator(in this case); but it is interesting I guess). Basically can not be different.

The variance only has any meaning when the statistics are acquired with the same circumstances every time: That is if the player sits down with the same group of opponents for the same span of time each day (and none of them ever improve/devolve their game).

E.g. If he plays on a table with super-tough opponents and wins 50$ a day for some time...but then one day sits down with 9 fish/whales then getting 1000$ off them isn't nearly as unlikely as it would be if he were to play his regular game.