Quick Check Up

[Actuary 3]

Actuary, I think you're a bit off on the end there... The 1.58 you calculate is, as you say, the standard deviation of the mean. That is, after those 250 games, you would expect to have earned14 +/- 1.58per game.

The Variance per game is E[X^2] - (E[X])^2,wher X represents the Random Variable of $$$ won/lost per gameAssuming the distribution described, that comes to:E[X] = 0.5 * 39 + 0.5 * -11 = 14, so (E[X])^2 = 196E[X^2] = 0.5 * 39^2 + 0.5 * (-11)^2 = 821E[X^2] - (E[X])^2 = 821 -196 = 625.Stdev = Sqrt(Variance) = 625^(1/2) = 25So, the StnDev per game is 25.The Variance of the TOTAL EARNED over 250 games, given our distribution (Win 1/2, Don't cash 1/2) = N * Var(X) = 250 * 625 = 156,250And the StndDEv = 395.3 +/- 2 Stndev = (14)*(250) +/- 790.6 = (2709, 4291)The Variance of the Mean = Var Total / N^2 = 156,250 / 250^2 = 2.5The StnDev is 1.58, for the Mean.I see my error.If I use 1.58 I have to use $11.If I use 250*$11, I have to use 395.3 for Stndev.ewww... While I'm surprised at this result, I was also surpirsed it worked out like it did the other way, but I was unable to see the error of my ways at the time.Only thing I disagree on is, since your Variance is highest in this case (I think) and would be lower if you placed in each position 1/10 times, that you need a a smaller sample here. But if you mean that the likelihood you are a Winner is high enough in the first example, and les known in other distributions, I see your point.you certainly schooled me here.:(that 0.23% seemd way to tight .. Lets take it to 1,000,000 SnG's, Total Var = 625,000,000, StnDev = 25,000, Or Range of 100,000 across 4 Stndev100,000 / ($11 * 1,000,000) = 0.91%My, oh my.I probably made more mistakes here. Trying to stay sharp.

[ramenandeggs 0]

after i learn stats and go through my Math of Poker, I might understand wth is going on, yea?*lost in the world of math*and to the op, calling with 5c 7c against a rock isn't completely hopeless, it is in a SNG so your point stands, but I hope you can see its merit in more regular cases like a deepstackament or a cash game where the rock will give huge implied odds since he goes broke every time if you hit the right flop. i can assure that you're making a mistake somewhere, even phil ivey admits to making mistakes. your stats crush me so maybe I don't know what I'm talking about, but, looking forward to your results after 300 sngs.

[Mr. Sparco 2]

I just noticed I completely missed your reply... Well, better late than never:

Only thing I disagree on is, since your Variance is highest in this case (I think) and would be lower if you placed in each position 1/10 times, that you need a a smaller sample here. But if you mean that the likelihood you are a Winner is high enough in the first example, and les known in other distributions, I see your point.

That was indeed my point, but you're absolutely right: if you take a more realistic case where you place in each position an equal number of times, the variance goes down by a factor of about 2.2, and so does the sample size you need to get to a specific standard deviation.Actually, you inspired me to write an article about these matters which will hopefully elucidate things even more. I'll post a link here when it's finished.

[Actuary 3]

Actually, you inspired me to write an article about these matters which will hopefully elucidate things even more. I'll post a link here when it's finished.

I've been marginalized by a better statisitcs mind :(Will the forum still have me?in the end, the profit variance to buy in ratio per tourney necessitated many more trials than I anticipated. And my personal experience as a non-aggressive player with steady results, biased my thinking going in.Welcome!!! Sparco

[litlebullet 0]

my head hurts.

[Mr. Sparco 2]

Actually, you inspired me to write an article about these matters which will hopefully elucidate things even more. I'll post a link here when it's finished.

Not only is it finished, I found out just now that it has been accepted for publication in the Two Plus Two Internet Magazine. So, for those still interested, here is the link:How Big is Big Enough?

[Actuary 3]

Not only is it finished, I found out just now that it has been accepted for publication in the Two Plus Two Internet Magazine. So, for those still interested, here is the link:How Big is Big Enough?

sweet.congrats, nerd :PI'll check it out when I'm not dead tired

[profxavier9 0]

my head hurts.