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Message: [QUOTE="maltz, post: 637561, member: 26654"] Ops I think I've made a mistake in calculation. Let's go back a little bit. ** Let's review how a coin flip is done. Say you [B]bet $1[/B], and your opponents (in the poker sense, you are playing against [B]all of your opponents as one entity[/B]) bet $1. You flip the coin. If you win, you get $2 ([B]pot size = $2[/B]). Your net win is $1. If you lose, you get nothing. Your net loss is $1. Next we can look at a situation of 60-40. When you invest $1 for 100 times, in average -- Your result is 60 x 2 + 40 x 0 = 120. You win $20 per 100 hands, with an average pot size of $2. We know the average pot size is 12 times of BB. BB in this case = 2/12 = 1/6. Therefore, your winning per 100 hand of a 60-40 coin is: 20 / (1/6) =[B] 120 (BB)[/B]. You are expected to win 120BB per 100 hands. Now this is [B]12 times better [/B]than your average earning of 10BB / 100 hands! (in my original post I said 24 which is incorrect, as I failed to consider the pot size is actually twice as large as your bet size.) In reality, your coin is 12 times worse than a 60-40 coin. Your coin is actually a 50.083 vs. 49.017 coin. So on my above post my numbers should be multipled by 2. *** Just a quick correction of all relative numbers: Your coin with [B]10BB earning: 50.83 vs. 49.17[/B] My coin with a [B]50BB earning (pot size 25BB): 52 vs. 48[/B] *** That's all the correction. Now let me revisit the method for calculating the standard deviation. The formula of standard deviation is given as: (The sum of variance / sample size)^(1/2) where variance = (individual sample - average)^2 This is what I wrote in the Excel spreadsheet. Let coin flip win rate = A% lose rate = (100-A)% Hand number = N Average = AVG = (A*2+(1-A)*0)/100 Standard Deviation (STDEV) = (((2-AVG)^2*A+(0-AVG)^2*(1-A))/N)^0.5 For 100 hands STDEV is more or less fixed at 1 (For 10 hands it is about 3.2, for 10000 hands it is about 0.1) Poker Pro's coin with hourly rate : standard deviation = 1:6 So we are aiming at a winning rate per 100 hands (in about an hour) of 1/6. This gives us the 50.083 vs. 49.917 coin flip. *** Well most people do play a lot of sessions in the casino, and when people play online they do have the option to gamble just a few hands with a pro. Anyways, you know what I mean -- the casino always knows how to run its business! [/QUOTE]

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