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| Tags: further, george, idiot, john, proof |
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#1
June 25th 05, 12:38 AM
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Further Proof that George John is an Idiot !!
Boy is he stupid! Self-proclaimed computer expert George John, whose
only proof of his computer expertise is his own statements about himself, who claims that he has worked for 25 years in the computer field yet his name is not associated with any recognized computer program or device, came up with the following duzie, which makes it clear that George John has never taken even the most basic college match or statistics course. Did he ever graduate from high school? On 24 Jun 2005 14:07:33 -0700, "George John" wrote: I'm not a probability/statistics expert (far from it!), so what I'm going to suggested is only a half-educated (at best -grin-) guess. Assume Sloan's performance follows the Normal Distribution with a mean of 1931 and standard deviation of 400. To break even against Bill Brock he will need a performance of 2042 or better. The probability of his doing so is roughly 0.390698 (using: http://davidmlane.com/hyperstat/z_table.html) So, based on this analysis (which may be totally flawed) I give Sloan about a 39% chance. Best regards, George John This is not the way to calculate the odds. As any college freshman will tell you, first you decide the probability of a win, a loss or a draw in an individual game. Unfortunately, the USCF rating formula does not tell you that, because it does not tell you the probability of a draw. In the traditional formula, if two players are playing a match and one is rated 200 points higher than the other, them the higherr rated player should win by 7.5-2.5 in a ten game match or by 24-8 in a 32 game match.. If the players are seperated by 100 points, the higher player should win by 20-12 in a 32 game match. However, this does not tell you how many games will be draws. If we can estimate the % of draws, then we can calculate exactly the probability of victory. For example, suppose that we decide that 25% of the games will be draws. That will be 8 games in a 32 game match. Of the remaining 24 games, Sloan should win 8 and Brock 16, so we reach the final score of 20-12. So,m according to this, Brock wins 50%, Sloan wins 25% and 25% are draws. Now, we take each possible outcome. W stands for a Sloan win, L stands for a Brock win and D stand for a draw. Now, we just list all the possible outcomes and the probability of each. WW means Sloan won the first two games and there fore the match. This will happen 6.25% of the time or 25% times 25%. Here are all of the possible outcomes: WW WDW WDD WDLW WDLD WDLL WLW WLDW WLDD WLDL WLL LWW LWDW LWDD LWDL LWL LDWW LDWD LDWL LDDW LDDD LDDL LDL LLWW LLWD LLWL LLD LLL So, there are 28 possible outcomes. Of these Sloan wins 15 and Brock wins 13. Now, calculate the probability of each outcome. .For example, the probability of LLWD (in which case Brock wins) is .5 x .5 x .25 x .25 Now, add them all up and you get Brock's chamces of winning the four game match. Sam Sloan 
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#2
June 25th 05, 01:44 AM
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Unfortunately, this is wrong. Two mistakes:
- You are accounting for short games incorrectly - Ties matter Take the simple case of a max of two games in a match. Let's say that you win if you can score 1.0 and Bill wins if he scores 1.5. Just as in this match, you don't play the second game if it isn't necessary. So what are the outcomes? (W- bill wins, T - tied, L - bill loses) WW B(ill wins) WT B WL S(am wins) TW B TT S TL S L S -- short game Say that T occurs 50% of the time, W occurs 25% and L occurs 25%. What are the odds? WW occurs .25*.25 = 6.25% (B) WT occurs .25*.5 = 12.5% (B) WL occurs .25*.25 = 6.25% TW occurs .5*.25 = 12.5% (B) TT occurs .5*.5 = 25% TL occurs .5*.25 = 12.5% L occurs .25*1.0 = 25% -- short game Total = 100% The B-favorable events add up to: 6.25+12.5+12.5 = 31.25% However, let's say T only occurs 10%, W then occurs 45% and L occurs 45% What are the odds? WW occurs .45*.45 = 20.25% (B) WT occurs .45*.1 = 4.5% (B) WL occurs .45*.45 = 20.25% TW occurs .1*.45 = 4.5% (B) TT occurs .1*.1 = 1% TL occurs .1*.45 = 4.5% L occurs .45*1 = 45% -- short game Total = 100% This time, the B-favorable events only add up to: 20.25+4.5+4.5 = 29.25% Ties matter. Sam Sloan wrote: Boy is he stupid! Self-proclaimed computer expert George John, whose only proof of his computer expertise is his own statements about himself, who claims that he has worked for 25 years in the computer field yet his name is not associated with any recognized computer program or device, came up with the following duzie, which makes it clear that George John has never taken even the most basic college match or statistics course. Did he ever graduate from high school? On 24 Jun 2005 14:07:33 -0700, "George John" wrote: I'm not a probability/statistics expert (far from it!), so what I'm going to suggested is only a half-educated (at best -grin-) guess. Assume Sloan's performance follows the Normal Distribution with a mean of 1931 and standard deviation of 400. To break even against Bill Brock he will need a performance of 2042 or better. The probability of his doing so is roughly 0.390698 (using: http://davidmlane.com/hyperstat/z_table.html) So, based on this analysis (which may be totally flawed) I give Sloan about a 39% chance. Best regards, George John This is not the way to calculate the odds. As any college freshman will tell you, first you decide the probability of a win, a loss or a draw in an individual game. Unfortunately, the USCF rating formula does not tell you that, because it does not tell you the probability of a draw. In the traditional formula, if two players are playing a match and one is rated 200 points higher than the other, them the higherr rated player should win by 7.5-2.5 in a ten game match or by 24-8 in a 32 game match.. If the players are seperated by 100 points, the higher player should win by 20-12 in a 32 game match. However, this does not tell you how many games will be draws. If we can estimate the % of draws, then we can calculate exactly the probability of victory. For example, suppose that we decide that 25% of the games will be draws. That will be 8 games in a 32 game match. Of the remaining 24 games, Sloan should win 8 and Brock 16, so we reach the final score of 20-12. So,m according to this, Brock wins 50%, Sloan wins 25% and 25% are draws. Now, we take each possible outcome. W stands for a Sloan win, L stands for a Brock win and D stand for a draw. Now, we just list all the possible outcomes and the probability of each. WW means Sloan won the first two games and there fore the match. This will happen 6.25% of the time or 25% times 25%. Here are all of the possible outcomes: WW WDW WDD WDLW WDLD WDLL WLW WLDW WLDD WLDL WLL LWW LWDW LWDD LWDL LWL LDWW LDWD LDWL LDDW LDDD LDDL LDL LLWW LLWD LLWL LLD LLL So, there are 28 possible outcomes. Of these Sloan wins 15 and Brock wins 13. Now, calculate the probability of each outcome. .For example, the probability of LLWD (in which case Brock wins) is .5 x .5 x .25 x .25 Now, add them all up and you get Brock's chamces of winning the four game match. Sam Sloan
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#3
June 25th 05, 02:06 AM
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Sam Sloan said: "Now, add them all up and you get Brock's chamces of
winning the four game match." Very good Sam now perhaps you can come up with a simple formula to solve this problem: You have 10 horses er players rather in a tournament. They all have Elo ratings. What is the formula to compute the odds on each player to win the race er tournament?
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#4
June 25th 05, 03:07 AM
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#5
June 25th 05, 03:50 AM
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Thank you for correcting my error. My error was that I just considered
the possibility of a win or a loss in the first game. I forgot to calculate what happens if the first game is a draw. I took a nap and in my sleep realized that I had made an error. I also calculatre that if we split the first two games 1-1, then my odds of winning the match are exactly 50%. This is because I need only one win or two draws in the last two games. Now, what I left out was: DWW DWD DWLW DWLD DWLL DDW DDDW DDDD DDDL DDLW DDLD DDLL DLWW DLWD DLWL DLDW DLDD DLDL DLL There are 19 possibilities above. I win 11 and lose 8, but since L occures twice as often as D or W the odds are slightly against me. Sam Sloan On 24 Jun 2005 19:07:32 -0700, Paul Rubin wrote: (Sam Sloan) writes: Now, add them all up and you get Brock's chamces of winning the four game match. That is actually a reasonable approach, but there's more cases to consider. I think the following is a complete list and the final result agrees with Kane. This is based on 25% draw probability (constant for each game) and having the white pieces is worth 50 points. Note that if Sloan gets white in the first round, his chances of winning the match are about 45%, while if he gets black, his chances are only about 20.5%. This match will possibly be decided by the color draw at the beginning, assuming colors are chosen that way. ================================================= =============== Win / Lose / Draw probability: Sloan white: W=0.288105 L=0.461895 D=0.250000 Sloan black: W=0.158576 L=0.591424 D=0.250000 *** Sloan gets white in first round WW--: Sloan wins, prob=0.083004 WLW-: Sloan wins, prob=0.038339 WLLW: Sloan wins, prob=0.017709 WLLL: Brock wins, prob=0.028391 WLLD: Brock wins, prob=0.015367 WLDW: Sloan wins, prob=0.009585 WLDL: Brock wins, prob=0.015367 WLDD: Sloan wins, prob=0.008317 WDW-: Sloan wins, prob=0.020751 WDLW: Sloan wins, prob=0.009585 WDLL: Brock wins, prob=0.015367 WDLD: Sloan wins, prob=0.008317 WDD-: Sloan wins, prob=0.018007 LWW-: Sloan wins, prob=0.038339 LWLW: Sloan wins, prob=0.017709 LWLL: Brock wins, prob=0.028391 LWLD: Brock wins, prob=0.015367 LWDW: Sloan wins, prob=0.009585 LWDL: Brock wins, prob=0.015367 LWDD: Sloan wins, prob=0.008317 LLWW: Sloan wins, prob=0.017709 LLWL: Brock wins, prob=0.028391 LLWD: Brock wins, prob=0.015367 LLL-: Brock wins, prob=0.098544 LLD-: Brock wins, prob=0.053337 LDWW: Sloan wins, prob=0.009585 LDWL: Brock wins, prob=0.015367 LDWD: Sloan wins, prob=0.008317 LDL-: Brock wins, prob=0.053337 LDDW: Sloan wins, prob=0.008317 LDDL: Brock wins, prob=0.013334 LDDD: Brock wins, prob=0.007217 DWW-: Sloan wins, prob=0.020751 DWLW: Sloan wins, prob=0.009585 DWLL: Brock wins, prob=0.015367 DWLD: Sloan wins, prob=0.008317 DWD-: Sloan wins, prob=0.018007 DLWW: Sloan wins, prob=0.009585 DLWL: Brock wins, prob=0.015367 DLWD: Sloan wins, prob=0.008317 DLL-: Brock wins, prob=0.053337 DLDW: Sloan wins, prob=0.008317 DLDL: Brock wins, prob=0.013334 DLDD: Brock wins, prob=0.007217 DDW-: Sloan wins, prob=0.018007 DDLW: Sloan wins, prob=0.008317 DDLL: Brock wins, prob=0.013334 DDLD: Brock wins, prob=0.007217 DDDW: Sloan wins, prob=0.004502 DDDL: Brock wins, prob=0.007217 DDDD: Sloan wins, prob=0.003906 Match probabilities: {'Sloan': 0.44910257290666628, 'Brock': 0.55089742709333378} *** Sloan gets black in first round WW--: Sloan wins, prob=0.025146 WLW-: Sloan wins, prob=0.014872 WLLW: Sloan wins, prob=0.008796 WLLL: Brock wins, prob=0.032805 WLLD: Brock wins, prob=0.013867 WLDW: Sloan wins, prob=0.003718 WLDL: Brock wins, prob=0.013867 WLDD: Sloan wins, prob=0.005862 WDW-: Sloan wins, prob=0.006287 WDLW: Sloan wins, prob=0.003718 WDLL: Brock wins, prob=0.013867 WDLD: Sloan wins, prob=0.005862 WDD-: Sloan wins, prob=0.009911 LWW-: Sloan wins, prob=0.014872 LWLW: Sloan wins, prob=0.008796 LWLL: Brock wins, prob=0.032805 LWLD: Brock wins, prob=0.013867 LWDW: Sloan wins, prob=0.003718 LWDL: Brock wins, prob=0.013867 LWDD: Sloan wins, prob=0.005862 LLWW: Sloan wins, prob=0.008796 LLWL: Brock wins, prob=0.032805 LLWD: Brock wins, prob=0.013867 LLL-: Brock wins, prob=0.206869 LLD-: Brock wins, prob=0.087445 LDWW: Sloan wins, prob=0.003718 LDWL: Brock wins, prob=0.013867 LDWD: Sloan wins, prob=0.005862 LDL-: Brock wins, prob=0.087445 LDDW: Sloan wins, prob=0.005862 LDDL: Brock wins, prob=0.021861 LDDD: Brock wins, prob=0.009241 DWW-: Sloan wins, prob=0.006287 DWLW: Sloan wins, prob=0.003718 DWLL: Brock wins, prob=0.013867 DWLD: Sloan wins, prob=0.005862 DWD-: Sloan wins, prob=0.009911 DLWW: Sloan wins, prob=0.003718 DLWL: Brock wins, prob=0.013867 DLWD: Sloan wins, prob=0.005862 DLL-: Brock wins, prob=0.087445 DLDW: Sloan wins, prob=0.005862 DLDL: Brock wins, prob=0.021861 DLDD: Brock wins, prob=0.009241 DDW-: Sloan wins, prob=0.009911 DDLW: Sloan wins, prob=0.005862 DDLL: Brock wins, prob=0.021861 DDLD: Brock wins, prob=0.009241 DDDW: Sloan wins, prob=0.002478 DDDL: Brock wins, prob=0.009241 DDDD: Sloan wins, prob=0.003906 Match probabilities: {'Sloan': 0.20503126482804437, 'Brock': 0.79496873517195532} Total probabilities: {'Sloan': 0.32706691886735534, 'Brock': 0.67293308113264461}
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#6
June 25th 05, 04:06 AM
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#7
June 25th 05, 04:13 AM
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#8
June 25th 05, 04:32 AM
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