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#31
June 25th 05, 01:38 AM
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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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#32
June 25th 05, 01:53 AM
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Incorrect. Please revise.
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#33
June 25th 05, 02:24 AM
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These are the exact odds.
Proportion Bill Brock's chance of draws to win 0.000000 0.57100561178634358345 0.010000 0.57962209945210672586 0.020000 0.58772755731246680136 0.030000 0.59534601566733954696 0.040000 0.60250097981664069971 0.050000 0.60921543006028599658 0.060000 0.61551182169819117451 0.070000 0.62141208503027197058 0.080000 0.62693762535644412167 0.090000 0.63210932297662336492 0.100000 0.63694753319072543705 0.110000 0.64147208629866607542 0.120000 0.64570228760036101669 0.130000 0.64965691739572599802 0.140000 0.65335423098467675633 0.150000 0.65681195866712902866 0.160000 0.66004730574299855190 0.170000 0.66307695251220106326 0.180000 0.66591705427465229945 0.190000 0.66858324133026799773 0.200000 0.67109061897896389484 0.210000 0.67345376752065572786 0.220000 0.67568674225525923396 0.230000 0.67780307348269014991 0.240000 0.67981576650286421260 0.250000 0.68173730161569715940 0.260000 0.68357963412110472705 0.270000 0.68535419431900265253 0.280000 0.68707188750930667291 0.290000 0.68874309399193252496 0.300000 0.69037766906679594596 0.310000 0.69198494303381267274 0.320000 0.69357372119289844236 0.330000 0.69515228384396899171 0.340000 0.69672838628694005797 0.350000 0.69830925882172737790 0.360000 0.69990160674824668854 0.370000 0.70151161036641372719 0.380000 0.70314492497614423038 0.390000 0.70480668087735393534 0.400000 0.70650148336995857902 0.410000 0.70823341275387389842 0.420000 0.71000602432901563051 0.430000 0.71182234839529951229 0.440000 0.71368489025264128056 0.450000 0.71559563020095667265 0.460000 0.71755602354016142543 0.470000 0.71956700057017127572 0.480000 0.72162896659090196077 0.490000 0.72374180190226921732 0.500000 0.72590486180418878256 0.510000 0.72811697659657639338 0.520000 0.73037645157934778675 0.530000 0.73268106705241869953 0.540000 0.73502807831570486901 0.550000 0.73741421566912203177 0.560000 0.73983568441258592543 0.570000 0.74228816484601228641 0.580000 0.74476681226931685197 0.590000 0.74726625698241535883 0.600000 0.74978060428522354437 0.610000 0.75230343447765714521 0.620000 0.75482780285963189867 0.630000 0.75734623973106354137 0.640000 0.75985075039186781068 0.650000 0.76233281514196044309 0.660000 0.76478338928125717610 0.670000 0.76719290310967374653 0.680000 0.76955126192712589131 0.690000 0.77184784603352934741 0.700000 0.77407151072879985175 0.710000 0.77621058631285314131 0.720000 0.77825287808560495361 0.730000 0.78018566634697102477 0.740000 0.78199570639686709263 0.750000 0.78366922853520889353 0.760000 0.78519193806191216466 0.770000 0.78654901527689264316 0.780000 0.78772511548006606571 0.790000 0.78870436897134816971 0.800000 0.78947038105065469194 0.810000 0.79000623201790136900 0.820000 0.79029447717300393863 0.830000 0.79031714681587813729 0.840000 0.79005574624643970185 0.850000 0.78949125576460437006 0.860000 0.78860413067028787800 0.870000 0.78737430126340596318 0.880000 0.78578117284387436251 0.890000 0.78380362571160881274 0.900000 0.78142001516652505116 0.910000 0.77860817150853881474 0.920000 0.77534540003756584011 0.930000 0.77160848105352186475 0.940000 0.76737366985632262544 0.950000 0.76261669674588385896 0.960000 0.75731276702212130215 0.970000 0.75143656098495069276 0.980000 0.74496223393428776704 David Kane wrote: Using what appear to be the same assumptions in your program, (Pdraw=0.25, White worth 50 points, rating delta 111), I also calculate different odds. (31% Sloan) Neglecting color (PW=0.22, PL = 0.53, PD = 0.25), PMatch (Sloan) = 30.4% "Paul Rubin" wrote in message ... "Tyrone Slothrop" writes: According to my latest calculation using the USCF formula, Brock is favored by about 56-44. But having gotten it wrong so many times before, I'm not enormously confident of this calculation either. If anyone cares, I'll post the program I did it with. How are you calculating this? The resulting odds I have calculated are different than this. It was just a random simulation using this Python script: http://www.nightsong.com/phr/chess/sloan-brock.py However, there could easily be an error. I haven't looked over it since right after I first wrote it.
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#34
June 25th 05, 02:34 AM
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This is not the match probability. You can easily
see that because the result doesn't depend on the length of a match. However, the values I gave were based on the assumed winning and drawing probabilities taken from Paul's calculation, which may not be correct. If a lower draw percentage is assumed, then Sloan's chances go up. (Up to 43% in the no draw case) "George John" wrote in message oups.com... 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
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#35
June 25th 05, 02:40 AM
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Please state your assumptions. You must
be doing something wrong. If P draw=.98, then it would be impossible for there to be a 111 point rating difference. "Tyrone Slothrop" wrote in message oups.com... These are the exact odds. Proportion Bill Brock's chance of draws to win 0.000000 0.57100561178634358345 0.010000 0.57962209945210672586 0.020000 0.58772755731246680136 0.030000 0.59534601566733954696 0.040000 0.60250097981664069971 0.050000 0.60921543006028599658 0.060000 0.61551182169819117451 0.070000 0.62141208503027197058 0.080000 0.62693762535644412167 0.090000 0.63210932297662336492 0.100000 0.63694753319072543705 0.110000 0.64147208629866607542 0.120000 0.64570228760036101669 0.130000 0.64965691739572599802 0.140000 0.65335423098467675633 0.150000 0.65681195866712902866 0.160000 0.66004730574299855190 0.170000 0.66307695251220106326 0.180000 0.66591705427465229945 0.190000 0.66858324133026799773 0.200000 0.67109061897896389484 0.210000 0.67345376752065572786 0.220000 0.67568674225525923396 0.230000 0.67780307348269014991 0.240000 0.67981576650286421260 0.250000 0.68173730161569715940 0.260000 0.68357963412110472705 0.270000 0.68535419431900265253 0.280000 0.68707188750930667291 0.290000 0.68874309399193252496 0.300000 0.69037766906679594596 0.310000 0.69198494303381267274 0.320000 0.69357372119289844236 0.330000 0.69515228384396899171 0.340000 0.69672838628694005797 0.350000 0.69830925882172737790 0.360000 0.69990160674824668854 0.370000 0.70151161036641372719 0.380000 0.70314492497614423038 0.390000 0.70480668087735393534 0.400000 0.70650148336995857902 0.410000 0.70823341275387389842 0.420000 0.71000602432901563051 0.430000 0.71182234839529951229 0.440000 0.71368489025264128056 0.450000 0.71559563020095667265 0.460000 0.71755602354016142543 0.470000 0.71956700057017127572 0.480000 0.72162896659090196077 0.490000 0.72374180190226921732 0.500000 0.72590486180418878256 0.510000 0.72811697659657639338 0.520000 0.73037645157934778675 0.530000 0.73268106705241869953 0.540000 0.73502807831570486901 0.550000 0.73741421566912203177 0.560000 0.73983568441258592543 0.570000 0.74228816484601228641 0.580000 0.74476681226931685197 0.590000 0.74726625698241535883 0.600000 0.74978060428522354437 0.610000 0.75230343447765714521 0.620000 0.75482780285963189867 0.630000 0.75734623973106354137 0.640000 0.75985075039186781068 0.650000 0.76233281514196044309 0.660000 0.76478338928125717610 0.670000 0.76719290310967374653 0.680000 0.76955126192712589131 0.690000 0.77184784603352934741 0.700000 0.77407151072879985175 0.710000 0.77621058631285314131 0.720000 0.77825287808560495361 0.730000 0.78018566634697102477 0.740000 0.78199570639686709263 0.750000 0.78366922853520889353 0.760000 0.78519193806191216466 0.770000 0.78654901527689264316 0.780000 0.78772511548006606571 0.790000 0.78870436897134816971 0.800000 0.78947038105065469194 0.810000 0.79000623201790136900 0.820000 0.79029447717300393863 0.830000 0.79031714681587813729 0.840000 0.79005574624643970185 0.850000 0.78949125576460437006 0.860000 0.78860413067028787800 0.870000 0.78737430126340596318 0.880000 0.78578117284387436251 0.890000 0.78380362571160881274 0.900000 0.78142001516652505116 0.910000 0.77860817150853881474 0.920000 0.77534540003756584011 0.930000 0.77160848105352186475 0.940000 0.76737366985632262544 0.950000 0.76261669674588385896 0.960000 0.75731276702212130215 0.970000 0.75143656098495069276 0.980000 0.74496223393428776704 David Kane wrote: Using what appear to be the same assumptions in your program, (Pdraw=0.25, White worth 50 points, rating delta 111), I also calculate different odds. (31% Sloan) Neglecting color (PW=0.22, PL = 0.53, PD = 0.25), PMatch (Sloan) = 30.4% "Paul Rubin" wrote in message ... "Tyrone Slothrop" writes: According to my latest calculation using the USCF formula, Brock is favored by about 56-44. But having gotten it wrong so many times before, I'm not enormously confident of this calculation either. If anyone cares, I'll post the program I did it with. How are you calculating this? The resulting odds I have calculated are different than this. It was just a random simulation using this Python script: http://www.nightsong.com/phr/chess/sloan-brock.py However, there could easily be an error. I haven't looked over it since right after I first wrote it.
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#36
June 25th 05, 02:44 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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#37
June 25th 05, 03:06 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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#38
June 25th 05, 04:01 AM
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For any one game, I just took:
E(total) = P(wins) + 0.5 P(tie) 1 - E(total) = P(lose) + 0.5 P(tie) P(win) + P(tie) + P(lose) = 1 where E(total) is the total single game expectation for Bill (=.6545). The probability of any one combination of four games is then: P(combination) = P(outcome1)*P(outcome2)*P(outcome3)*P(outcome4) Sum(P(combination)) for those combinations that win for Bill resulted in my table. Did I go wrong somewhere? David Kane wrote: Please state your assumptions. You must be doing something wrong. If P draw=.98, then it would be impossible for there to be a 111 point rating difference. "Tyrone Slothrop" wrote in message oups.com... These are the exact odds. Proportion Bill Brock's chance of draws to win 0.000000 0.57100561178634358345 0.010000 0.57962209945210672586 0.020000 0.58772755731246680136 0.030000 0.59534601566733954696 0.040000 0.60250097981664069971 0.050000 0.60921543006028599658 0.060000 0.61551182169819117451 0.070000 0.62141208503027197058 0.080000 0.62693762535644412167 0.090000 0.63210932297662336492 0.100000 0.63694753319072543705 0.110000 0.64147208629866607542 0.120000 0.64570228760036101669 0.130000 0.64965691739572599802 0.140000 0.65335423098467675633 0.150000 0.65681195866712902866 0.160000 0.66004730574299855190 0.170000 0.66307695251220106326 0.180000 0.66591705427465229945 0.190000 0.66858324133026799773 0.200000 0.67109061897896389484 0.210000 0.67345376752065572786 0.220000 0.67568674225525923396 0.230000 0.67780307348269014991 0.240000 0.67981576650286421260 0.250000 0.68173730161569715940 0.260000 0.68357963412110472705 0.270000 0.68535419431900265253 0.280000 0.68707188750930667291 0.290000 0.68874309399193252496 0.300000 0.69037766906679594596 0.310000 0.69198494303381267274 0.320000 0.69357372119289844236 0.330000 0.69515228384396899171 0.340000 0.69672838628694005797 0.350000 0.69830925882172737790 0.360000 0.69990160674824668854 0.370000 0.70151161036641372719 0.380000 0.70314492497614423038 0.390000 0.70480668087735393534 0.400000 0.70650148336995857902 0.410000 0.70823341275387389842 0.420000 0.71000602432901563051 0.430000 0.71182234839529951229 0.440000 0.71368489025264128056 0.450000 0.71559563020095667265 0.460000 0.71755602354016142543 0.470000 0.71956700057017127572 0.480000 0.72162896659090196077 0.490000 0.72374180190226921732 0.500000 0.72590486180418878256 0.510000 0.72811697659657639338 0.520000 0.73037645157934778675 0.530000 0.73268106705241869953 0.540000 0.73502807831570486901 0.550000 0.73741421566912203177 0.560000 0.73983568441258592543 0.570000 0.74228816484601228641 0.580000 0.74476681226931685197 0.590000 0.74726625698241535883 0.600000 0.74978060428522354437 0.610000 0.75230343447765714521 0.620000 0.75482780285963189867 0.630000 0.75734623973106354137 0.640000 0.75985075039186781068 0.650000 0.76233281514196044309 0.660000 0.76478338928125717610 0.670000 0.76719290310967374653 0.680000 0.76955126192712589131 0.690000 0.77184784603352934741 0.700000 0.77407151072879985175 0.710000 0.77621058631285314131 0.720000 0.77825287808560495361 0.730000 0.78018566634697102477 0.740000 0.78199570639686709263 0.750000 0.78366922853520889353 0.760000 0.78519193806191216466 0.770000 0.78654901527689264316 0.780000 0.78772511548006606571 0.790000 0.78870436897134816971 0.800000 0.78947038105065469194 0.810000 0.79000623201790136900 0.820000 0.79029447717300393863 0.830000 0.79031714681587813729 0.840000 0.79005574624643970185 0.850000 0.78949125576460437006 0.860000 0.78860413067028787800 0.870000 0.78737430126340596318 0.880000 0.78578117284387436251 0.890000 0.78380362571160881274 0.900000 0.78142001516652505116 0.910000 0.77860817150853881474 0.920000 0.77534540003756584011 0.930000 0.77160848105352186475 0.940000 0.76737366985632262544 0.950000 0.76261669674588385896 0.960000 0.75731276702212130215 0.970000 0.75143656098495069276 0.980000 0.74496223393428776704 David Kane wrote: Using what appear to be the same assumptions in your program, (Pdraw=0.25, White worth 50 points, rating delta 111), I also calculate different odds. (31% Sloan) Neglecting color (PW=0.22, PL = 0.53, PD = 0.25), PMatch (Sloan) = 30.4% "Paul Rubin" wrote in message ... "Tyrone Slothrop" writes: According to my latest calculation using the USCF formula, Brock is favored by about 56-44. But having gotten it wrong so many times before, I'm not enormously confident of this calculation either. If anyone cares, I'll post the program I did it with. How are you calculating this? The resulting odds I have calculated are different than this. It was just a random simulation using this Python script: http://www.nightsong.com/phr/chess/sloan-brock.py However, there could easily be an error. I haven't looked over it since right after I first wrote it.
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#39
June 25th 05, 04:06 AM
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Doh. I feel like Homer Simpson.
I forgot to put the boundary conditions that P(win) = 0, P(lose) =0, P(tie) = 0, and in forgetting this important step, I allowed negative probabilities in my calculation. But I can just truncate my table at a draw probability of 69%. How's this? Proportion Bill Brock's chance of draws to win 0.000000 0.57100561178634358345 0.010000 0.57962209945210672586 0.020000 0.58772755731246680136 0.030000 0.59534601566733954696 0.040000 0.60250097981664069971 0.050000 0.60921543006028599658 0.060000 0.61551182169819117451 0.070000 0.62141208503027197058 0.080000 0.62693762535644412167 0.090000 0.63210932297662336492 0.100000 0.63694753319072543705 0.110000 0.64147208629866607542 0.120000 0.64570228760036101669 0.130000 0.64965691739572599802 0.140000 0.65335423098467675633 0.150000 0.65681195866712902866 0.160000 0.66004730574299855190 0.170000 0.66307695251220106326 0.180000 0.66591705427465229945 0.190000 0.66858324133026799773 0.200000 0.67109061897896389484 0.210000 0.67345376752065572786 0.220000 0.67568674225525923396 0.230000 0.67780307348269014991 0.240000 0.67981576650286421260 0.250000 0.68173730161569715940 0.260000 0.68357963412110472705 0.270000 0.68535419431900265253 0.280000 0.68707188750930667291 0.290000 0.68874309399193252496 0.300000 0.69037766906679594596 0.310000 0.69198494303381267274 0.320000 0.69357372119289844236 0.330000 0.69515228384396899171 0.340000 0.69672838628694005797 0.350000 0.69830925882172737790 0.360000 0.69990160674824668854 0.370000 0.70151161036641372719 0.380000 0.70314492497614423038 0.390000 0.70480668087735393534 0.400000 0.70650148336995857902 0.410000 0.70823341275387389842 0.420000 0.71000602432901563051 0.430000 0.71182234839529951229 0.440000 0.71368489025264128056 0.450000 0.71559563020095667265 0.460000 0.71755602354016142543 0.470000 0.71956700057017127572 0.480000 0.72162896659090196077 0.490000 0.72374180190226921732 0.500000 0.72590486180418878256 0.510000 0.72811697659657639338 0.520000 0.73037645157934778675 0.530000 0.73268106705241869953 0.540000 0.73502807831570486901 0.550000 0.73741421566912203177 0.560000 0.73983568441258592543 0.570000 0.74228816484601228641 0.580000 0.74476681226931685197 0.590000 0.74726625698241535883 0.600000 0.74978060428522354437 0.610000 0.75230343447765714521 0.620000 0.75482780285963189867 0.630000 0.75734623973106354137 0.640000 0.75985075039186781068 0.650000 0.76233281514196044309 0.660000 0.76478338928125717610 0.670000 0.76719290310967374653 0.680000 0.76955126192712589131 0.690000 0.77184784603352934741 Tyrone Slothrop wrote: For any one game, I just took: E(total) = P(wins) + 0.5 P(tie) 1 - E(total) = P(lose) + 0.5 P(tie) P(win) + P(tie) + P(lose) = 1 where E(total) is the total single game expectation for Bill (=.6545). The probability of any one combination of four games is then: P(combination) = P(outcome1)*P(outcome2)*P(outcome3)*P(outcome4) Sum(P(combination)) for those combinations that win for Bill resulted in my table. Did I go wrong somewhere? David Kane wrote: Please state your assumptions. You must be doing something wrong. If P draw=.98, then it would be impossible for there to be a 111 point rating difference. "Tyrone Slothrop" wrote in message oups.com... These are the exact odds. Proportion Bill Brock's chance of draws to win 0.000000 0.57100561178634358345 0.010000 0.57962209945210672586 0.020000 0.58772755731246680136 0.030000 0.59534601566733954696 0.040000 0.60250097981664069971 0.050000 0.60921543006028599658 0.060000 0.61551182169819117451 0.070000 0.62141208503027197058 0.080000 0.62693762535644412167 0.090000 0.63210932297662336492 0.100000 0.63694753319072543705 0.110000 0.64147208629866607542 0.120000 0.64570228760036101669 0.130000 0.64965691739572599802 0.140000 0.65335423098467675633 0.150000 0.65681195866712902866 0.160000 0.66004730574299855190 0.170000 0.66307695251220106326 0.180000 0.66591705427465229945 0.190000 0.66858324133026799773 0.200000 0.67109061897896389484 0.210000 0.67345376752065572786 0.220000 0.67568674225525923396 0.230000 0.67780307348269014991 0.240000 0.67981576650286421260 0.250000 0.68173730161569715940 0.260000 0.68357963412110472705 0.270000 0.68535419431900265253 0.280000 0.68707188750930667291 0.290000 0.68874309399193252496 0.300000 0.69037766906679594596 0.310000 0.69198494303381267274 0.320000 0.69357372119289844236 0.330000 0.69515228384396899171 0.340000 0.69672838628694005797 0.350000 0.69830925882172737790 0.360000 0.69990160674824668854 0.370000 0.70151161036641372719 0.380000 0.70314492497614423038 0.390000 0.70480668087735393534 0.400000 0.70650148336995857902 0.410000 0.70823341275387389842 0.420000 0.71000602432901563051 0.430000 0.71182234839529951229 0.440000 0.71368489025264128056 0.450000 0.71559563020095667265 0.460000 0.71755602354016142543 0.470000 0.71956700057017127572 0.480000 0.72162896659090196077 0.490000 0.72374180190226921732 0.500000 0.72590486180418878256 0.510000 0.72811697659657639338 0.520000 0.73037645157934778675 0.530000 0.73268106705241869953 0.540000 0.73502807831570486901 0.550000 0.73741421566912203177 0.560000 0.73983568441258592543 0.570000 0.74228816484601228641 0.580000 0.74476681226931685197 0.590000 0.74726625698241535883 0.600000 0.74978060428522354437 0.610000 0.75230343447765714521 0.620000 0.75482780285963189867 0.630000 0.75734623973106354137 0.640000 0.75985075039186781068 0.650000 0.76233281514196044309 0.660000 0.76478338928125717610 0.670000 0.76719290310967374653 0.680000 0.76955126192712589131 0.690000 0.77184784603352934741 0.700000 0.77407151072879985175 0.710000 0.77621058631285314131 0.720000 0.77825287808560495361 0.730000 0.78018566634697102477 0.740000 0.78199570639686709263 0.750000 0.78366922853520889353 0.760000 0.78519193806191216466 0.770000 0.78654901527689264316 0.780000 0.78772511548006606571 0.790000 0.78870436897134816971 0.800000 0.78947038105065469194 0.810000 0.79000623201790136900 0.820000 0.79029447717300393863 0.830000 0.79031714681587813729 0.840000 0.79005574624643970185 0.850000 0.78949125576460437006 0.860000 0.78860413067028787800 0.870000 0.78737430126340596318 0.880000 0.78578117284387436251 0.890000 0.78380362571160881274 0.900000 0.78142001516652505116 0.910000 0.77860817150853881474 0.920000 0.77534540003756584011 0.930000 0.77160848105352186475 0.940000 0.76737366985632262544 0.950000 0.76261669674588385896 0.960000 0.75731276702212130215 0.970000 0.75143656098495069276 0.980000 0.74496223393428776704 David Kane wrote: Using what appear to be the same assumptions in your program, (Pdraw=0.25, White worth 50 points, rating delta 111), I also calculate different odds. (31% Sloan) Neglecting color (PW=0.22, PL = 0.53, PD = 0.25), PMatch (Sloan) = 30.4% "Paul Rubin" wrote in message ... "Tyrone Slothrop" writes: According to my latest calculation using the USCF formula, Brock is favored by about 56-44. But having gotten it wrong so many times before, I'm not enormously confident of this calculation either. If anyone cares, I'll post the program I did it with. How are you calculating this? The resulting odds I have calculated are different than this. It was just a random simulation using this Python script: http://www.nightsong.com/phr/chess/sloan-brock.py However, there could easily be an error. I haven't looked over it since right after I first wrote it.
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#40
June 25th 05, 04:07 AM
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