Hello again:
The first four games ended in draw. Maintining the parameters of former simulations:
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White advantage: 40.0 Elo.
Supposed rating difference: 47.0 Elo.
1000000 simulations:
Carlsen wins: 643900
Anand wins: 147459
Drawn matches: 208641
Approximated elapsed time: 1.50 seconds.
Supposing again 30% of chances for Carlsen in case of a tied match: 64.39% + 0.3*20.8641% = 70.64923% ~ 70.65% after 1e+6 simulations.
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Changing the draw model (now the maximum draw ratio expected for an insane number of games is 70% for two equal players):
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Maximum draw ratio: 60%.
White advantage: 40.0 Elo.
Supposed rating difference: 47.0 Elo.
1000000 simulations:
Carlsen wins: 627426
Anand wins: 185337
Drawn matches: 187237
Approximated elapsed time: 1.50 seconds.
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Maximum draw ratio: 65%.
White advantage: 40.0 Elo.
Supposed rating difference: 47.0 Elo.
1000000 simulations:
Carlsen wins: 635084
Anand wins: 168222
Drawn matches: 196694
Approximated elapsed time: 1.51 seconds.
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Maximum draw ratio: 70%.
White advantage: 40.0 Elo.
Supposed rating difference: 47.0 Elo.
1000000 simulations:
Carlsen wins: 643900
Anand wins: 147459
Drawn matches: 208641
Approximated elapsed time: 1.50 seconds.
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Maximum draw ratio: 75%.
White advantage: 40.0 Elo.
Supposed rating difference: 47.0 Elo.
1000000 simulations:
Carlsen wins: 654550
Anand wins: 121974
Drawn matches: 223476
Approximated elapsed time: 1.51 seconds.
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Maximum draw ratio: 80%.
White advantage: 40.0 Elo.
Supposed rating difference: 47.0 Elo.
1000000 simulations:
Carlsen wins: 666458
Anand wins: 89648
Drawn matches: 243894
Approximated elapsed time: 1.52 seconds.
A higher probability of draw benefits the stronger player (it is Carlsen with my parameters, which does not mean that it is true). Supposing again 30% of chances for Carlsen in case of a tied match:
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Expected winning chances for Carlsen after game 4; 1e+6 simulations each time:
Maximum draw ratio: 60%: 62.7426% + 0.3*18.7237% = 68.35971% ~ 68.36%.
Maximum draw ratio: 65%: 63.5084% + 0.3*19.6694% = 69.40922% ~ 69.41%.
Maximum draw ratio: 70%: 64.3900% + 0.3*20.8641% = 70.64923% ~ 70.65%.
Maximum draw ratio: 75%: 65.4550% + 0.3*22.3476% = 72.15928% ~ 72.16%.
Maximum draw ratio: 80%: 66.6458% + 0.3*24.3894% = 73.96262% ~ 73.96%.
I hope no typos. Once again, small changes in the draw model bring big changes in winning probabilities from my POV. These simulations are more black art than anything else.
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Games 3 and 4 were fine IMHO. It is good to see some fight spirit, much more than in games 1 and 2.
Regards from Spain.
Ajedrecista.