Carlsen Will DESTROY! Anand - World Chess Championship 2013.

[Ajedrecista]

Hello Kai:

All our results contradict a bit the betting odds of major betting houses. They give 69% to Carlsen and 31% to Anand, with the odds to go into tiebreak at 30%.

I only took a quick glance to LadBrokes and they more less give the probabilities you say. We probably look to the same web.

I have randomly assumed equal opportunities for both Anand and Carlsen if the tiebreak is reached. Then the probabilities would be:

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Carlsen wins: 54%.
Anand wins:   16%.
Drawn match:  30%.

With equal opportunities in the tiebreak:

Carlsen wins: 54% + (30%)/2 = 69%.
Anand wins:   16% + (30%)/2 = 31%.

I toyed a little with Elo difference and draw ratio parameters, running 1e+6 and 1e+7 simulations as fast filters. This is what I got after 1e+9 simulations with Elo difference = 20 and draw ratio = 86%:

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1e+9 simulations:

Carlsen wins:            543435023 (54.34%)
Anand wins:              158639839 (15.86%)
Drawn matches:           297925138 (29.79%)

Approximated elapsed time: 1232.50 seconds.

The draw ratio of Anand's classical time control games was over 83% (10 out of 12 games) in the last WCC against Gelfand.

Regards from Spain.

Ajedrecista.

[Laskos]

I have randomly assumed equal opportunities for both Anand and Carlsen if the tiebreak is reached.

Anand is known to excel at faster time controls, so in case of a tiebreak I used 70% for Anand, and 30% for Carlsen. Then I assume a reasonable draw ratio of 77%. With 30 Elo points gap, I get in one million simulations:

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Carlsen wins :  62.5%
Anand wins:     16.8%
Drawn match:    20.7%

After the tiebreak

Carlsen wins: 68.7%
Anand wins:   31.3%

So, with these assumptions, the odds of a drawn 12 game match seem overvalued by betters (or the gain is too small to bet on that). There are more people betting on the winner than on the tiebreak possibility, so 69%/31% is more reliable than ~30% for a drawn match.

Then the probabilities would be:

Code: Select all

Carlsen wins: 54%.
Anand wins:   16%.
Drawn match:  30%.

With equal opportunities in the tiebreak:

Carlsen wins: 54% + (30%)/2 = 69%.
Anand wins:   16% + (30%)/2 = 31%.

I toyed a little with Elo difference and draw ratio parameters, running 1e+6 and 1e+7 simulations as fast filters. This is what I got after 1e+9 simulations with Elo difference = 20 and draw ratio = 86%:

Code: Select all

1e+9 simulations:

Carlsen wins:            543435023 (54.34%)
Anand wins:              158639839 (15.86%)
Drawn matches:           297925138 (29.79%)

Approximated elapsed time: 1232.50 seconds.

The draw ratio of Anand's classical time control games was over 83% (10 out of 12 games) in the last WCC against Gelfand.

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hi again:

I have randomly assumed equal opportunities for both Anand and Carlsen if the tiebreak is reached.

Anand is known to excel at faster time controls, so in case of a tiebreak I used 70% for Anand, and 30% for Carlsen. Then I assume a reasonable draw ratio of 77%. With 30 Elo points gap, I get in one million simulations:

Code: Select all

Carlsen wins :  62.5%
Anand wins:     16.8%
Drawn match:    20.7%

After the tiebreak

Carlsen wins: 68.7%
Anand wins:   31.3%

So, with these assumptions, the odds of a drawn 12 game match seem overvalued by betters (or the gain is too small to bet on that). There are more people betting on the winner than on the tiebreak possibility, so 69%/31% is more reliable than ~30% for a drawn match.

Then the probabilities would be:

Code: Select all

Carlsen wins: 54%.
Anand wins:   16%.
Drawn match:  30%.

With equal opportunities in the tiebreak:

Carlsen wins: 54% + (30%)/2 = 69%.
Anand wins:   16% + (30%)/2 = 31%.

I toyed a little with Elo difference and draw ratio parameters, running 1e+6 and 1e+7 simulations as fast filters. This is what I got after 1e+9 simulations with Elo difference = 20 and draw ratio = 86%:

Code: Select all

1e+9 simulations:

Carlsen wins:            543435023 (54.34%)
Anand wins:              158639839 (15.86%)
Drawn matches:           297925138 (29.79%)

Approximated elapsed time: 1232.50 seconds.

The draw ratio of Anand's classical time control games was over 83% (10 out of 12 games) in the last WCC against Gelfand.

Regards from Spain.

Ajedrecista.

I ran 100 million simulations with your parameters (Elo difference = 30 and draw ratio = 77%) just to confirm your numbers:

Code: Select all

1e+8 simulations:

Carlsen wins:             62621170 (62.62%)
Anand wins:               16712563 (16.71%)
Drawn matches:            20666267 (20.67%)

Approximated elapsed time:  125.68 seconds.

More less: 62.62% + (30%)*(20.67%) ~ 68.82% for Carlsen under your assumptions; for Anand: 100% - 68.82% = 31.18%. Your numbers are confirmed, as expected.

I toyed again with the parameters until I got something like {Carlsen wins, Anand wins, drawn match} ~ {60%, 10%, 30%}; in that case: 60% + (30%)*(30%) = 69% and 100% - 69% = 31%. I got very good approximations with Elo difference = 25.2 and draw ratio = 87.6% after 100 million simulations:

Code: Select all

1e+8 simulations:

Carlsen wins:             60015189 (60.02%)
Anand wins:                9993052  (9.99%)
Drawn matches:            29991759 (29.99%)

Approximated elapsed time:  122.02 seconds.

It was a good exercise of handmade tuning by the old method of trial and error.

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hello:

Sorry for bumping this thread but the WCC is getting closer and I discovered this recent ChessBase article by chance:

Are the chess World Champions just lucky? Part 3

This article is somewhat statistical, just like the posts by Kai and me in this topic. Who knows which outcome will have the WCC...

Regards from Spain.

Ajedrecista.

[IGarcia]

Hello:

Sorry for bumping this thread but the WCC is getting closer and I discovered this recent ChessBase article by chance:

Are the chess World Champions just lucky? Part 3

This article is somewhat statistical, just like the posts by Kai and me in this topic. Who knows which outcome will have the WCC...

Regards from Spain.

Ajedrecista.

After several assumptions and simulations he concludes (in part 2):

The brevity of the match mitigates Anand’s disadvantage: in a 24 game match with a 66% draw rate, he loses in 98% of the match simulations and wins only 0.7% of the matches. But in a twelve game match, maybe he’ll just get lucky.

Besides the article is interesting, in the end, the problem is the lack of samples. His conclusion can be resumed by a child:

in a 12 game match, If strongest (by ELO) wins is because its strongest. If not, was luck.

[Laskos]

Hello:

Sorry for bumping this thread but the WCC is getting closer and I discovered this recent ChessBase article by chance:

Are the chess World Champions just lucky? Part 3

This article is somewhat statistical, just like the posts by Kai and me in this topic. Who knows which outcome will have the WCC...

Regards from Spain.

Ajedrecista.

Most of the betters are still stuck at 69%/31%, but one already has 73%/27%, approaching these computer simulations. Sill, the article overvalues Carlsen's odds, and I have more confidence in betters than in these simulations.

[Laskos]

Interesting, Jesus. The folks who are betting in UK give 2 to Anand and 4/11 to Carlsen, in percentages, 69% to Carlsen and 31% to Anand.

I think that the simulation with 54 Elo points gap (adjusted by the particular gameplay between these two players) and 66% draw rate is the best. That gives

Carlsen wins: 75.7%
Anand wins: 11.2%
Drawn match: 13.1%

It seems to approach to what the betters think.

Jesus, it seems that the betters start to converge to out simulations:

4/13 Carlsen, 19/7 Anand the best bets, meaning 74% for Carlsen. One month ago it was 69% for Carlsen. We should have placed on Carlsen large amounts when we first performed the simulations.

[Albert Silver]

Interesting, Jesus. The folks who are betting in UK give 2 to Anand and 4/11 to Carlsen, in percentages, 69% to Carlsen and 31% to Anand.

I think that the simulation with 54 Elo points gap (adjusted by the particular gameplay between these two players) and 66% draw rate is the best. That gives

Carlsen wins: 75.7%
Anand wins: 11.2%
Drawn match: 13.1%

It seems to approach to what the betters think.

Jesus, it seems that the betters start to converge to out simulations:

4/13 Carlsen, 19/7 Anand the best bets, meaning 74% for Carlsen. One month ago it was 69% for Carlsen. We should have placed on Carlsen large amounts when we first performed the simulations.

Match play is completely different from tournament play. I don't think the stats can be properly calculated to factor this in. Consider Aronian, a great tournament player, who has consistently fumbled in matches.

[Uri Blass]

Interesting, Jesus. The folks who are betting in UK give 2 to Anand and 4/11 to Carlsen, in percentages, 69% to Carlsen and 31% to Anand.

I think that the simulation with 54 Elo points gap (adjusted by the particular gameplay between these two players) and 66% draw rate is the best. That gives

Carlsen wins: 75.7%
Anand wins: 11.2%
Drawn match: 13.1%

It seems to approach to what the betters think.

Jesus, it seems that the betters start to converge to out simulations:

4/13 Carlsen, 19/7 Anand the best bets, meaning 74% for Carlsen. One month ago it was 69% for Carlsen. We should have placed on Carlsen large amounts when we first performed the simulations.

Match play is completely different from tournament play. I don't think the stats can be properly calculated to factor this in. Consider Aronian, a great tournament player, who has consistently fumbled in matches.

Let talk about tournament time control and not faster time control.

Aronian drew his last match 3-3 against kramnik in april 2012 when the difference in rating was very small(only 19 elo).

Earlier in may 2011 he drew 2-2 against Alexander Grischuk inspite of health problems in this specific match based on my memory.
He had only 61 elo advantage in this match.

I see no evidence to support the theory that aronian is worse in matchs and I think that he was unlucky to suffer from health problems or to have matchs that are too short.

Note also that Carlsen has 95 elo rating advantage relative to anand and I do not remember Aronian lose a match with this big rating advantage.

Uri

[kasinp]

Interesting, Jesus. The folks who are betting in UK give 2 to Anand and 4/11 to Carlsen, in percentages, 69% to Carlsen and 31% to Anand.

I think that the simulation with 54 Elo points gap (adjusted by the particular gameplay between these two players) and 66% draw rate is the best. That gives

Carlsen wins: 75.7%
Anand wins: 11.2%
Drawn match: 13.1%

It seems to approach to what the betters think.

Jesus, it seems that the betters start to converge to out simulations:

4/13 Carlsen, 19/7 Anand the best bets, meaning 74% for Carlsen. One month ago it was 69% for Carlsen. We should have placed on Carlsen large amounts when we first performed the simulations.

Match play is completely different from tournament play. I don't think the stats can be properly calculated to factor this in. Consider Aronian, a great tournament player, who has consistently fumbled in matches.

Let talk about tournament time control and not faster time control.

Aronian drew his last match 3-3 against kramnik in april 2012 when the difference in rating was very small(only 19 elo).

Earlier in may 2011 he drew 2-2 against Alexander Grischuk inspite of health problems in this specific match based on my memory.
He had only 61 elo advantage in this match.

I see no evidence to support the theory that aronian is worse in matchs and I think that he was unlucky to suffer from health problems or to have matchs that are too short.

Note also that Carlsen has 95 elo rating advantage relative to anand and I do not remember Aronian lose a match with this big rating advantage.

Uri

I agree. In addition, most opinions on match play are based on ridiculously small data samples. I see no evidence to support a sweeping statement about (for instance) Aronian's performance in match play.

PK