# Carlsen vs karjakin

• #21

Do you know ....?

What the probability of Carlsen winning chance in 12 games head to head vs Karjakin, given the statistics of 15 games they played? Assume a win is 1 point, a draw is 0.5, a lose is 0.

The computation is quite complex.

There are 3 outcomes when they play 1 game: 0, 0.5, and1.

There are 5 outcomes when they play 2 games: 0, 0.5, 1, 1.5, and 2.

There are 7 outcomes when they play 3 games: 0, 0.5, 1, 1.5, 2, 2.5, and 3.

There are 9 outcomes when they paly 4 games : 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5 and 4.

So, there are 25 outcomes when they play 12 games.

Continued ......

• #22

The number of outcomes of the event C1 = {Carlsen wins in 1 game head to head with Karjakin } = 1 i.e. 1.

The number of outcomes of the event C2 = {Carlsen wins in 2 games head to head with Karjakin } = 2 i.e. 1.5 and 2.

So, The number of outcomes of the event C12 = {Carlsen wins in 12 game head to head with Karjakin } = 12 i.e. 6.5, 7,.....12.

Continued.....

• #23

There are 3 outcomes in 1 game head to head, 0, 0.5 and 1

There are 9 outcomes in 2 games head to head : 0,0; 0,0.5; 0,1; 0.5,0; 0.5,0.5; 0.5,1; 1,0; 1, 0,5; and 1,1.

So, there are 3^12 = 531,441 outcomes in 12 games head to head.

Fantastics.

Continued ....

• #24

I have calculated the chance of {Carlen wins in 1 game head to head} is 26,67%. Draw = 66,67%, and lose = 6,67%

the chance of {Carlen wins in 2 games head to head} is 42.67%.

Draw = 48%, and lose = 9.33 %.

Instead of calculating the exact chance of Carlsen wins in 12 games head to head, we can conclude.

1. We know the chance of Carlsen wins in 12 games head to head is less than they draw.

2. Based on 1, Carlsen wins in 12 games head to head is always less than 50%.

Finish.

• #25

I am not happy with my answer on the last post, post #27.

So I try to find a software to do the calculation, so far in vain.

So, I run simulation on Excel Worksheet with Random number generator.

And, SURPRISE!! My post #27 is completely wrong.

But noone do anything with it.

Continued ......

• #26

The results of simulations are completely a surprise. I run 4 simulations with each they play 25 matches of 12 games head to head in each match.

Here are the results:

Simulation 1: 22 win for Carlsen wins with his score above 6 point = 88%

1 draw when they both score 6 points =4%

2 times Karjakin wins with his score above 6 points = 8%

Simulation 2: 18 wins for Carlsen = 72%

4 draws = 16 %

3 wins for Karjakin = 12%

Simulation 3: 16 wins for Carlsen = 64 %

5 draws = 20%

4 wins for Karjakin = 16%

Simulation 4: 20 wins for Carlsen = 80 %

1 draw = 4%

3 wins for Karjakin = 12%

Convincingly, Carlsen will win at least 16 matches when they play 25 matches of 12 games head to head.

Convincingly, Karjakin only will win less than 6 matches when they play 25 matches of 12 games head to head.

Convincingly they will draw at least once of 6-6, but less than 6 times of draw 6-6.

So, if anyone is interested in this math analysis, they can easily produce a senior university or graduate project or even a master thesis. Good Luck.

One last thing, please somebody prove me wrong in all of this. I will be very very happy.

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