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Subject: Simulating the result of a single game by random numbers - Update!

Author: Christoph Fieberg

Date: 12:21:04 07/10/01

```I refer to to description of my program which simulates the result of a chess
game given under
http://www.icdchess.com/forums/1/message.shtml?178041

Deeper analysis showed amazing facts:
The advantage playing White for the weaker player is often twice as high as for
the stronger player given the same rating difference!

In case the rating difference is 50 – 170 points I found that the advantage is
20 - 31 Elo-points if White is the stronger player but 43 - 60 Elo-points if
Black is the stronger player. (Example: 2500 – 2350: adjusted difference is
2510/2515.5 – 2340/2334.5; but for 2350 – 2500: adjusted difference is
2371.5/2380 – 2478.5/2470)

In case the rating difference is more than 170 points the advantage is 20 – 46
Elo-points if White is stronger and 43 – 87 if Black is stronger.

However, for a rating difference below 50 points it seems that there is not such
an effect any more. I found that with about 85% likelihood the advantage is 21 –
56 Elo-points and with 15% likelihood the advantage is 0 – 79 Elo-points for
both cases (White player stronger, Black player stronger).

The second amazing fact is that I did not find that the conditioned draw
percentage (depending on the success rate) dropped below 50% and that in case
the higher rated player plays White the conditioned draw rate is somewhat higher
than if the lower rated player plays White.

I found a value in the range of 60% - 68% in case the rating difference is more
than 50 Elo-points and the stronger player plays White. If the weaker player
plays White the value is in the range 53 – 65%. For a difference below 50
Elo-points the value is 50% - 68% idependingly whether the stronger player plays
White or not.

Example:
Analysis of 9806 games with White 2570-2670 and Black 2370-2470

=> average 2598 – average 2427, rating difference 171 Elo-points
Results: 1-0 = 60.45%, ½ =31.37%, 0-1 = 8.18% => conditioned draw rate = 65.73%
(Success rate = 76.14%, Elo advantage White = 30.6 points)

comparing to analysis of 9403 games with White 2370-2470 and Black 2570-2670

=> average 2428 – average 2598, rating difference 170 Elo-points
Results: 1-0 = 13.00%, ½ = 43.15%, 0-1 = 43.85% => conditioned draw rate =
62.39%
(Success rate = 65.42%, Elo advantage White = 52.9 points)

I implemented these findings in my program. Adantage points and draw rates are
choosen randomly within in the appropriate ranges.

The program will be published on Frank Qusisinsky's chess pages (I will provide
the link later). I am a very amateurish programmer, the program is programmed in
Basic and runs under QBX (QuickBasic)[DOS-mode!], but at least it works and
provides nice results. It is able to simulate a single or double round robin for
up to 8 players and is able to state the likelihood for a certain player to
reach a certain rank (based on a choosen number of simulations).

Best regards,
Christoph Fieberg

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