# Computer Chess Club Archives

## Messages

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

Author: Christoph Fieberg

Date: 10:24:32 08/02/01

```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.

I will provide you with the link when the program will be published on the
web(Frank Quisinsky offered to do it). I am a very amateurish programmer, the
program is programmed in Basic and runs under QuickBasic, 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

```