Hello again:

simonhue wrote:Ajedrecista wrote:
This tool is great!

http://www.chess-db.com/public/perfprob.jsp
I did not know about its existance. I wonder what are the algorithm for this calculator... I remind that I used a probability of draw of 22% that could be too high (it was only an assumption).

I use a trinomial distribution; any info about this online tool will be much appreciated. Thank you very much for the link!

Regards from Spain.

Ajedrecista.

The draw rates are derived from practical statistics:

http://www.chess-db.com/public/research/draw_rate.html
In Ivanov's case ~18% range.

The tool works by enumerating all possible outcomes, and calculating the probability for each to occur. Then summing all this.

Thank you very much: it is what I wanted to know.

My tool uses an average of opponent's ratings (which is only an approximation) instead of each individual rating but I also knew that lowering my input probability of draw will bring closer results to ones of that online tool:

Probability to achieve exactly 0.0 points: 0.138820124747056877, ~1/7

Probability to achieve exactly 0.5 points: 0.238072629609693951, ~1/4

Probability to achieve exactly 1.0 points: 0.251974802537574517, ~1/3

Probability to achieve exactly 1.5 points: 0.185493573683177635, ~1/5

Probability to achieve exactly 2.0 points: 0.107187749981418433, ~1/9

Probability to achieve exactly 2.5 points: 0.049993388386886888, ~1/20

Probability to achieve exactly 3.0 points: 0.019559795430256514, ~1/51

Probability to achieve exactly 3.5 points: 0.006478139355314301, ~1/154

Probability to achieve exactly 4.0 points: 0.001847704350396042, ~1/541

Probability to achieve exactly 4.5 points: 0.000454071696103204, ~1/2202

Probability to achieve exactly 5.0 points: 0.000096905701835080, ~1/10319

Probability to achieve exactly 5.5 points: 0.000017842617809472, ~1/56045

**Probability to achieve exactly 6.0 points: 0.000002839414544516, ~1/352185**

Probability to achieve exactly 6.5 points: 0.000000384105179786, ~1/2603453

Probability to achieve exactly 7.0 points: 0.000000043967536769, ~1/22744053

Probability to achieve exactly 7.5 points: 0.000000004093525465, ~1/244288207

Probability to achieve exactly 8.0 points: 0.000000000305136562, ~1/3277221165

Probability to achieve exactly 8.5 points: 0.000000000015997155, ~1/62511114977

Probability to achieve exactly 9.0 points: 0.000000000000556751, ~1/1796132763944

---

Probability to achieve >= 0.0 points: 0.999999999999999927, ~1/1

Probability to achieve >= 0.5 points: 0.861179875252943049, ~1/1

Probability to achieve >= 1.0 points: 0.623107245643249098, ~1/1

Probability to achieve >= 1.5 points: 0.371132443105674580, ~1/2

Probability to achieve >= 2.0 points: 0.185638869422496945, ~1/5

Probability to achieve >= 2.5 points: 0.078451119441078511, ~1/12

Probability to achieve >= 3.0 points: 0.028457731054191623, ~1/35

Probability to achieve >= 3.5 points: 0.008897935623935108, ~1/112

Probability to achieve >= 4.0 points: 0.002419796268620807, ~1/413

Probability to achieve >= 4.5 points: 0.000572091918224764, ~1/1747

Probability to achieve >= 5.0 points: 0.000118020222121559, ~1/8473

Probability to achieve >= 5.5 points: 0.000021114520286479, ~1/47360

**Probability to achieve >= 6.0 points: 0.000003271902477007, ~1/305632**

Probability to achieve >= 6.5 points: 0.000000432487932491, ~1/2312203

Probability to achieve >= 7.0 points: 0.000000048382752704, ~1/20668522

Probability to achieve >= 7.5 points: 0.000000004415215934, ~1/226489488

Probability to achieve >= 8.0 points: 0.000000000321690469, ~1/3108578264

Probability to achieve >= 8.5 points: 0.000000000016553906, ~1/60408700663

Probability to achieve >= 9.0 points: 0.000000000000556751, ~1/1796132763944

Doing a little of trial and error, if I input D = 15.4% (there are better values, for sure):

Code: Select all

```
Probabilities_in_a_trinomial_distribution, ® 2013.
--------------------------------------------------------------------
Probabilities of all possible scores in a match between two engines.
--------------------------------------------------------------------
Write down the number of games of the match (up to 50):
9
Write down the engines rating difference (between -800 Elo and 800 Elo):
-345.44
Probability of a draw (%) between 0 % and 24.08 %
15.4
Write down the clock rate of the CPU (in GHz), only for timing the elapsed time of the calculations:
3
The results have been saved to Probabilities.txt file.
End of the calculations. Approximated elapsed time: 40 ms.
Thanks for using Probabilities_in_a_trinomial_distribution. Press Enter to exit.
```

Code: Select all

```
Probabilities for a match of 9 games (rounded up to 0.0001%):
Rating difference (rounded up to 0.01 Elo): -345.44 Elo.
Probability of a win = W ~ 4.3414 %
Probability of a draw = D ~ 15.4000 %
Probability of a lose = L ~ 80.2586 %
----------------------------------------------------
Points: 9.0/ 9
+ 9 = 0 - 0
P ~ 0.0000 %
Probability of win 9.0 points out of 9: 0.0000 %
----------------------------------------------------
Points: 8.5/ 9
+ 8 = 1 - 0
P ~ 0.0000 %
Probability of win 8.5 points out of 9: 0.0000 %
----------------------------------------------------
Points: 8.0/ 9
+ 7 = 2 - 0
P ~ 0.0000 %
+ 8 = 0 - 1
P ~ 0.0000 %
Probability of win 8.0 points out of 9: 0.0000 %
----------------------------------------------------
Points: 7.5/ 9
+ 6 = 3 - 0
P ~ 0.0000 %
+ 7 = 1 - 1
P ~ 0.0000 %
Probability of win 7.5 points out of 9: 0.0000 %
----------------------------------------------------
Points: 7.0/ 9
+ 5 = 4 - 0
P ~ 0.0000 %
+ 6 = 2 - 1
P ~ 0.0000 %
+ 7 = 0 - 2
P ~ 0.0000 %
Probability of win 7.0 points out of 9: 0.0000 %
----------------------------------------------------
Points: 6.5/ 9
+ 4 = 5 - 0
P ~ 0.0000 %
+ 5 = 3 - 1
P ~ 0.0000 %
+ 6 = 1 - 2
P ~ 0.0000 %
Probability of win 6.5 points out of 9: 0.0000 %
----------------------------------------------------
Points: 6.0/ 9
+ 3 = 6 - 0
P ~ 0.0000 %
+ 4 = 4 - 1
P ~ 0.0001 %
+ 5 = 2 - 2
P ~ 0.0002 %
+ 6 = 0 - 3
P ~ 0.0000 %
Probability of win 6.0 points out of 9: 0.0003 %
----------------------------------------------------
Points: 5.5/ 9
+ 2 = 7 - 0
P ~ 0.0000 %
+ 3 = 5 - 1
P ~ 0.0003 %
+ 4 = 3 - 2
P ~ 0.0011 %
+ 5 = 1 - 3
P ~ 0.0006 %
Probability of win 5.5 points out of 9: 0.0020 %
----------------------------------------------------
Points: 5.0/ 9
+ 1 = 8 - 0
P ~ 0.0000 %
+ 2 = 6 - 1
P ~ 0.0005 %
+ 3 = 4 - 2
P ~ 0.0037 %
+ 4 = 2 - 3
P ~ 0.0055 %
+ 5 = 0 - 4
P ~ 0.0008 %
Probability of win 5.0 points out of 9: 0.0106 %
----------------------------------------------------
Points: 4.5/ 9
+ 0 = 9 - 0
P ~ 0.0000 %
+ 1 = 7 - 1
P ~ 0.0005 %
+ 2 = 5 - 2
P ~ 0.0080 %
+ 3 = 3 - 3
P ~ 0.0260 %
+ 4 = 1 - 4
P ~ 0.0143 %
Probability of win 4.5 points out of 9: 0.0487 %
----------------------------------------------------
Points: 4.0/ 9
+ 0 = 8 - 1
P ~ 0.0002 %
+ 1 = 6 - 2
P ~ 0.0094 %
+ 2 = 4 - 3
P ~ 0.0691 %
+ 3 = 2 - 4
P ~ 0.1015 %
+ 4 = 0 - 5
P ~ 0.0149 %
Probability of win 4.0 points out of 9: 0.1950 %
----------------------------------------------------
Points: 3.5/ 9
+ 0 = 7 - 2
P ~ 0.0048 %
+ 1 = 5 - 3
P ~ 0.0980 %
+ 2 = 3 - 4
P ~ 0.3599 %
+ 3 = 1 - 5
P ~ 0.2115 %
Probability of win 3.5 points out of 9: 0.6741 %
----------------------------------------------------
Points: 3.0/ 9
+ 0 = 6 - 3
P ~ 0.0579 %
+ 1 = 4 - 4
P ~ 0.6383 %
+ 2 = 2 - 5
P ~ 1.1253 %
+ 3 = 0 - 6
P ~ 0.1837 %
Probability of win 3.0 points out of 9: 2.0053 %
----------------------------------------------------
Points: 2.5/ 9
+ 0 = 5 - 4
P ~ 0.4528 %
+ 1 = 3 - 5
P ~ 2.6612 %
+ 2 = 1 - 6
P ~ 1.9550 %
Probability of win 2.5 points out of 9: 5.0690 %
----------------------------------------------------
Points: 2.0/ 9
+ 0 = 4 - 5
P ~ 2.3600 %
+ 1 = 2 - 6
P ~ 6.9346 %
+ 2 = 0 - 7
P ~ 1.4555 %
Probability of win 2.0 points out of 9: 10.7501 %
----------------------------------------------------
Points: 1.5/ 9
+ 0 = 3 - 6
P ~ 8.1995 %
+ 1 = 1 - 7
P ~ 10.3259 %
Probability of win 1.5 points out of 9: 18.5254 %
----------------------------------------------------
Points: 1.0/ 9
+ 0 = 2 - 7
P ~ 18.3140 %
+ 1 = 0 - 8
P ~ 6.7268 %
Probability of win 1.0 points out of 9: 25.0408 %
----------------------------------------------------
Points: 0.5/ 9
+ 0 = 1 - 8
P ~ 23.8613 %
Probability of win 0.5 points out of 9: 23.8613 %
----------------------------------------------------
Points: 0.0/ 9
+ 0 = 0 - 9
P ~ 13.8173 %
Probability of win 0.0 points out of 9: 13.8173 %
```

Then, my results are much more similar than before with respect to the web you linked to.

Regards from Spain.

Ajedrecista.