# Win probability statistics

- Updated Thursday, September 24th 2015 @ 00:28:48
I did some simulations on semifinals and finals matches, based on historic win percentages of each individual pair of bots.

For estimating the win percentages per pair of bots, I used all game results since the 6th of August, and I included only those games, where both bots played with their final version. If there were less than 10 games (actually 10 of bot 1 as player1 and 10 of bot 2 as player1), I also counted older games, where one of the bots or both played with an older version. If then still there were less than 10 games, then I estimated the rest based on the difference in ELO's.

For the semifinals, I use the real schema. For the finals, I simulate with random schemas.

After the first two rounds of the semifinals (round 1 and loosers round 2), these are my estimated percentages for the winner of Warlight 2:

GreenTea 28% Zoulander 28% Anila8 24% LuckyBot 9% Pinky 5% RealityBomb 3% TheBrain 2% locutus 1% CarrotBot 1%

And the expected win amounts in EUR:

GreenTea 452 Zoulander 437 Anila8 401 LuckyBot 210 Pinky 157 TheBrain 105 RealityBomb 98 locutus 66 CarrotBot 64 chaos 30 Legioner 14 Invader 2 ButterReborn 2 Fury 1 Bolt 1

Regards, Ad

- Created Thursday, September 24th 2015 @ 02:16:08
Haha interesting calculations. I wonder what is going to happen. I am always surprised by the results in the game!

- Created Thursday, September 24th 2015 @ 10:02:22
Very nice :D.. we shall see this sunday!

- Created Thursday, September 24th 2015 @ 18:34:52
The EUR 210 prize looks for me optimistic after losing in the 1st round :)))

- Created Thursday, September 24th 2015 @ 20:50:19
@Cheeser: that's not so strange. You still have a good chance to make it to the finals: 72% according to my simulations:)

I'll publish new calculations tonight after the next round:)

- Updated Friday, September 25th 2015 @ 08:01:28
Win probabilities and expected EUR amounts after winners round 3:

- Zoulander 30% 467
- GreenTea 25% 425
- Anila8 22% 386
- Pinky 8% 239
- LuckyBot 9% 196
- RealityBomb 2% 95
- locutus 1% 95
- TheBrain 1% 85
- chaos 0% 31
- CarrotBot 0% 14
- ButterReborn 0% 2
- Invader 0% 2
- Fury 0% 1
- Bolt 0% 1

Most notable difference with the previous list is that Pinky went up quite a bit and CarrotBot went down quite a bit. That's because the match Pinky - CarrotBot was won by Pinky, whereas the probability was about 50-50 for this match.

Furthermore GreenTea and Zoulander swapped places. That's because I fixed a small bug in the calculations. Note however that the differences in the top 3 are still small

The best chance to make it to the finals in the loosers pool are:

- RealityBomb - 68%
- LuckyBot - 62%
- chaos - 45%

- Updated Friday, September 25th 2015 @ 19:41:23
Your percentages take into account that bots play multiple times against each other? Something like if bot A wins 70% against bot B then, depending on the amount of games played bot A gets a nearby 100% win chance in total? I guess you don't even know the format of the finals, last time less games were played.

- Updated Friday, September 25th 2015 @ 20:19:27
@Norman: I think in your case bot A gets a nearby 100% chance TO WIN 1 GAME of all :)

For bot A to win 7 games of 12 and lose 5 is equal to COMBIN(12;7) * (0.7)^7 * (0.3)^5 = 15%

And so on...

- Created Friday, September 25th 2015 @ 20:31:29
Yes, I take the number of games per match into account: in the semifinals, a match is over when the best player wins 7 games, with a difference of at least 2. This means that a win percentage per game of 70% leads to a win percentage per match of 95%. A win percentage of 60% per game leads to a win percentage per match of about 80%.

For the finals, I assume that a match is over when the best player wins 3 games. That was at least the format of the Heads up Omaha finals.

By the way, the percentages will probably change significantly when the finals schema is known. It makes quite a difference whether you play against the nr. 1 or the nr. 8 in the first round of the finals. The current calculations are based on random finals schemas.

I don't pretend that my calculations are 100% scientifically correct, but given the limited information, I think they give a pretty good indication of the real win chances. And it was fun to calculate:)

- Created Friday, September 25th 2015 @ 23:29:34
Hi AdsRiskbot, thanks for interesting topic! Intuitively i feel that your calculations are correct. However i think count of games between bots are not enough to make good predictions of bots power.

- Created Saturday, September 26th 2015 @ 02:11:35
@GreenTea: I agree that the number of games is quite limited, especially for the bots, for which a new version was uploaded just before lockdown (which was the case for almost all bots in the old top 10). In that case I included some games of older versions as well in the estimated win percentage, but the reliability of those predictions may drop considerably if the new version is really different than the older versions.

- Updated Saturday, September 26th 2015 @ 02:36:45
Win probabilities and expected EUR amounts after loosers round 4:

- Zoulander 29% 448
- GreenTea 25% 423
- Anila8 24% 402
- Pinky 10% 275
- RealityBomb 4% 132
- LuckyBot 5% 114
- locutus 1% 94
- TheBrain 1% 84
- CarrotBot 1% 55
- Fury 0% 7
- Bolt 0% 5
- iNet 0% 1

Best chances to make it to the finals:

- RealityBomb 84%
- CarrotBot 46%
- LuckyBot 34%

Note that LuckyBot has a fairly small chance to make it to the finals, because his next opponent is CarrotBot, which is a tough opponent for him. But if he makes it to the finals, his chances are quite good.

- Created Saturday, September 26th 2015 @ 09:26:58
Bolt would take the 5 EUR and run. Thanks for doing it Ad, it's indeed interesting :)

I feel sad I haven't had time to put more work into Bolt (or the other competitions for that matter).

I'm working on a lot of open source stuff right now, perhaps most notably a smart scraping framework, maybe some of you guys are interested ^^

- Updated Sunday, September 27th 2015 @ 00:13:10
And RealityBomb is facing the bot which just crushed him 7-1. Actually it isn't surprising me that RealityBomb does, compared to the other finalists, very well against weaker bots while struggling against stronger bots. This is because he is exploiting weak patterns in the opponents play (opponent deployed last turn almost nothing to an important spot so he also won't do this turn) and thus gets exploited himself when facing a kinda sound opponent.