Page 4 of 4

Re: Gaming activity

Posted: Fri Oct 06, 2017 1:34 pm
by Kratzer
Thank you, Hagbard, for these insights. Very interesting! Good to know our community is active and growing! :)

Re: Gaming activity

Posted: Sat Oct 07, 2017 7:20 pm
by Hagbard
Distribution of tafl move times.

100000 tafl moves drawn from games since 2015 were analyzed for move times.
The diagram shows that this site has fast players!

Image


8000 tafl games since 2015 were analyzed for game times (time length of the games):

Image

Re: Gaming activity

Posted: Tue Dec 12, 2017 9:14 pm
by Hagbard
Probability of tie in a match of two games of Copenhagen Hnefatafl, when the players are equally strong.

Copenhagen game balance +1.50 means probability of
white win: 60%
black win: 40%

The match is a tie if both players win as black or if they both win as white.
Probability for this to happen is
60% * 60% + 40% * 40% = 52%.

To get a winner of the match, white must win in one game and black
in the other or reverse. Probability for this to happen is
60% * 40% + 40% * 60% = 48%.

So the outcome (tie or winner) of a two games match of Copenhagen with two equally strong players is like flipping a coin.

If a winner must be found, as fx. in the world championship tournament, a series of matches until one wins will most likely not be long:
The probability of one tie is 52%.
The probability of two ties in a row is 52% * 52% = 27%.
The probability of three ties in a row is 52% * 52% * 52% = 14%.
Etc.

Re: Gaming activity

Posted: Wed Dec 13, 2017 12:13 am
by Casshern
Hagbard wrote:
So the outcome (tie or winner) of a two games match of Copenhagen with two equally strong players is like flipping a coin.

If a winner must be found, as fx. in the world championship tournament, a series of matches until one wins will most likely not be long:
The probability of one tie is 52%.
The probability of two ties in a row is 52% * 52% = 27%.
The probability of three ties in a row is 52% * 52% * 52% = 14%.
Etc.
This is a very interesting statistic. I would prefer this method of tiebreaker (opponents playing two additional games), opposed to tiebreakers like game length or pieces captured. Or as I previously suggested, if players split games in consecutive rounds, each winning a game as black and a game as white, then I think the third round tiebreaker should only be one game to decide the winner. Which player plays which color should be decided randomly, either by a coin flip or a hat pull, by the umpire. In the event of a tie in the fifth game, players would switch colors and continue playing until a winner is found.

If players split games in two consecutive rounds (the round robin round and the addition tiebreaker round, no previous rounds), winning all games as either black or white, then perhaps we could use tiebreakers of game length or pieces captured to determine a winner. Although I am opposed to such tiebreakers, I understand this is the real world and players can potentially continue to split games. So, such tiebreakers is could at least be a means to find a winner. Anyways, the need for an extra tiebreaker round has been rare to this point. I think for sure we should not go past a third round to determine a tournament champion. Depending on the players playing pace, the games could potentially last for months.

This is all just food for thought moving forward. I don’t know what’s the best tiebreaker method. I just prefer playing games not having to worry about game length, pieces captured, or if you lost a game to a weak or strong opponent.

Re: Gaming activity

Posted: Wed Dec 13, 2017 11:04 am
by Hagbard
Probability of tie in a match of two tafl games as consequence of game balance.

Game balance 1.00 (perfect) means probability of
white win: 50%
black win: 50%
The match is a tie if both players win as black or if they both win as white. Probability for this to happen is
50% * 50% + 50% * 50% = 50.0%

Game balance +1.50 means probability of
white win: 60%
black win: 40%
Probability for a match to be a tie is 60% * 60% + 40% * 40% = 52.0%

Game balance +1.60 means probability of
white win: 61.5%
black win: 38.5%
Probability for a match to be a tie is 61.5% * 61.5% + 38.5% * 38.5% = 52.6%

Game balance +1.70 means probability of
white win: 63.0%
black win: 37.0%
Probability for a match to be a tie is 63% * 63% + 37% * 37% = 53.4%

Game balance +1.80 means probability of
white win: 64.3%
black win: 35.7%
Probability for a match to be a tie is 64.3% * 64.3% + 35.7% * 35.7% = 54.1%

Game balance +1.90 means probability of
white win: 65.5%
black win: 34.5%
Probability for a match to be a tie is 65.5% * 65.5% + 34.5% * 34.5% = 54.8%

Game balance +2.00 means probability of
white win: 66.7%
black win: 33.3%
Probability for a match to be a tie is 66.7% * 66.7% + 33.3% * 33.3% = 55.6%

...

Game balance +infinite means probability of
white win: 100%
black win: 0%
Probability for a match to be a tie is 100% * 100% + 0% * 0% = 100%

==========================================================================

More ties means simultaneously fewer matches with a winner.
Calculation of ratio ties/winner:

Game balance 1.00 (perfect): 50% / 50% = 1
Game balance 1.50: 52.0% / 48.0% = 1.08
Game balance 1.60: 52.6% / 47.4% = 1.11
Game balance 1.70: 53.4% / 46.6% = 1.15
Game balance 1.80: 54.1% / 45.9% = 1.18
Game balance 1.90: 54.8% / 45.2% = 1.21
Game balance 2.00: 55.6% / 44.4% = 1.25
...
Game balance +infinite: 100% / 0% = infinite

The game balance where the perfect ratio 1 deviates by 10% and becomes ratio 1.10 is reached at
game balance 1.56

This matches well the intuitive sensation (at least mine) that unbalanced tafl games work well up to a limit of a bit more than game balance 1.50
(Fx. Copenhagen bal. +1.51, Fetlar bal. +1.41, Sea Battle 9x9 +1.55, Brandubh +1.32 and so on).

Re: Gaming activity

Posted: Wed Dec 13, 2017 7:26 pm
by Hagbard
Corey Hart ("Brench") says in an educational video (time 6.00):
https://www.youtube.com/watch?v=5Cr2fZXKoW8
That's not as balanced as chess. But real game balance is very diffucult in an asymmetric game, and given that the asymmetry is part of the charm of this particular game ... that kind of game balance is really good enough.
I think if a variant of hnefatafl or any tafl game is too balanced, it does begin to lose some of its charm.
This is an interesting view! Perhaps part of the explanation, why the Copenhagen Hnefatafl (game balance +1.51) functions so well?