LG rating for a 50-50 game?

Imagine a game here where players take turns flipping a coin, and the first player to flip heads wins. Over time, players' records would converge toward 50-50.

Over time, would everyone's LG rating for that game also be very close to 1500?

I ask because I've read references to the effects of time on our ratings, and wondered exactly what that was.

Cheers!

The active players would have an average rating somewhat higher than 1500, since some players lose their games on time.

Ignoring the timeouts I would expect a gaussian distribution of the ratings. (Apart from the problem that some players would probably find a way to cheat even in this game ;-) )

Not quite gaussian I think, since the rating increment is small when a high ranked played beats a low ranked player.

One way to manipulate one's rating would be to resign on the first move whenever one meets a lower ranked player.

Yes, the average of -everyone's- rating would be 1500 (as for all rated LG games other than Go). But the average of -active- players' ratings would be more or less than 1500 when the average ratings of dropouts was less or more than 1500.

Rather than going through all the coin flips, you could just give an immediate victory, to the 1st player in 2/3 of the games.

Since there is no skill, engines would be useless.

Since there is chance, Man-in-the-Middle would not work.

Cheating could still be done by using aliases. The probability of winning a tournament would be proportional to the number of identities you entered into it.

While the first player could resign before the first move when his or her expected ratings gain is negative, the second player doesn't get a chance to resign if the first player wins on the first move.

You're right that the first player has 2/3 chance of winning, corresponding to about 120 points rating difference. So one should take that into consideration.

Someone proposed this game to be implemented in LG. I'd like to see that!!

But instead, a bit more "intrincated" (but still pure-luck) game.

You toss a coin, if it's heads it's a point for you. If not it's a point for the opponent. The first to have 3 points wins.

I bet the bots would have far more points than other people ;-)

What about implementing Rock-paper-scissors ?

That would be great, Richard! Then we could help to prove or disprove the idea that there is some (small amount) of skill involved. There are even books about rock-paper-scissors strategy.

I strongly prefer the "toss a coin" game. But Rock-paper-scissors would be fun :-)

Here is an alternative to tossing a coin or rock-paper-scissors.

Two players A and B both pick a real number between 0 and 1. Let's say A picks a and B picks b.

A wins if 0 < a - b < 1/2 or b - a > 1/2. Otherwise, B wins.

I don't think Rock-Paper-Scissors is very interesting for human play, but it does make sense to create computer championships. The need of thousands of games to produce meaningful results makes it very boring for humans to explore this game.

The idea is the tournament master introduces some idiot-players on purpose. Idiot-players play preestablished sequences or have other predictable behavior such as repeating each time they lose, etc. This way, smart-players have to exploit the weaknesses of idiot-players and win more than (win, draw, loss) = (1/3,1/3,1/3). Random-players are unpredictable and smart-players win only (1/3,1/3,1/3) against them, but random players also win (1/3,1/3,1/3) against idiot-players, unlike smart-players. Therefore, the championship makes sense and smart-players win in the long term.

You don't need idiot players to break symmetry. If you have a tournament with prize points awarded only to those who finish in the top, say, 25%, everyone has incentive to abandon random strategy that is guaranteed to win about half the time. The task, then, is to divine what everyone else may do and beat that.

For instance, a winning strategy may be to sacrifice a few games at the beginning of a long series in order to appear predictable, and then to play in such a way as to beat the strategy one's opponent has been deceived into playing.

Prisoners' Dilemma bots went down similar paths a few decades ago.

I totally dig the idea of Rock Paper Scissors!

How about Rock Paper Scissors for bots only with 1000 rounds per match.

Oops someone already suggested it :-)

Ingo A. suggested 'Ratings Rally' which was a similar idea, years back. You had a limited time to make a move, which would result in a random outcome, so your strategy was to time moves when the ratings were most in your favour.

I think Rock Paper Scissors is silly and does not belong here. If we are going to have RPS, then maybe we could also have Tic Tac Toe and maybe War. If you want to add a game, add something with some depth, maybe Chinese Chess or Checkers.

Such bot competitions have already been done: http://webdocs.cs.ualberta.ca/~darse/rsbpc.html

Yes, Fatphil, I didn't intend to pose a new idea. I was just recalling Ingo's Rating Rally.

I'm sure RoRoRo would be far better than me in Rating Rally, if fine-tuned ;)