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Definition of luck-to-skill ratio

Posted By: MaX
Date: Monday, 10 August 2009, at 2:19 p.m.

In Response To: Definition of luck-to-skill ratio (Frank Berger)

Frank said:

"You buy two identical computers and install your favorite chess programm, let's say Shredder and let them play each other with identical settings. When a game isn't draw, which explanation makes more sense: one of the computers was stronger in this game or there is a certain degree of luck involved?"

I'm confident that for any game where an optimal strategy exists (and where we forget about adapting our own optimal startegy to our opponent, or worse, to our perception of our opponent) the only thing you need to look at is your total error. After that you do the math in "Actual Result = Net Skill + Net Luck". In tic-tac-toe, as soon as you make a mistake against a perfect opponent, this will cost you the game (i.e. net skill will be fully responsible of the actual result, no luck).

Now, is there' more luck in chess or BG ? I don't know, I'm not even a chess player. It's easy to say BG just because of the dice, but how to prove it?

Can't we do the following ?

- let 2 equally strong players (e.g. the same bg bot) play BG against each other for N 11pt matches and record the outcomes.

- let 2 equally strong players (e.g. Shredder) play chess aganist ech other for N matches and record the outcomes.

Repeat the above M times and then plot the histogram (distribution) of the results. For example, with N = 4 and M = 100, you could get:

R Nbg Nch -4 10 02 -3 00 03 -2 20 05 -1 00 10 0 40 60 +1 00 10 +2 20 05 +3 00 03 +4 10 02

R is the actual result (for player A, a win is +1 a loss is -1, a draw is 0), Nbg is the number of times (over the M repetions) that A has experieced R as actual result (and Nch is the same in chess). A result like the above would tend to prove that there's less luck in chess (not considering that to have statsig you would probably need many more trials M and likely a larger N too). In the above data, on average each player wins 50%, but in BG the outcome has a larger variance than in chess. Skill being equal (and CONSTANT, thanks to bots) this must be due to luck. With larget M and N you may be able to see with which probability the actual result will be in the range (for example) -5% - +5% of the average.

Would the above make sense ?

MaX.

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