Life In 19x19

jlt wrote:The last three probabilities imply that all players have the same Elo rating. This not consistent with the first probability.

Uberdude wrote:Elo ratings are not consistent with reality

Skill at go involves a number of different subskills. If we assign a number to represent the level of each subskill, then we get a vector which represents overall skill at go. Reducing this vector to a single number (rating) loses information. That means that any calculation of probability between two players based upon their ratings will have some degree of error. Furthermore, transitivity will not hold. Even using dan/kyu ranks, which cover a much broader range of skill than Elo ratings, is not enough to guarantee transitivity. Skill at go is only partially ordered.

The example given is extreme to illustrate the point. Real cases where, say, Player A1 can beat Player B1 with probability 60% while the other probabilities remain 50% certainly seem possible.

Yes the presumption is that transitivity does not always hold, and that causes ordering to matter. I've heard Yoda Norimoto had quite good results against Lee Changho when Lee was dominating in the 90's. Others can think of other examples.

By the way, to the extent that this is an actual issue, a mixed strategy seems to be the correct one where some randomizing goes on. (Japan would want to align Yoda so that he faces Lee Changho, and Korea would want to prevent that from happening. So it would be like hide and seek)

jlt wrote:Suppose (as in Elo's theory) that there exist positive numbers a(i) and b(j) such that the probability that player A_i wins against player B_j is a(i)/(a(i)+b(j)).

mhlepore wrote:Probability that A1 beats B1 = 1
...
Probability that A2 beats B1 = 0.5

Your assumptions doesn't seem to match (p=1).

My attempt with my model proposed earlier, which may be closer to practical reality: we represent each player as a normally distributed random variable with known ev and deviation (his distribution of point drops in each game (compared to perfect play), independent of opposition for simplicity - a doubtful assumption OC). The player whose number/performance sample turns out to be above the opponent's wins the game in question.

I took a quick look at a random example (two teams two players each), and in this model order seems to matter slightly (even without rps-like dependencies, each player showing the same strength against each opponent).

This seems to be related to that each player can have different deviation (at least in this example order matters only if deviations are not the same).

Yes, of course I am aware that representing go skill with a single number (Elo rating) is not enough, but in the absence of other information, we have no other way to estimate winning probabilities than using Elo's theory. A better way to estimate the probability that A wins against B would be to use a formula which uses both Elo ratings and past game records of A against B.

First game in a week: Mateusz Surma vs Andy Liu. AGA putting out their big gun first.

Uberdude wrote:First game in a week: Mateusz Surma vs Andy Liu. AGA putting out their big gun first.

In the Surrounding Game documentary, Andy Liu is mentioned as having a goal to win 40 times in a row in fast training games against 9d players on Tygem.

Not sure if he ever achieved that goal, but winning 6 in a row in this match should be relatively easy, just talking numbers-wise

sorin wrote: In the Surrounding Game documentary, Andy Liu is mentioned as having a goal to win 40 times in a row in fast training games against 9d players on Tygem.

Maybe I should watch it again, but as I recall it wasn't clear at what rank he started that 40 game set. There was this implication that if you had a long winning streak, then maybe a top pro would deign to play you. I think AlphaGo master proved that, yes, they will.

Calvin Clark wrote:

sorin wrote: In the Surrounding Game documentary, Andy Liu is mentioned as having a goal to win 40 times in a row in fast training games against 9d players on Tygem.

Maybe I should watch it again, but as I recall it wasn't clear at what rank he started that 40 game set. There was this implication that if you had a long winning streak, then maybe a top pro would deign to play you. I think AlphaGo master proved that, yes, they will.

I think it was purely a personal challenge. It was definitely reported during the time he was fighting to become 1p, so he must have been already 9d Tygem, but he may have challenged himself like that earlier in his career.

Math is definitely against one winning 40 times in a row as long as they play opponents within 2-3 stones strength.

sorin wrote:

Calvin Clark wrote:

sorin wrote: In the Surrounding Game documentary, Andy Liu is mentioned as having a goal to win 40 times in a row in fast training games against 9d players on Tygem.

Maybe I should watch it again, but as I recall it wasn't clear at what rank he started that 40 game set. There was this implication that if you had a long winning streak, then maybe a top pro would deign to play you. I think AlphaGo master proved that, yes, they will.

I think it was purely a personal challenge. It was definitely reported during the time he was fighting to become 1p, so he must have been already 9d Tygem, but he may have challenged himself like that earlier in his career.

Math is definitely against one winning 40 times in a row as long as they play opponents within 2-3 stones strength.

(edit: managed to somehow not add my comment at all, now added)

If you play enough games then the chances of eventually seeing a winning streak of 40 tends towards certainty. (just by luck if not skill.) Iirc this was slightly similar to Andy Liu's approach.

Winning a set of 6 specific, high pressure games is a different challenge. Not to say he won't have a good go.

MikeKyle wrote: If you play enough games then the chances of eventually seeing a winning streak of 40 tends towards certainty. (just by luck if not skill.)

Against equally strength players, it would take are really large number of games

sorin wrote:

MikeKyle wrote: If you play enough games then the chances of eventually seeing a winning streak of 40 tends towards certainty. (just by luck if not skill.)

Against equally strength players, it would take are really large number of games

Yes. If winning probability of an individual game is 0.5, then probabliity of winning any given 40 in a row is 0.5^40 = 0.0000000000009. Thus one would have to play about 762 billion games before having at least 50% chance of encountering such a winning streak.

If all his opponents are about 2 stones weaker, and if the winning probability against each is about 90%, then you can expect to play about 600-700 games to get a 40-game winning streak.

Mateusz won in classic 'make a complicated mess when losing in endgame and outfight opponent' style.

Uberdude wrote:Mateusz won in classic 'make a complicated mess when losing in endgame and outfight opponent' style.

After seeing the R12-S13-K18 exchange, I'm hoping this game will get me that much closer to appreciate the fact that a match is not over until it is over.

Yes, Mateusz's games often illustrate the benefit of not playing aji keshi and keeping groups without two clearly defined eyes so that if fighting later breaks out nearby you have chances to attack them. This game he was of course fortunate Andy didn't play quite enough honte and a few bad timesujis, but it takes skill to creae positions that allow your opponent ample opportunity to mess up.