3 ms·
This is a bit of a digression, but: It's an interesting question what (if anything) that larger dynamic range means. One thing you'll hear people say sometimes
by gjm11 28d ago
This is a bit of a digression, but: It's an interesting question what (if anything) that larger dynamic range means.
One thing you'll hear people say sometimes -- I've said it myself -- is that this shows that in some sense go is a "deeper" game than chess; there's more to know and understand, more variety of possible human skill.
That might well be true. It certainly feels a more elegant game, and involves longer tactical sequences, and so forth. But this may be misleading.
Consider the game of treblechess. To play a game of treblechess, you play three games of ordinary chess and look at the overall result.
Suppose that when we play ordinary chess, I win with probability W, lose with probability L, and draw with probability D = 1-(W+L). And suppose separate games are independent of one another (which might not be true in reality, but never mind). What happens when we play treblechess?
I win 3/0 with probability W^3. I win 2.5/0.5 with probability 3W^2D, because that happens when I draw any one of our three games and win both of the other two. I win 2/1 with probability 3(W^2L+WD^2), because that happens when I win two and lose one or win one and draw two, and for each of those there are three choices for which game is which. So I win at treblechess with probability W^3 + 3(W^2(1-W)+WD^2).
I can draw by getting one each of WDL (probability 6WDL) or by drawing all three (probability D^3).
Suppose that when we play chess I win 40% of the time, draw 50% of the time, and lose 10% of the time. Then our Elo difference is about 107 points. In triplechess, I will win 65.2% of the time, draw 24.5% of the time, and lose 10.3% of the time. Our Elo difference is about 214 points.
If in ordinary chess I win 65% of the time, draw 25% of the time and lose 10% of the time -- about the same odds as for treblechess in the last example -- then our chess Elo difference is about 215 points. At treblechess I will win 84% of the time, draw 11% of the time, and lose 5% of the time, and our Elo difference will be about 375 points.
If in ordinary chess I win 15%, draw 75%, lose 10%, then our Elo difference is about 17 points; in treblechess I will win 31%, draw 49%, lose 20% and our Elo difference will be about 41 points.
Treblechess Elo differences are on the order of double ordinary chess Elo differences! Clearly treblechess is a game with twice the depth of ordinary chess!
But it isn't. It's just longer and gives more opportunities for the better player to come out ahead overall.
Go is also a longer game than chess, though of course not in the same way as treblechess is. Perhaps the larger Elo range of go is more because of that than it is because of actual deeper strategy and tactics?
- Nifty3929 28d agoAs an amateur (but competent) player of both, when I play go it almost feels like I'm playing multiple smaller games at the same time on the same board. Even if I might be struggling in one area, I can make it up in another. So it's very hard for a lesser opponent to beat me, even if they do gain an advantage in one area. Likewise in reverse when I'm playing a superior opponent. I might get in a nice kill, but next thing I know we're playing a different battle on the other side of the board and I get crushed. So I think there's truth to what you're saying.
- phatfish 28d agoMaybe the depth of a game is related to whether it will scale. Go is played on different board sizes and still works. If you make a Backgammon board bigger it would just be a slog and no real increase in tactical challenge. Chess rules dictate a set size of board, which I guess has been refined over time. If a Go board is made bigger or smaller it just adjusts the problem space, the rules and core of the game remain the same.
- zelphirkalt 28d agoPerhaps interesting: Japanese chess, Shogi, is usually played on a 9x9 board, but there are many variants, which are played on bigger boards. Though games take longer and those variants are played rarely. It scales, but I think it's fair to state, that Go scales much better, due to its simplicity (simple != easy).
- hyperpape 28d agoI’ve thought about this before and come to very similar conclusions. The ELO range between the best and worst players is meaningful, but you can’t just read off the depth of the game from it in the senses we most care about.