A Novel Can’t Stop Variant

You’ll need — A Can’t Stop board, and four dice of different colors (I use Black, White, Red & Green).

1. Roll the dice.
2. Split them — If all players still involved in a roll agree on a split, use it. If there is any disagreement, then if B/W & R/G result in a legal play, use that, otherwise go B/R & W/G. Finally B/G & W/R.
3. Advance the markers normally from the bottom of the columns.
4. Each player decides secretly and simultaneously whether to stop. Players who stop mark their advance (from their prior markers).
5. Continue until everyone withdraws or craps out.

I’ve just described Diamant, except it uses cards. [OK, I’ve skipped one point.] I played it twice and it’s gotten good reviews. But here’s the thing — Suppose that everyone backs out at the appropriate time (when expected value indicates you have more to lose than gain) and you stick out for a few more rolls and get lucky. Now everyone is behind you and has to press their luck. They can’t duck out too early, or you’ll just end to. So around the time when expected value equals loss again, you can duck out. If they get lucky, it’s even. If not, a runaway.

In Diamant, there are only five rolls, so this is pretty bad. The cards mean that things can’t go on forever. And the point that I’ve skipped — ducking out may actually get you some gems (steps up the column in our game).

So, while I enjoy Diamant, I think that the limited amount of time for comeback hampers it. While I won’t be buying this, that’s more a reflection of the price tag. If this were a $15 game, I’d probably buy it. Also, I’m not in the need of fillers that handle many players.

Random computer gaming

A special program has solved 5×5 Go. Researchers still haven’t made a master level program that plays the full (19×19) game. Dr. Peter Drake (Mundungus on BGG) has a page with useful links if you are interested.

And, apropos of my recent thoughts on Can’t Stop (and Larry’s comment), Jim Cobb has released a new computer version.

I have nothing clever to say, but figured a few of you may be interested. (I also figure most of you have already seen these, but hey, you never know).

Update August 4th, 2005 — I’ve updated the link to Roll or Don’t.

Can’t Stop Theory

I’ve been thinking that I should write a simple computer opponent to explore various AI techniques (neural nets, genetic algorithms). Of course, I’m mainly in the ‘thinking about’ stage.

Can’t Stop seems like a good choice because the rules are simple. If you could value a position then it’s simple — split the dice to maximize your position, then check
[% failure to advance] * [current unbanked gains] is greater than [expected gain when you succeed]. If the first number is greater, stop.

But the real issue is — how to quantify a position. A zeroeth order approximation is to call capping a column 1, and then each step on a column is worth 1/X, where X is the length of the column (counting the cap as a space).

Michael Keller’s “World Game Review” [Issue 7, page 5] analyzes the game with this formula and provides a mnemonic for when to stop (“Math is hard”).

But that doesn’t seem right. The value depends on how far up the column everyone else is? [The WGR admits this as a problem, but offers no solution]. If ‘7’ is almost capped, the first few steps of ‘7’ should be basically valueless (so your advancement on other columns count).

So tweak the formula. I’m wondering how. I suspect that the best bet is to perhaps develop a generic formula per column(mybase, mycurrent, opponents bases) and then use a genetic algorithm to see where the coefficients drift toward (you can also have an ‘aggressiveness’ gene, that biases a strategy towards rolling or stopping….)

It should be possible to write a reasonable opponent, but I’ll admit that I have no idea what the ‘best’ algorithm will look like….[it may also vary based on # of players].