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New model for money game cube decision points

Posted By: Mark Higgins
Date: Tuesday, 27 March 2012, at 3:41 p.m.

In Response To: New model for money game cube decision points (higonefive)

Keeler and Spencer's approach was really quite cool in that it abstracted everything about the game into the dynamics of one variable: the cubeless probability of winning the game. The weakness with their model is that it assumes the game-winning probability diffuses continuously, so you can never get a great roll and jump past the cash point, losing your market. That means it tends to overestimate the cubeful equity.

Janowski's model does account for those jumps with his cube efficiency parameter. He notes that cube efficiency is a function of game state and depends on volatility of the position, distance from the optimal double point, and width of the doubling window. But in practice it was difficult to calculate it in a specific game state, so people tend to use a constant cube efficiency, or perhaps different values for different broad game states.

My model is another take on the same thing: I model game evolution through jumps in game-winning probability each turn, and the size of those jumps I call the "jump volatility". If you assume a constant jump volatility it's basically equivalent to Janowski's model with a constant cube efficiency.

The main benefit, I think, is that jump volatility is a well-defined statistical quantity that you can estimate in your current game state. If you are a bot you do it with a 2-ply lookahead. But humans can use bot self-play to get a feel for jump volatility in benchmark game states and estimate from there.

Janowski also developed a more general model where each player has a different cube life index. It seems like there should be some congruence between my model with a local & average jump volatility, and Janowski's two-index model, but I've yet to find it. Rick and I are having some interesting email conversations about this one.

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