RE: [Bug-gnubg] 2-ply vs. 3-ply

[Ian Shaw]

rambiz khalili [mailto:address@hidden wrote:

> there is still one sentence in your mail which i don't think i really
understand-due to my not perfect command of 
> English possibly. you write: "...each side is trying to maximise it's
own equity by giving it's opponent the worst 
> possible best move. " what do you mean by the "worst possible best
move"?! 

Consider a game without dice, such as noughts-and-crosses (tic-tac-toe).
If both sides aim for a win directly by trying for three-in-a-row
without considering the opponents move, then the player who goes first
wins. This doesn't happen in real life; noughts-and-crosses, properly
played, leads to a draw.  

By "worst possible best move", I mean that, for example, you pick the
move that forces a certain draw rather than giving your opponent the
choice of a win or a loss. You know your opponent will make the best
move she can. When choosing your move, you act with this knowledge. You
don't choose the move that will allow you to win if she makes a mistake,
but loses if she plays her best move. You pick the move that blocks her
winning move, even though this reduces your own chance to win. 

The best strategy is to choose the play that MINImizes your opponents
MAXimum equity. The term "minimax" is used to describes this strategy.

In backgammon, this is complicated by the use of dice. You don't know
what your opponents best move is, because you don't know what she will
roll on her next turn. Minimax strategy is still used, but adapted so
that you pick the move where your opponent has the lowest AVERAGE equity
for all combinations of dice on her next roll.

Regards,
Ian Shaw