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What is XG Thinking here?

Posted By: Tom Keith
Date: Sunday, 14 September 2014, at 1:08 p.m.

In Response To: What is XG Thinking here? (Dmitriy Obukhov)

This just may be an artifact of XG's conversion of the breakdown of wins, losses, and gammons to match equity. For example, suppose X wins a single game 35% of the time, wins a gammon 10% of the time, loses a single game 40% of the time, and loses a gammon 15% of the time. When the cube is at 2, it is easy to convert this to match equity:

  Event Probability   Match equity   Product  
  X wins 2 .450  +1.000  +0.450  
  X loses 2 .550  −1.000  −0.550  
  Total 1.000   −0.100  

When the cube is at 1, you know and I know that the bot should still use the same formula because (assuming perfect play) the cube will end up on 2 anyway. But a bot might not know that; a bot might naively assume the cube stays at 1. In that case, the match equity calculation breaks down like this:

  Event Probability   Match equity   Product  
  X wins 2 .10  +1.000  +0.100  
  X wins 1 .35  +0.685  +0.234  
  X loses 1 .40  −0.685  −0.274  
  X loses 2 .15  −1.000  −0.150  
  Total 1.00    −0.090  

So the choice the bot faces is "double", which has an equity of −0.100, or "no double", which has an equity of −0.090. By this calculation, "no double" is better by 0.010.

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