## Thursday, March 15, 2012

### Match equity table with MWC

Most people show match-winning chance (MWC) in their match equity table instead of equity. Of course the standard conversion of equity = 2 MWC - 1 holds. Here are my calculated match equity tables showing MWC:

1-away2-away3-away4-away5-away6-away7-away8-away9-away10-away11-away12-away
1-away5068.175.581.784.589.091.093.594.696.196.897.7
2-away
5059.566.173.679.283.486.789.491.793.494.8
3-away

5057.064.570.875.679.883.386.488.990.9
4-away

5057.463.969.273.777.981.584.587.0
5-away

5056.662.267.271.875.979.482.5
6-away

5055.961.166.070.474.477.8
7-away

5055.260.465.069.273.0
8-away

5055.259.964.368.3
9-away

5054.859.463.6
10-away

5054.658.9
11-away

5054.3
12-away

50

I left out the bottom half of the table for readability, but all values there are just 100 less the corresponding value in the top half.

And here are the corresponding post-Crawford MWCs (for player n-away, opponent 1-away):

1-away2-away3-away4-away5-away6-away7-away8-away9-away10-away11-away12-away
1-away5048.631.930.618.717.711.310.66.76.34.03.7

These compare well to the "Mec26" MWC table here, mostly within 0.2%. Those are based on GNUbg rollouts for post-Crawford MWCs and using a gammon probability of 26.0% (vs 27.6% in mine). The biggest differences are in 1-away,2-away and 1-away,3-away where the MWC is different by about 0.5%.

Another modern MET is the G11 table. Again, not much difference between my calculated MET and this one, though bigger differences (especially near the diagonal) than with Mec26.