Introduction I have created a new form of Match Equity Table (MET) that may be of interest to some of you. This MET originated through using a re-worked form of the methodology described by Tom Keith. I believe it is significantly different from many previously calculated MET’s. In its development, I deliberated on: My MET is calculated up to [31-away, 31-away] and I call it the Variable MET (VM) because a user can easily enter his own g+bg rate as a percentage and generate his own table. The VM is really a tool for making MET’s. The link to do so is Variable MET. You may need to wait up to 30 secs for the table to refresh when entering a new gammon rate. Entering a gammon rate and viewing the new table generated is all you should be able to do. Seeding of the Variable MET If you choose to enter 28.35% in my MET you will get a result that is very close to the Kazaross XG2 MET (K-XG2). This is by design since I used the K-XG2 MET as a benchmark and then altered the seeds in the Variable MET to create a close K-XG2 imitation. The 28.35% came from doing nearly 60K rollouts in XG (3-ply move and cube) of the sensible opening plays for money and taking the mean. E.g. an opening roll of 64 was rolled out played as 64S, 64P and 64R and care was taken to weight the final average appropriately. 28.35% initially seemed high to me and I am unsure how the money g+bg rate compares to a match play g+bg rate in general, though one 2-ply Gnubg rollout I performed suggested to me the g+bg rate might be a touch lower at 9a9a than for money. Regardless, 28.35% appears to have worked well in practice in the Variable MET (Version 0.0) for helping obtain seeds for a benchmark. Following are the Post/Pre error tables for the VM using 28.35%. Note: I think the magnitude of the above discrepancies are very good. The next results come from my wanting to see if I could take the VM, change nothing in it except the input (g+bg)% and then get a table resembling the G11 MET. If you use the value 26.825% you get the following error tables. Note: The mean absolute discrepancy of 0.0487 is satisfactory in my opinion though the 7a1a Post-Crawford discrepancy (-0.2299) is of larger magnitude than I hoped for. Overall, the 1a Post-Crawford error results and the 1a Pre-Crawford results are too low. If 26.4% is the VM input then the 1a errors in both tables improve a lot. However, the absolute discrepancy of the tables as a whole raises to 0.0695. It is difficult to confirm the veracity of using 26.825% for the purposes of imitating the G11 MET. Using Gnubg 1.05 several rollouts at 0-ply move/2-Ply pruning indicated a (g+bg)% of ~27.15% for money. However, I believe Robert-Jan Velduizen (Zorba) generated G11 in 2003 using the Gnubg 0.13 build (0-ply play, 2- ply 100%/25%). This setting and build would have produced different(weaker) rollout results than the rollouts Gnubg 1.05 would have produced, so perhaps using 26.825% (or even 26.4%) as the VM input is reasonable. Usefulness I see two main ways that the Variable MET may be useful: 1. As a tool for extending an existing rolled out MET. For example, someone one day might roll out a [9a, 9a] MET using XG 4-ply play, XGR cube to the 100,000+ level. With the appropriate choice of g+bg entry into the VM the transition effect between 9a and 10a could potentially be minimised. 2. Creating a new MET on its own. For a made-up example: I might do numerous rollouts with XGR++ and find that the underlying g+bg percentage for money is (say) 28.5%. If we use that value in the VM we obtain a new MET that may be of benefit. Personally, I am more interested in finding out what the underlying g+bg rate is for the typical word-class PR3 player and creating a ‘PR3 MET’. Does someone know this rate already? Summary The Variable MET is work in progress. I have developed it to a stage that I feel comfortable to share, though please feel free to make suggestions. I think more work on the Variable Met needs to occur before finalising any new MET with it.
