SImlab: Points/Schmoints result

My simulation work got bogged down, but before it did I had a result that I didn't understand.  I still do not understand it, but I think I should put it "out there" anyway.  Maybe someone else can use it.

I was interested in the comparative strengths and weaknesses of two different evaluation scales.  The first is the standard HCP scale, Ace=4, King=3 and so on.  The second is a scale dubbed "Schmoints" by an author I'd like to credit - but I've lost the link.    Ace=6, King=4, Queen=2, Jack=1.  Obviously this weighs aces and kings more heavily; it is preferred by many theorists.  The scale was (I think) first used by the "four Aces" team in the 1930's, with all values half of the Schmoints value.

I ran a simulation that attempted to test the scales' relative performance: North and South will have balanced hands, no five card holding in any suit, and 25 HCP total; South will have 15-17 total HCP.  In 1000 deals I count the number of double-dummy tricks taken, according to the number of Schmoints in the combined hands.  As expected, it's better to have more Schmoints:

Average tricks for 31 schmoints = 8.33

Average tricks for 32 schmoints = 8.46

Average tricks for 33 schmoints = 8.61

Average tricks for 34 schmoints = 8.74

Average tricks for 35 schmoints = 9.0

This seemed a nice confirmation of the theory that Schmoints are a bit more accurate.  So I ran a similar simulation, holding total Schmoints constant at 33 (the middle value from the previous run).  It turns out that for constant Schmoints, it's better to have more HCP!

Average tricks for 23 hcp = 7.56

Average tricks for 24 hcp = 8.27

Average tricks for 25 hcp = 8.61

Average tricks for 26 hcp = 8.97

Average tricks for 27 hcp = 9.0

It's comforting to see that both of these independent simulation runs had the same average number of tricks for the case where the HCP=25 and Schmoints=33.  (The numbers above are rounded.  In one run the number was 8.607527 and in the other it was 8.608808.)   I don't know why both runs had exactly 9 tricks at the high end - probably there were few cases and all had 9 tricks.  And I still don't know what to conclude from the two runs taken together.

I'm happy to forward my Deal319 inputs to people who would like to expand on this work.  Send me a message on Bridgewinners.