Not much to write about unfortunately. We got a terrible distribution with five Sixes, five Eights and zero Sevens. Not to mention zero turnovers. At least we got a few in-suit builds.

Bart mentioned that only 5% of distributions would be worse than what we actually have. I would be interested in how he actually measured that. Did he choose to focus on Sixes, Sevens and Eights before the hand or during the hand? Is he measuring the worst differential between any two consecutive ranks or three consecutive ranks? Is he applying the cryptographic Keccak-256 hash function to our game state and looking for any series of 81 digits that form a valid Sudoku? I brought up similar issues in an earlier post.

The other problem worth mentioning is four Kings are already in play. Change them to all Queens and our prospects will be much better (even though we still don’t get a turnover). The only bright spot is it is illegal for the computer to send over a very inconvenient Backgammon doubling cube centred on ‘2’.

GM asks what criterion I use to determine how “bad” a hand is when I say only 5% are worse than ours.

It is what I call “bumpiness”, which is the sum of the differences in count of every pair of adjacent ranks. So for instance a complete suit has bumpiness of 0, and KKJJ99 has bumpiness of 10, as counts are K=2, Q=0, J=2, 10=0, 9=2, 8=0 (and 7-A are 0). When evaluating a particular set of N cards for how bad it is, I deal 100,000 or so random “deals” of N cards and compute the bumpiness of each one, and then see how our particular set stands with regard to the distribution.

Below is program output for our final position. Imagine it in a fixed-pitch font like Courier New to see the table as intended.

Remaining: A 2 3 4 5 6 7 8 9 T J Q K
72 left. 6 5 6 7 5 3 8 3 5 7 6 7 4
Strangeness is 0.9504 (bumpinesss 26)

I’m actually counting here the number of cards we have NOT seen, as opposed to the ones we have, since I have generally been more interested in running this towards the end of a game, but the two are equivalent.

“Bumpiness” is by no means the only criterion for what makes for “how good our luck is”, but it seems to me like it’s a decent measure of one component. The lower the bumpiness, the more moves you can make (assuming you can get to the relevant cards).

GM asks what criterion I use to determine how “bad” a hand is when I say only 5% are worse than ours.

It is what I call “bumpiness”, which is the sum of the differences in count of every pair of adjacent ranks. So for instance a complete suit has bumpiness of 0, and KKJJ99 has bumpiness of 10, as counts are K=2, Q=0, J=2, 10=0, 9=2, 8=0 (and 7-A are 0). When evaluating a particular set of N cards for how bad it is, I deal 100,000 or so random “deals” of N cards and compute the bumpiness of each one, and then see how our particular set stands with regard to the distribution.

Below is program output for our final position. Imagine it in a fixed-pitch font like Courier New to see the table as intended.

C:\Cpp Programs>spiderwing

89562k856a236k6j1234568-kk889

Remaining: A 2 3 4 5 6 7 8 9 T J Q K

72 left. 6 5 6 7 5 3 8 3 5 7 6 7 4

Strangeness is 0.9504 (bumpinesss 26)

I’m actually counting here the number of cards we have NOT seen, as opposed to the ones we have, since I have generally been more interested in running this towards the end of a game, but the two are equivalent.

“Bumpiness” is by no means the only criterion for what makes for “how good our luck is”, but it seems to me like it’s a decent measure of one component. The lower the bumpiness, the more moves you can make (assuming you can get to the relevant cards).

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