What I did was for every possible initial hand, determine the best strategy by adding up the payouts for all possible continuations and choosing the strategy with the best average payout. This took quite a lot of computer time (about 120 hours on a pretty fast machine), but in the end I ended up with a list of strategy's that has a net advantage of 1.2%.
I wonder about your analysis here Edwin... (how much computer power did it take??!)
Let me know if I do something wrong on one of the following lines:
Number of possible hands 53 x 52 x 51 x 50 x 49 / 120* = 2.9 million
possible ways to discard 1+ 5 + 10 + 10 + 5 + 1 = 32 (== 92.8 m discard-hands)
for each of the 32, possible draws are 48 + 48.47/2 + 48.47.46/6 + 48.47.46.45/24 + 48.47.46.45.44/120 respectively
== 1 + 48 + 1128 + 17296 + 194580 + 1712304
respectively for each group
so for each of 2.9 million hands, there are
1 + 240 + 11280 + 172960 + 972900 + 1712304 possible outcomes (2,869,685)
thus,
(1) for each of the 2.9 million hands:
(2) you looked at the 32 possible plays.
(3) in each case (of the 32) you examined all possible 2.8 million outcomes (there are about 2.8 million possible outcomes altogether -- some of the 32 have less, some more, possibile outcomes)
(4) indeed of the 32 ways to play each hand, you TALLIED over the 2.8 million possible outcomes viz a viz each of the 32 possibilities, and decided, for that particular hand (ie, of the 2.9 million hands - see point 1) what the actual BEST play of the 32 plays possible, is, ie looking to maximize outcome for that one hand
Thus for the 2.9 million hands of joker poker, you actually have an enormous table of the single best way statstically (of the 32 possibile plays) to play that particular hand ?!
You had to determine the payout of roughly 8.12 x 10^12 (!) hands to do this. (Hell, I imagine you just "wrote down" a big hash first with the payout of each of the 2.9 million sorted jokerpoker hands, rather than "calculating" that each time - that would have been the least of your troubles eh!)
Thus, you have the PURE joker poker play book - for all 2.9 million hands, you have written down the best possible (of the 32) discard plays!! You figured it out by, for each of the 32 x 2.9 million, figuring out every possible result (ie depending on how the remains of the deck is shuffled) and figuring which is the 32 is thus highest-paying-out
Is that what you did Edwin?? Are computers that fast (10^13 rsults to look at?), I have no grasp of the problem??!!!
I may well have screwed a factor of 10 or so here and there, but still. is the above right??? Please let me know! Perhaps I forgot to fold something down or some such. :O
JP!!
*naturally, ordering doesn't matter
Edwin
runty
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