While I did end up with the 'PURE joker poker play book', it is not as large as you think: it only contains 178633 entry's.
You correctly assessed that order does not matter, but also the suit does not matter in many occasions. For example: the two following hands are identical, except for the suits:
1. Ace of hearts, Two of clubs, Five of clubs, Six of clubs, King of spades 2. Ace of clubs, Two of spades, Five of spades, Six of spades, King of hearts
It is easily seen that the optimal strategy for both hands will be the same.
But wait!!
Suits matter because of Flushes (also straight flushes, royal flushes and the like)
For instance, with hand (1), some players assert that the best approach is to discard the ace and king. Note that you are only two cards away from a straight flush.
(Some video poker strategy manuals suggest badically thats it IS worth going for "long shots," two card draws, for the high paying flush + straight hands) (Your analysis could answer this question!)
Or -- in fact -- did you mean Edwin that the above hands are the same -- because you're just swapping suites?
ie, your final "rule book" is composed of a "free form" system with reagards suits.
ie, your rule book likes something like this:
5-X, 6-X, 9-Y, 10-Y, K-Z
where X, Y and Z can be any suite.
Hence in that example, you have covered, let me think, four, right? different "raw" hands with one meta-hand where you variableize the suites ???
For each of those 178633 really different hands, I did try all 32 strategy's. There is 1 strategy that keeps all cards, five the keep four cards, ten that keep three cards, ten that keep two cards, five that keep one card and one that keeps no cards at all. The total number of calculations for those 32 strategy's combined then is:
1 + 5.48 + 10.48.47/2 + 10.48.47.46/6 + 5.48.47.46.45/24 + 1.48.47.46.45.44/120 = 2869685
This brings the total number of calculations down to 5.13 x 10^11, which is certainly doable if the 'calculation' is simply a table lookup as you suggest.
intrgiuing ... I had no idea about that. (I'm an "ivory tower" programmer :-) heh...)
In fact, my program was not that smart, as I did not take into account that order did not matter in drawing the new cards (oops, thanks for pointing this out).
uh oh!
I did add a few more optimizations though, and I estimate my initial run did about 7 x 10^12 lookups and the second run (I made a slight error in the scoring function, so I had to run it again) contained a few more optimizations, reducing it to about 3 x 10^12.
Both runs combined took about 120 hours on an Athlon XP 1800+ with 512 MB RAM. Combining all optimizations (including the one you suggested, that order for the new cards does not matter) would bring the 5.13 x 10^11 down to about 7 x 10^10... which would be about an hour on that machine. So I wasted quite a bit ;)
fascinating. thans for the info. (I wouldn't have believed it! I had no idea computers are so fast!) I am however curious about the Flush aspect of what you say above??
Edwin
a nice old
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