only the 7 7 7 rules
btw gold card is black jack = jack spade and jack clover.
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Algorithm to solve rush-21 game as quickly as possible :)
I need an algorithm to solve this game as efficient as possible.
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The game is here : http://www.gamecolony.com/
Please read the rules first.
And this is some method that can be used
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11's complement method
* Use an Ace or any two cards that add up to eleven, and throw a 10 or face card with it.
* There are a total of 16 cards that are worth 10: four tens, four jacks, four queens, and four kings.
* There are a total of 16 11-pairs: four 9-2 pairs, four 8-3 pairs, four 7-4 pairs, and four 6-5 pairs.
* There are, of course four single card 11's, the aces.
* This strategy culminates with four unused 11s with a total remainder of 44 points unused.
* You can only score 16 21's using this method.
Revised 11's complement method.
* Try to score a 21 with 5-5-5-6.
* Make all other 21's with the 11's complement method.
* You will have have four unused cards left over, with 23 points unused.
* You can only score 17 21s using this method.
Perfect play method
* Try to score a 21 with 6-6-9.
* Then make a 17th 10 with 5-5.
* Play the rest of the game with the 11's complement method.
* You will have a single card, a 2, left over.
* You score the maximum of 18 21's using this method.
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Answers
What if you get a card that can't be played under any of the above methods?
You may want to try to minimize the probability of that happening, assuming that cards are drawn at random from the remaining distribution of cards.
Given the remaining distribution of cards, you could find the number of ways of completing the columns.
But the as efficient as possible criterion may conflict with the as quickly as possible criterion
From a game theory perspective, what's your goal?
Are you wanting to play hundreds of games in the hopes of eventually getting a perfect one, regardless of what it does to your average score?
Are you wanting to maximize your average number of points scored?
Are you wanting to maximize your chance of scoring over a certain level?
Are you wanting to keep your worst-case score as high as possible?
Or are you trying for a complex combination of the above goals?
So how many distinguishable game states are there in a game tree?
First, the draw pile. There are 4 each of 2s through 9s. There are 14 10s, red jacks, queens, and kings. 2 black (gold) jacks. 4 aces. So the discard pile can have 5^8 * 15 * 3 * 5 states, or a total of 87890625 states. A little less than 90 million.
Each stack can be in one of the following states:
empty (1)
one seven (1)
two sevens (1)
1 card & value anywhere from hard 2 to hard 10 (9)
1 card & value soft 11 (1)
2 cards & hard value from 4 to 20 (17)
2 cards & soft value from 12 to 20 (9)
3 cards & hard value from 6 to 20 (15)
3 cards & soft value from 13 to 20 (8)
4 cards & hard value from 8 to 20 (13)
4 cards & soft value from 14 to 20 (7)
These total to 82 distinct states for each stack. Some of these can only happen in one stack (like a four card hard 8 uses all 4 2s or a soft 14 uses all aces), but I'm looking for a conservative number here. So the stacks can have roughly 82^4 states, 45212176.
The exposed draw card can be one of the 11 distinct categories of cards, so that's a factor of 11.
For perfect play, you only need to keep track of the contents of the draw pile, the current stacks, and the top draw card. So, the exhaustive game tree has something less than 87890625*45212176*11 =~ 4^15 nodes. At one byte per record, that's 3.9 petabytes.
So easy. Buy google, use all their servers to exhaustively analyze the game, then use it to automate your play. :)
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by: ozoPosted on 2007-05-31 at 09:24:17ID: 19189501
Are you ignoring the Gold Card and 7-7-7 rules?