Optimal strategy for Open-Face Chinese Poker
February 19th, 2013 at 9:00:56 AM
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How difficult would it be do devise one through simulations? The game is gaining popularity in poker rooms all around the world and although it's a solvable game, there is no publicly available perfect strategy for the game.
In the game, played with up to 4 players, each players gets 5 cards that they use to make 3 hands. Players 2-4 have an advantage because they get to see how the players before set their cards. Then players get cards one at a time until they made 2 hands of 5 cards and one of 3 cards. The bottom hand must be the best and the middle hand must be better than the 3 card hand or the player loses every hand. Otherwise each winning hand pays 1 point, a losing hand costs 1 point and royalties are worth:
Back hand: straight 2 pts, flush 4 pts, full house 6 pts, quads 8 pts, straight flush 10 pts, royal flush 20 pts
Middle hand: straight 4 pts, flush 8 pts, full house 12 pts, quads 16 pts, straight flush 20 pts, royal flush 40 pts
Top hand: pair 66 is worth 1 point, pair 77 is worth 2 points, etc. Trip 2 worth 10 points, trip 3 worth 11 points, ... trip aces worth 22 points.
If you have a royalty but still lose the hand, you pay 1 + winner's royalty - your royalty, for example
If you have a back straight and he has a flush, you lose 1 + 4 - 2 = 3 points.
If someone wins all 3 hands he gets an extra 3 points.
In the game, played with up to 4 players, each players gets 5 cards that they use to make 3 hands. Players 2-4 have an advantage because they get to see how the players before set their cards. Then players get cards one at a time until they made 2 hands of 5 cards and one of 3 cards. The bottom hand must be the best and the middle hand must be better than the 3 card hand or the player loses every hand. Otherwise each winning hand pays 1 point, a losing hand costs 1 point and royalties are worth:
Back hand: straight 2 pts, flush 4 pts, full house 6 pts, quads 8 pts, straight flush 10 pts, royal flush 20 pts
Middle hand: straight 4 pts, flush 8 pts, full house 12 pts, quads 16 pts, straight flush 20 pts, royal flush 40 pts
Top hand: pair 66 is worth 1 point, pair 77 is worth 2 points, etc. Trip 2 worth 10 points, trip 3 worth 11 points, ... trip aces worth 22 points.
If you have a royalty but still lose the hand, you pay 1 + winner's royalty - your royalty, for example
If you have a back straight and he has a flush, you lose 1 + 4 - 2 = 3 points.
If someone wins all 3 hands he gets an extra 3 points.
February 19th, 2013 at 10:29:48 AM
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With all cards up, the matrix of possibilities will probably be too large to solve optimally. We haven't even totally perfected HU LHE yet, and that has much more theoretical interest than this game at least for now and has years of work already toward it.
But hopefully next year, they'll move up OFC to a bracelet event at least. Well, at least if they don't take away a draw event for it...lol
But hopefully next year, they'll move up OFC to a bracelet event at least. Well, at least if they don't take away a draw event for it...lol
February 19th, 2013 at 7:20:39 PM
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The possibilities are not as large as they look like. After the initial draw, you can put each card in up to 3 places. After you fill in the top hand, you only get 2 choices for each draw. After your initial hand is set, you have between 2^3=6 and 3^6*2=1458 ways to set your remaining cards.
