Most Reasonable Hand Ranking for Five Card Draw played with a Joker
October 13th, 2015 at 8:23:12 AM
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In a home poker game, Five Card Draw is played with a fully wild Joker. One additional house rule is that among the same pattern, wild hands are always the weakest. For example, (Joker)-A-A-4-3 is beaten by 2-2-2-10-9, or any other natural three of a kind for that matter.
I find this as a neat solution to the "Wild Card Poker Paradox", since there are 82368 wild trips combinations, which is greater than the number of natural combinations, which is 54912. If one regard wild hands as different from the natural variety, then it makes perfect sense to say that natural trips beats wild trips, which in turn is better than two pair (123552 combinations) combination-wise.
However, this rule has some side effects. For example, when you have a joker and four other unconnected cards, in this case although you nominally have one pair, in reality your hand is merely a "high card hand" that is just better than Ace high. This is clearly unfair to you since a wild one pair hand (169848 combinations) is much less probable than a natural one pair hand (1098240 combinations). Hence you should be allowed to play your highest pair. By the same reason, wild full house and wild flush hands are also treated unfairly. As for wild straights it might be better not to apply that rule, since a wild straight is only marginally more likely than the natural pattern (10332 vs 10200).
In other words, a better rule is that if a hand is wild AND its pattern is three of a kind, four of a kind or a straight flush (including royal flush), then that hand is the weakest among the same pattern. In addition, by the same logic, it may also be appropriate to force the joker in straights or flushes to play as the lowest possible card. In particular, note that there are only 1972 Ace-high natural flushes but there are 2696 wild flushes, which are always Ace high by default. But when one consider that a wild flush has only four natural ranks, then they are naturally disadvantaged. This will also cause an effect similar to above.
The other house rule is that royal flush ranks better than five of a kind. This is clearly unreasonable as there are only 13 ranks but the joker can replace any of the 20 specific cards. Nevertheless, the side effect is that this separates royal flush from all other straight flushes. Therefore, wild royal becomes better than a natural straight flush that is not Ace high. Noting that the former has 24 combinations but the latter has 36, whether wild royal should be favored is not an affair on combinations, but a matter of pattern consistency.
Personally, I feel that royal flush is named as a distinct pattern only because it is the highest natural hand possible in a single deck. But since its constitution is no different than other straight flushes, they should be treated equally no matter if the hand is wild or not. If any other nominally higher straight flush can lose to a lower one because of the presence of a joker, wild royal should also rank lower than any natural straight flush as usual.
What do you think of such considerations? To what extent do you follow the "wild-unfavoring" rule? Feel free to discuss.
P.S. For the hand combinations and probability, refer to the "5-Card Stud with Fully-Wild Joker" table in the following link:
I find this as a neat solution to the "Wild Card Poker Paradox", since there are 82368 wild trips combinations, which is greater than the number of natural combinations, which is 54912. If one regard wild hands as different from the natural variety, then it makes perfect sense to say that natural trips beats wild trips, which in turn is better than two pair (123552 combinations) combination-wise.
However, this rule has some side effects. For example, when you have a joker and four other unconnected cards, in this case although you nominally have one pair, in reality your hand is merely a "high card hand" that is just better than Ace high. This is clearly unfair to you since a wild one pair hand (169848 combinations) is much less probable than a natural one pair hand (1098240 combinations). Hence you should be allowed to play your highest pair. By the same reason, wild full house and wild flush hands are also treated unfairly. As for wild straights it might be better not to apply that rule, since a wild straight is only marginally more likely than the natural pattern (10332 vs 10200).
In other words, a better rule is that if a hand is wild AND its pattern is three of a kind, four of a kind or a straight flush (including royal flush), then that hand is the weakest among the same pattern. In addition, by the same logic, it may also be appropriate to force the joker in straights or flushes to play as the lowest possible card. In particular, note that there are only 1972 Ace-high natural flushes but there are 2696 wild flushes, which are always Ace high by default. But when one consider that a wild flush has only four natural ranks, then they are naturally disadvantaged. This will also cause an effect similar to above.
The other house rule is that royal flush ranks better than five of a kind. This is clearly unreasonable as there are only 13 ranks but the joker can replace any of the 20 specific cards. Nevertheless, the side effect is that this separates royal flush from all other straight flushes. Therefore, wild royal becomes better than a natural straight flush that is not Ace high. Noting that the former has 24 combinations but the latter has 36, whether wild royal should be favored is not an affair on combinations, but a matter of pattern consistency.
Personally, I feel that royal flush is named as a distinct pattern only because it is the highest natural hand possible in a single deck. But since its constitution is no different than other straight flushes, they should be treated equally no matter if the hand is wild or not. If any other nominally higher straight flush can lose to a lower one because of the presence of a joker, wild royal should also rank lower than any natural straight flush as usual.
What do you think of such considerations? To what extent do you follow the "wild-unfavoring" rule? Feel free to discuss.
P.S. For the hand combinations and probability, refer to the "5-Card Stud with Fully-Wild Joker" table in the following link:
October 13th, 2015 at 9:56:19 AM
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If poker was just about who has the higher cards then that would make sense. But because poker is about game strategy using card rankings, then the variations add unnecessary complications. You got your cards, play 'em.
A falling knife has no handle.
October 13th, 2015 at 11:07:28 AM
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Interestingly, this problem (and all sorts of cumbersome exception handling) is resolved by treating the hand rank by its simple hand rank, regardless of how it is formed.
Joker-A-A is an A-A-A, and 4-5-6-joker-8 is 4-5-6-7-8. A flush is a flush, a royal a royal, and so on.
In game design, the goal is to NOT add excess complexity and a multitude of cumbersome exceptions when adding features, - including when that feature is adding a joker. And no, it is not "unfair" to treat a hand rank at its presented face value, regardless of whether it has a joker or not. A flush is a flush, a straight is a straight, and so on, and this is reasonable. Nothing could be fairer, cleaner or more straightforward. You get those cards, you play those cards, whatever you cards get for your hand you play.
Adding "Wild this...but Natural that in that particular case....," then you add a host of cumbersome game-play issues that don't need to be there when you can treat hand ranks as their simple hand ranks.
Pai Gow Poker treats hand ranks at their face value and game-play value regardless of how it is formed, (the only exception is the 7-card natural straight flush that is only used to trigger the rarest possible jackpot as the top progressive award only.)
Needlessly complicate a game with rules you can do without, - and you kill that game design.
Joker-A-A is an A-A-A, and 4-5-6-joker-8 is 4-5-6-7-8. A flush is a flush, a royal a royal, and so on.
In game design, the goal is to NOT add excess complexity and a multitude of cumbersome exceptions when adding features, - including when that feature is adding a joker. And no, it is not "unfair" to treat a hand rank at its presented face value, regardless of whether it has a joker or not. A flush is a flush, a straight is a straight, and so on, and this is reasonable. Nothing could be fairer, cleaner or more straightforward. You get those cards, you play those cards, whatever you cards get for your hand you play.
Adding "Wild this...but Natural that in that particular case....," then you add a host of cumbersome game-play issues that don't need to be there when you can treat hand ranks as their simple hand ranks.
Pai Gow Poker treats hand ranks at their face value and game-play value regardless of how it is formed, (the only exception is the 7-card natural straight flush that is only used to trigger the rarest possible jackpot as the top progressive award only.)
Needlessly complicate a game with rules you can do without, - and you kill that game design.
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
October 13th, 2015 at 12:09:52 PM
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Quote: PaigowdanInterestingly, this problem (and all sorts of cumbersome exception handling) is resolved by treating the hand rank by its simple hand rank, regardless of how it is formed.
I think we have a winner.
You can't have tied rank three of a kind hands in a single deck game with a single wild.
The things that do come into play - it is now possible to have a five of a kind hand, which will always win.
It is possibly reasonable to have a contingency for a natural straight, flush, or straight flush vs a wild version of the same hand, where the wild would lose, but due to the rarity of the single wild occurring, it's also reasonable to say that those hands would chop the pot.
I'm not running math on it, but my instincts tell me that in a casual home game, you might see one extra chop due to a wild-natural tie every 8 months or so.
May the cards fall in your favor.
October 13th, 2015 at 8:44:36 PM
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Inmate,
Welcome to the forum; great first post.
Welcome to the forum; great first post.
If the House lost every hand, they wouldn't deal the game.
