[bonanova]

We usually think of things that are scarce as being more valuable.

Take that thought to the evaluation of poker hands.

Enumerate the card groups that give you a straight flush

Enumerate the card groups that give you four of a kind.

Which hand should be ranked higher?

[Izzy]

Okay, so we know from poker that a straight flush actually is worth more than four of a kind, but let me reconsider.

There are 13 ways to get four of a kind. That part was simple. Now the straights I have to think about. Assuming A can be played as high or low,

A2345(4)

23456(4)

34567(4)

45678(4)

56789(4)

910JQK(4)

19JQKA(4)

That would be 28.

If you're going by that alone, then yeah, four of a kind should be ranked higher. I've started it off, now someone should come in here and start doing the probability of actually getting those cards, 'cos I'm crap at that. I want to say getting four four's is 1/13, but I'm pretty sure this is going to end up like Unreality's riddle where you have to take other people getting cards into account. Of course, this probability would change between different styles of poker, as I'm far more likely to get a good hand in Texas Hold 'Em and know how to bet on it, whereas in Five Card Draw I don't.

Just as my guess, I'm going to say the straight flushes are harder to get, and therefore should be worth more.

[Guest]

Straight flush = 1/64,974

4 of a kind = 1/4165

While there are actually more combinations of straight flushes, getting 4 cards with five chances is easier than 5 cards with 5 chances. Gotta watch count your "outs". ^__^

*I admit to looking up the odds to support this, but I already knew the answer.

[Guest]

my guess

4 of a kind has 13x3x2x1 x 5 ways.

straight flush has 10x1x1x1x1 x 4 ways.

Apparently 4 of a kind must be ranked lesser???

[HoustonHokie]

Four of a kind:

There are 13 combinations (A-K) and each can be obtained with 48 different kickers, so the number of Four of a Kinds is 13 * 48 = 624.

Straight Flush:

There are 10 Straight Flushes in each suit (A high to 5 high), so the number of Straight Flushes is 10 * 4 = 40.

Therefore the Straight Flush beats a Four of a Kind, because it is more rare.

[Guest]

Okay, so we know from poker that a straight flush actually is worth more than four of a kind, but let me reconsider.

There are 13 ways to get four of a kind. That part was simple. Now the straights I have to think about. Assuming A can be played as high or low,

A2345(4)

23456(4)

34567(4)

45678(4)

56789(4)

910JQK(4)

19JQKA(4)

That would be 28.

If you're going by that alone, then yeah, four of a kind should be ranked higher. I've started it off, now someone should come in here and start doing the probability of actually getting those cards, 'cos I'm crap at that. I want to say getting four four's is 1/13, but I'm pretty sure this is going to end up like Unreality's riddle where you have to take other people getting cards into account. Of course, this probability would change between different styles of poker, as I'm far more likely to get a good hand in Texas Hold 'Em and know how to bet on it, whereas in Five Card Draw I don't.

Just as my guess, I'm going to say the straight flushes are harder to get, and therefore should be worth more.

The probability of four of a kind is not 1 in 13 it is 52/52*3/51*2/50*1/49 regardless of the number of people in the game or which game you are playing. That is 4.802 X 10^-5 probability. For a flush the probability would be 52/52*4/51*3/50*2/49*2/48 which is equal to 4.00 X 10^-6

[Guest]

Four of a kind:

There are 13 combinations (A-K) and each can be obtained with 48 different kickers, so the number of Four of a Kinds is 13 * 48 = 624.

Straight Flush:

There are 10 Straight Flushes in each suit (A high to 5 high), so the number of Straight Flushes is 10 * 4 = 40.

Therefore the Straight Flush beats a Four of a Kind, because it is more rare.

That, and we have to take into account the iterative process of poker, through which a straight is an "all or nothing" thing, whereas you can try getting a "4 of a kind" without losing a pair or a 3 of a kind....

Edited March 2, 2009 by hellmake

[Guest]

I'm not getting the point of this thread. It's framed in such a way to make us think that what is scarce isn't necessarily more valuable than something less scarce and implies that a four of a kind is more rare than a straight flush. Since it's not, why those two hands and not two others? Maybe the OP thinks differently?

[bonanova]

I'm not getting the point of this thread. It's framed in such a way to make us think that what is scarce isn't necessarily more valuable than something less scarce and implies that a four of a kind is more rare than a straight flush. Since it's not, why those two hands and not two others? Maybe the OP thinks differently?

Prove it's not, based on "scarce"ness.

[Guest]

Prove it's not, based on "scarce"ness.

I'm sure you're aware that all of the probability and gambling odds sites have done the math on this already. There are 40 possible straight flushes and there are 624 possible hands including four of a kind. A straight flush is more scarce than a four of a kind. Where are you going with this? I'm not seeing the brain teaser here.

[bonanova]

I'm sure you're aware that all of the probability and gambling odds sites have done the math on this already. There are 40 possible straight flushes and there are 624 possible hands including four of a kind. A straight flush is more scarce than a four of a kind. Where are you going with this? I'm not seeing the brain teaser here.

Four of a kind.

The OP suggests that the solver enumerate the ways to create these two hands.

For the straight flush you get 40, ten for each suit, and that's all there is to it.

For the FOAK, you get 13, one for each rank.

If the solver stops there, he concludes it's a rarer hand, which would be true if he were dealt only 4 cards.

The teaser is simply to remember the 48 ways to fill the 5th card.