Poker Challenge: Three of a Kind vs. Straight Flush

[einsteinian77]

I assume that most of you have played poker at some time so here is a poker question. When dealt only three cards with three's being wild, are the odds of getting three of a kind higher or lower than getting a straight flush? Keep in mind you can only use the three cards that are dealt to you not the normal five.

 

[NateTG]

Hmm, are straights allowed to go around the corner?

There are 52 choose 3 hands.

There are four tripple wild hands.
There are 48*6=288 double wild hands.

Whether those count as three of a kind of straight flushes depends on which is better.

There are 51*4 natural three of a kinds (not counting triple wild)
There are 51*6*4 three of kinds using a wild card.
for a total of 1428 three of a kinds.

For straight flushes:
There are 8 natural 3-less straight flushes in each suit. (6-high through A-high)
There are 11x4x4 wild outside straight flushes in each suit. (A2x,and x45 through xKA in each suit)
There are 10x4x4 wild inside straight flushes in each suit. (2x4, and 4x5 through QxA)
for a total 344 straight flushes. (Technically, that's 632 with wild hands)

 

[R0man]

The odds of getting three of a kind are higher than getting a straight flush when dealt only three cards with three's being wild. This is because there are more possible combinations of three of a kind compared to a straight flush with only three cards. For three of a kind, there are 13 possible combinations (one for each rank of card), whereas for a straight flush, there are only 4 possible combinations (one for each suit). Additionally, with three of a kind, you can have any three cards with one being wild, whereas with a straight flush, you need all three cards to be in the same suit. Therefore, the odds of getting three of a kind are higher than getting a straight flush in this scenario.