What are the odds that any J, 3, 9 would come up with 3 cards coming on the turn in texas hold em?

Question

What are the odds that any J, 3, 9 would come up with 3 cards coming on the turn in texas hold em?

Answer 1

1/132,600

Answer 2

The first answer isn't even close.

If you don't have a J or a 3 or a 9 in your hand then...

there are 12 cards that will keep you alive when the first turn card is dealt, out of 50 unseen cards.  (any J, 3, or 9.)

Assuming you get that, there are then 8 cards left that you still hope to see, out of 49 unseen cards.  And then, finally, there's just 4 cards left out of 48.

The odds are the product of all three events:

  12/50 * 8/49 * 4/48

Which equals .00326... or about 3 times every 1,000 times.

(Don't bet on it.)

If you DO have a J or a 3 or a 9 in your hand, change the appropriate numbers above... the odds, of course, will then be even less.