Wizard of Odds: Pai Gow Poker Probabilities

On the Wizard of Odds website for Pai Gow Poker, it shows the number of possible 4 of a kind hands to be 307,742.
I calculate: 307,568... small difference, but I am curious.

Can you share how you calculate this number? My numbers agree with most of the odds, but this one is giving me trouble.
I suspect the issue comes down to 4 of a kind with Aces issue.

My calculations are as follows:

For 2 through K: there are 12 possible 4 of a kind.

For each of those hands, you have to choose 3 more cards from the remaining 49.
This is a 49 choose 3 problem. 49!/(3! * (49-3)!)
Total (2-K): 12 * 49!/(3! * (49-3)!) = 221,088

For Aces/Wild: There are 5 possible 4 of a kinds. One hand with 4 natural Aces, and 4 hands with 3 naturals and a wild. (5 choose 4)
For each of these hands, you have to choose three cards from the remaining deck that is not an additional Ace. Or 3 from 48 cards.

Total (Ace): 5* 48!/(3!*(48-3)!) = 86,480

Grand Total of 4 of a Kind: 221,088 + 86,480 = 307,568

So where did I go wrong?

By the way, I was doing the checking because I just got pai gow for my Android, and after 3000+ hands played, it is amazing how close the percentages are coming to the statistical averages.

Thanks,
lazlo

Quote: lazlo

On the Wizard of Odds website for Pai Gow Poker, it shows the number of possible 4 of a kind hands to be 307,742...

Actually the Wizard of Odds has 307,472 possible fours of a kind, but that's not the problem.

Here's a hint to help you: As-Ah-Ad-joker-2d-3d-4d.

Straight Flushes-- I knew I missed something simple.

Thanks.