Garbage hand turns into quad on 2 out of 3 lines! Odds?

Had a first for me that has to be extremely rare. Was playing triple play and had a garbage hand, hit the draw button and got 4 10's on the middle line and 4 Kings on the top line! What are the odds drawing 2 quads and how would I figure it out? I've never seen this before, even on a 10, 50 or 100 play machine. Seems like it's got to be much more rare than a dealt royal. Thanks!

I know someone here will check my math..

But I get the probability of throwaway quads as 344/1533939. So to get two of them on a triple play game would be:

3 x (1533595/1533939) x (344/1533939)^2 = 0.00000015 (approx) One in 6.63 million????

This is the probability of getting two quads *given* you have been dealt a throwaway hand. (I'm defining this as a hand with no pair).


344 = 8 possible quad choices x 43 options for the 5th card
1533939 = (47*46*45*44*43) / (5*4*3*2*1)

Here's what I get:

There are (47)C(5) = 1,533,939 different 5-card draws remaining in the deck.

Of these, there are 8 ways to draw 4 of a kind (you can't draw a 4 of a kind with any of the 5 ranks that were in the cards you discarded), and for each one, there are 43 possible cards for the fifth card, or 8 x 43 = 344 5-card draws that include a 4 of a kind.

The probability of doing it once is 344 / 1533939, or about 1 in 4459.

The probability of doing it exactly twice out of three hands is (344 / 1533939)² x (1 - 344 / 1533939) x 3 (since any of the three hands can be the one that's not the 4 of a kind), which is about 1 / 6,629,419.

The probability of doing it at least twice is this plus the probability of all three hands drawing quads = 1 / 6,628,923.

Not long ago, I was thinking how cool would it be -- playing 50 or 100 play, and hold 1 card, and end up getting 1 of each winning hand (1 RF, 1 SF, 1 4oak, 1 FH, etc.). However, as far as I know, it's only possible on JOB, BP, BPD, DB, and AF (Aces & Faces bonus / double bonus)...and perhaps joker poker. It wouldn't be possible on DW, since you'd never hold a T, J, Q, or K by itself -- and by holding a 2 you can't hit a natural RF. Not possible on DDB or DBDW [games with kickers, except Double Double Aces & Faces], either. It would be possible on BP or DB, since holding a J, Q, or K [those are the only 3 correct holds that you'd make that'd let you make a winning combination of each payoff], since you could still get AAAJ, 2222J, etc.

What piqued my curiosity is that I threw all the cards away and re-drew a four of a kind and a three of a kind, initially I thought I redrew 2 different 4oaks, but one was a card short. :(