Volatility on 4 card keno

I'm not too good with combinations & permutations and all that stuff. :( Let's say, theoretically, I found a 4-card keno game with a progressive on the 7/7. If I hit 7/7, on any of the 4 cards, I win the progressive (each card has a different JP amount....sorta like the triple play RF VP progressives, in this completely theoretical example).

Assuming I'm placing my numbers so none overlap, how would I figure out what the variance is for such a game? Or rather, how do I find the payout distribution? Sometimes you'll hit 4/7 on one card and 5/7 on another, for example. One such result is hitting two separate 7/7's and one 6/7 (not that it's likely....).

I'd like to learn how to do the math for this, not for someone to do the math for me. I'm not actually looking at a 7/7 keno progressive (or am I?), but something else entirely (but the math will work out the same way once I get the concept).


I know how to do it if you're just playing 1 card at a time....but not if you're playing different 7-spot numbers (ie: A is 1,2,3,4,5,6,7 and B is 11,12,13,14,15,16,17) at the same time.


Paging: @Wizard, @MathExtremist, @CrystalMath, @ThatDonGuy

You need to calculate the probability of each event. In the case of 2 cards with 7 spots, there will be a total of 64 outcomes (0 to 7 hits on A times 0 to 7 hits on B).

For standard keno, I always use the hypergeometric distribution, but in this case, you must calculate each card successively based on the prior results.

If you match 'a' out of A spots and 'b' out of B spots, the formula is:
=hypgeomdist(a,A,20,80) * hypgeomdist(b,B,20-a,80-A)

If you play 3 cards:
=hypgeomdist(a,A,20,80) * hypgeomdist(b,B,20-a,80-A) * hypgeomdist(c,C,20-a-b,80-A-B)