Extra Draw Keno

Hi,

Can anyone explain the Maths for Extra Draw Keno on this page:
http://wizardofodds.com/games/keno/appendix/10/

I can work out the basic return for 20 balls out of 80, using the equation (x:y)*(80-x:20-y)/(80:20)

But I can't work out the return from the extra 3 balls. I tried using the above equation with 60 and 3 instead of 80 and 20, working out the probability of getting 1, 2 or 3 extra balls and multiplying by the right payout, but it doesn't match the Wizards figures. I also divided the extra return by 2 due to the extra stake.

Thanks for any help!

Let's just look at the simplest case: 3 spot

1. Using the formula stated above, these are the probabilities of hitting n spots:

spots hit	probability
0	0.416504382
1	0.430866602
2	0.138753651
3	0.013875365

2. After the first 20 draws, you have 60 open spots on the board and you have 3 draws (should you choose to do so). The wizard's table only shows that continuing is a good deal if you already hit 2 spots. So, this is the only one I will look at. There are only possible outcomes: you don't get the third spot or you do hit the third spot. The probability of hitting the additional spot is (x:y)*(60-x:3-y)/(60:3), where x and y are both 1 (p=0.05).

3. Calculate the return: r = p(hitting 2 spots in original 20 draws) * [p(hitting 1 additional spot in the next 3 draws) * increase in win - cost of additional wager]

r = 0.138753651 * [0.05 * (30-3) - 1] = 0.048563778

Sorry I've only just had chance to come back to this - thanks for the explanation!