Keno EV Question

[MHoydilla]

Whats the total EV of betting a 3 spot in Keno with a payscale like this:

# Hits Payout(per 1 bet)

0 - 0
1 - 0
2 - 2
3 - 45

If also posible how high would 3 for 3 have to pay to make this a break even game, my buddy said 47 and I bet him a $20 that it would have to higher but I am not really sure how to figure it out. Thanks in advance any help is appreciated.

[Siegmund]

Assuming this is a standard "draw 20 out of 80" Keno game:

There are 80C3 = 82160 tickets you might play.

Of these, 60C3 = 34,220 will miss entirely.
20C1*60C2 = 35,400 will hit 1 number.
20C2*60C1 = 11,400 will hit 2 numbers.
20C3 = 1,140 will hit all 3 numbers.

Your return on your money is (11400*2+1140*45)/82160 ~ 90.2%, a lot worse than roulette, but better than some other keno bets.

To break even, you require a payoff P such that 11400*2+1140*P = 82160, or 52.07 units.

Congratulations on being $20 richer. How much of that are you tipping?