[Daliman]

I was thinking a bit about probabilities in bowling, and I think I came up with a good way to book a significant edge in a bowling pool. My idea is to run a pool in my league where anyone can get in for $5; if they then bowl all 3 games over their average, I will give them back $15. If they bowl 2 games over average, I will give them their $5 back. Anything less than 2 games over average get s them nada. My initial calculations, all things being equal, and assuming a 50% chance of bowling over average were:
12.5% will bowl all 3 over average(.50X.50X.50)
25% will bowl 2 games over average(.50x.50)
Therefore, if 100 people enter, there is $500 in the pot
12.5, hell, let's just make it 13 people win $15=$195
25 people win $5=125
195+125=320 paid out; ergo, a 36% edge for me, right? Seemed too good to be true. Possibly because it is. If only 37.5% bowl 2 or 3 games over average, that would mean that 62.5% of all bowlers bowl only 1 game or less over average per 3 game series. Crud, that can't be right. There's only 4 options, 3,2,1 or 0 games over average, Shooting EXACTLY average obviously NOT considered over). There's gotta be more than 25% of people shooting over average So I rethought it a bit and figured that since the chance of getting 3 games under or over average is 12.5% each-that totals 25% for all 3 under or over. Therefore, the rest of the people will shoot either 2 games under or over 37.5% of the time each(75%x2). Hmm, that seems to make sense. Let's figure in that i'm going to get cherry-picked a bit in this by people who have a better than average chance of being over average and bump those figures to 15% and 40% and see where I stand.
100 entries=$500 in pot
15 over 3 games x$15 =$225
40 over 2 games x $5 =$200
$225+$200=$425 paid out. $75 profit on $500=15% edge
So, I figure that I'd have at least a 15% edge here, which should be plenty to whether a few high scoring nights in my league, so long as I get enough entries. plus, it seems to me that many bowlers will think I'm a sucker for propositioning it. Would I be? Is there something amiss in my calculations? If so, please set me straight. If not, and you use my idea, I expect a 5% cut of any and all profits.

P.S. This was also posted on SSB