Yet another bowling question

[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

[cavalier]

Daliman, I love it! Finally, someone that thinks like me!

I think you are more correct in your second calculations.

I would also consider the following. As a league goes on, deeper and deeper into the league, more and more weeks/scores build up. Averages tend to move less. Players, however, can still improve. You might be "exposed" to players who improve late in the season since they will become part of those who bowl over average every game.
A semi-related story... making money using bowling balls and a little positive expectation
I am actually one of them right now, and I'm in position to profit from it already.

I started bowling in the summer. I ended a 10 week league with a 144 throwing a straight ball.

After 12 weeks in the fall league, I was a 150 straight ball roller. I took a lesson, bought a fingertip ball and began throwing the curve.

I then placed a bet with a team mate. $50 for whoever ends the season with the higher average. He was 156, I was 154 at the time. I told him I needed motivation.

2 weeks after the lessons I went nuts bowling at every bowling special there was.

Currently, my last 48 games have a 181.45 average. I'm 2 pins ahead of my opponent and averaging about 65 pins more than him weekly! The 30 pins came from being able to throw more strikes. The spares still go down with the straight ball. He was a 150 bowler who was already throwing a curve. His chance for improvement was much less than mine, and his need for action was there for me to profit from! /forums/images/icons/grin.gif

One more way I'm making this same guy pay for my improvement. 10 cents a pin, per game. After each game, the "damage" is rounded up to the next $1. He's paying for about 1/2 of my league fees weekly now!!!

p.s. I'm going to look into running this pool in my league..

[Bozeman]

The error in your first calculation is the 25%=.5*.5 chance of 2 plus games. You need to include the probability of losing in your third game (and also the # of combinations). To bowl 2 plusses and then one minus will happen .5*.5*.5=12.5% of the time, similar for -++ and +-+, so there is 3*12.5=37.5% chance, as your second calculation effectively found.

In addition, it is probably easier to bowl below your average than above because of the vagaries of bowling scoring, so you probably have an even better than 12.5% edge.

Craig

[cavalier]

I asked around my league last night and got a bunch of guys saying "sounds interesting" and "ask around", but no one said, "I'm in".

</font><blockquote><font class="small">In reply to:</font><hr />
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


[/ QUOTE ]


I've been around gamblers a long time and if there's one thing I have seen it is that they like to think they have an easy chance to win. They only win if they get all 3 games over average ( which they probably think is too hard to begin with ). If we can modify it to give them profit at 2 OR 3 games, they might bite. /forums/images/icons/grin.gif


From the math, we know that there will be about 15% with 3 games and 40% with 2 games.

So, $5 entry from 100 guys = $500 in pool.
Pay $10 for 3 over and $7 for 2 over.

15 over 3 games x $10 = 150
40 over 2 games x $7 = 280

$150 + $280 = $430 -&gt; $70 profit on $500 = 14% edge.

Still have a good edge and the game might be more appealing.

You stand to get about 70 cents out of every player.

The more the merrier, obviously. If you only get 10-20 guys a week it might not be worth the hassles/risk.

[Ray Zee]

as long as most everyone does it you might be okay. but in bowling certain lanes favor certain players and they will almost always go over in those spots. if many of your bets just come from those people you will get fried.
plus you have to use the right average. if its from three game series then you may be okay again. but the second game and third are a big favorite to be higher than the first. lots more things to take into account than averages.
i used to bet a guy that averaged over 200 he couldnt shoot 200. but i moved him around the lanes each game. i always slaughtered him. if i left him in one spot on a pair he would eat me alive.

[KUBowler99]

Ray,

What do you mean you 'moved him around the lanes'? Did you make the individual move on the approach and still shoot over 200? The guy's either an idiot or so full of himself that he thinks it's possible.

I've been bowling the majority of my life (I'm 29). I bowled in college for the University of Kansas. There are certain areas on a lane that are 'unplayable' or at least 'unscorable' in every house in the country. You may be able to score on a lane crossing the 10-board (2nd arrow) and then move to a shot on the 20th or 25th board (4th or 5th arrow) and become clueless. The opposite would also be true. The majority of house bowlers would fail miserably.

A more interesting and even (although still in your favor) proposal would be to bet an above average to good bowler they couldn't score above their average bowling each frame across 12 lanes. The difference in topography of a lane bed from lane to lane, the quality of construction, and the minute changes in the oil patterns would make this extremly challenging, especially for the 190-200 average house bowler.

Just a thought.

[Ray Zee]

just move him around until you find lanes that he has trouble hitting the pocket. then you got him. if he starts to get it move him again.
i did the bowling thing back in the seventies when guys like, tita semez, mike lemongelo, ernie slegal, were king.

[scalf]

/forums/images/icons/laugh.gif i remember chris schenckel stating one of the players in the saturday bowloff had just won a big 7 cs tourney..wonder if that was you??? /forums/images/icons/cool.gif