#1
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Is my use of binomial distribution correct?
I had to relearn everthing I learned in high school about binomial distribution to figure out the probelm below (and by learn, of course, I mean found an online binomial distribution calculator). So, I'd appreciate someone making sure I'm going about this the right way.
PROBLEM: For the last couple of weeks of the NFL season I'm going to run a 7-game progressive parlay for some friends. The payouts online sports books give are: 7 of 7 - 40:1 6 of 7 - 4:1 5 of 7 - 1:2 Well, since the progressive parlays I'll be running cost my friends $20, I really don't want to be messing with a bunch of $10 payouts. So, I'll just up the other payouts to even things out. So, using a 52% success rate against the spread for Joe Public, I get: 7 right .0102807 of the time 6 right .0664292 of the time 5 right .1839579 of the time So, the sports book payout structure offers $15.38 of value per $20 progressive parlay. If I payout $850 for 7 right and $100 for 6 right, my payout structure will offer the same $15.38 of value per $20 progressive parlay. Does everything look kosher? Thanks. |
#2
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Re: Is my use of binomial distribution correct?
[ QUOTE ]
7-game progressive parlay [/ QUOTE ] I was under the impression progressive meant that it grew each week someone didn't hit it. But based on your description the payouts will be constant from week to week. If: -the payouts are a constant $850 for 7/7 and $100 for 6/7 -there is a 52% chance of success on each game The EV of the game is $15.38. If you charge $20 per go at this you stand to profit. |
#3
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Re: Is my use of binomial distribution correct?
I'm not really sure why it's called a progressive parlay. A regular parlay only pays out if you're perfect, where as a progressive parlay pays a smaller amount if you miss one (or more) games. I think a 12-game progressive parlay pays 12, 11, 10 and 9 correct picks, at 900:1, 80:1, 10:1 and 3:1 respectively.
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#4
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Re: Is my use of binomial distribution correct?
[ QUOTE ]
The EV of the game is $15.38. If you charge $20 per go at this you stand to profit. [/ QUOTE ] That's kind of the idea :-P So, I did everything right, both mine and the sportsbooks +EV are the same? |
#5
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Re: Is my use of binomial distribution correct?
1-7-21-35-35-21-7-1
128 total. |
#6
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Re: Is my use of binomial distribution correct?
[ QUOTE ]
So, I did everything right, both mine and the sportsbooks +EV are the same? [/ QUOTE ] Yes. The only difference is a fraction of a cent. |
#7
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Re: Is my use of binomial distribution correct?
[ QUOTE ]
1-7-21-35-35-21-7-1 128 total. [/ QUOTE ] That's only true if its a 50/50 proposition. Since I stipulated 52% in this problem I had to use binomial distribution to find out the weighted probabilities. For instance, if you could pick games correctly 99.99% of the time, hitting 0 of 7 would happen much less than 1 out of 128. |
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