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.

Re: Is my use of binomial distribution correct?
 

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7-game progressive parlay

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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.

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.

Re: Is my use of binomial distribution correct?
 

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The EV of the game is $15.38. If you charge $20 per go at this you stand to profit.

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That's kind of the idea :-P

So, I did everything right, both mine and the sportsbooks +EV are the same?

Re: Is my use of binomial distribution correct?
 

1-7-21-35-35-21-7-1

128 total.

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.

Re: Is my use of binomial distribution correct?
 

[ QUOTE ]
1-7-21-35-35-21-7-1

128 total.

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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.