# Gambling Statistics

**URL:** <https://boards.straightdope.com/t/gambling-statistics/592788>\
**Category:** Factual Questions\
**Created:** [August 15, 2011, 3:47pm UTC](https://boards.straightdope.com/t/gambling-statistics/592788 "2011-08-15T15:47:58Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![randomface](https://avatars.discourse-cdn.com/v4/letter/r/5fc32e/32.png) [@randomface](https://boards.straightdope.com/u/randomface)\
**Post date:** [August 15, 2011, 3:47pm UTC](https://boards.straightdope.com/t/gambling-statistics/592788/1 "2011-08-15T15:47:58Z")

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I did not take statistics at any point in my academic career. I kinda wish I had sometimes. This is one of those times.

I had 8 scratch off tickets. The odds of breaking even or better were listed as 1 in 4.32. I “won” 6 of those 8 tickets. How do I calculate the odds of this occurring? All the examples I have seen use a coin toss, which has a 50% chance, and I cannot figure out how to convert that process to this example. Can anyone help? Thanks.

tl;dr I won 6 of out 8 tickets, each has 1 in 4.32 odds. How unlikely was that?

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**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\
**Post date:** [August 15, 2011, 5:48pm UTC](https://boards.straightdope.com/t/gambling-statistics/592788/2 "2011-08-15T17:48:35Z")

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> [@randomface](#):
>
> I had 8 scratch off tickets. The odds of breaking even or better were listed as 1 in 4.32. I “won” 6 of those 8 tickets. How do I calculate the odds of this occurring?

Type  
28\*(1/4.32)^6\*(1 - 1/4.32)^2  
at the Google prompt to see 0.00254427602, or 2.54%.  
In this expression all but the “28” should be clear. C(8,6) = 28 is the number of ways of choosing 6 objects out of 8. (C(8,6) = (C8,2) = 8\*7/2.)

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**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\
**Post date:** [August 15, 2011, 6:50pm UTC](https://boards.straightdope.com/t/gambling-statistics/592788/3 "2011-08-15T18:50:42Z")

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I see there are several Binomial Probability calculators available online, such as the ones [here](http://stattrek.com/tables/binomial.aspx) and [here](http://www.stat.tamu.edu/~west/applets/binomialdemo.html).

In your example, the number of trials (n) would be 8.  
The number of successes (x) would be 6.  
And the probability of success on each trial (p) would be, **if I’m interpreting what you say correctly** , 1 / 4.32, or 0.231481481.