# Why pay double if the chance is the same?

**URL:** <https://boards.straightdope.com/t/why-pay-double-if-the-chance-is-the-same/719141>\
**Category:** Factual Questions\
**Created:** [May 3, 2015, 4:14am UTC](https://boards.straightdope.com/t/why-pay-double-if-the-chance-is-the-same/719141 "2015-05-03T04:14:13Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![qualityleashdog](https://avatars.discourse-cdn.com/v4/letter/q/9f8e36/32.png) [@qualityleashdog](https://boards.straightdope.com/u/qualityleashdog)\
**Post date:** [May 3, 2015, 4:14am UTC](https://boards.straightdope.com/t/why-pay-double-if-the-chance-is-the-same/719141/1 "2015-05-03T04:14:13Z")

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I like to pay the daily 3. If you pick 3 different numbers, in any order (combo), you get X payout. But if you pick two identical numbers plus a third, you get double the payout. Why? Each number is independent of the last number drawn, so why double the odds? Here’s a link to the payouts and policy: [Daily 3 Drawing | Hoosier Lottery | Hoosier Lottery](https://www.hoosierlottery.com/games/daily-3)

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**Author:** ![Alley\_Dweller](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alley_dweller/32/430_2.png) [@Alley\_Dweller](https://boards.straightdope.com/u/Alley_Dweller)\
**Post date:** [May 3, 2015, 4:28am UTC](https://boards.straightdope.com/t/why-pay-double-if-the-chance-is-the-same/719141/2 "2015-05-03T04:28:09Z")

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I think you are comparing a 6-way box with a 3-way box.

Let’s say you play a 6-way box and choose the numbers 1-2-3.  
You win if any of the following number combinations are chosen:

1-2-3  
1-3-2  
2-1-3  
2-3-1  
3-1-2  
3-2-1

But if you play a 3-way box and choose the numbers 1-1-2,  
you win if any of the following number combinations are chosen:  
1-1-2  
2-1-1  
1-2-1

So in the first case, you have 6 chances to win. In the second case, you have 3 chances to win.

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**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\
**Post date:** [May 3, 2015, 4:31am UTC](https://boards.straightdope.com/t/why-pay-double-if-the-chance-is-the-same/719141/3 "2015-05-03T04:31:54Z")

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If I understand correctly.

If you pick 1 2 3, then you win on any of 6 ordered draws: 123 132 213 231 312 321.

If you pick 1 2 2, you win on only three ordered draws: 122 212 and 221 so it’s twice as hard to do hence double the payoff.

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**Author:** ![qualityleashdog](https://avatars.discourse-cdn.com/v4/letter/q/9f8e36/32.png) [@qualityleashdog](https://boards.straightdope.com/u/qualityleashdog)\
**Post date:** [May 3, 2015, 9:08pm UTC](https://boards.straightdope.com/t/why-pay-double-if-the-chance-is-the-same/719141/4 "2015-05-03T21:08:49Z")

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Okay, the above does make sense. I call it combo because that’s what I play, straight + box, but it does make sense when you say 6-way compared to 3-way. I think what had me confused was that other states don’t alter the payouts on 3-way vs. 6-way.