# Odds problem - roll a pair of dice

**URL:** <https://boards.straightdope.com/t/odds-problem-roll-a-pair-of-dice/767763>\
**Category:** Factual Questions\
**Created:** [October 6, 2016, 1:41pm UTC](https://boards.straightdope.com/t/odds-problem-roll-a-pair-of-dice/767763 "2016-10-06T13:41:48Z")\
**Posts on this page:** 1\
**Showing post:** 306

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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:** [October 9, 2016, 2:11pm UTC](https://boards.straightdope.com/t/odds-problem-roll-a-pair-of-dice/767763/306 "2016-10-09T14:11:08Z")

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> [@jtur88](#):
>
> I don’t see why all these motivational therapy issues keep coming up. To me, the problem is quite straightforward.
> 
> An honest examiner … satisfies the requirement to move on to the next step, so he comes out of the room and announces that much (only) about what he has seen. He asks me what is the probability that there is a pair of sixes on the table. I calculate the odds an tell him. What else do you need to know, in order to be assured that you have sufficient information?

I agree! It’s fairly clear that this was the puzzle intended; and some of the alternate protocols proposed are far-fetched.

I think the people showing alternate protocols should avoid these complaints by incanting something like “Strictly speaking, the puzzle should be written less ambiguously (as **jtur88** has done above) but …”

What doubles the confusion is that some Dopers are computing the wrong probability for the model they select. Thus there are two intertwined subthreads: a vehement argument over where the problem statement is crystal clear or ambiguous (which belongs in IMHO or Mundane-Pointless I think, not GQ), and separate disagreements involving probability arithmetic. (When someone writes “1/6” it isn’t clear whether they’re using an alternate model, miscalculating for the normal model, or just making a typo.)

~ ~ ~ ~ ~ ~ ~

As I said upthread, this puzzle is in the Monty Hall category. Several weeks ago I posted another such

> [@Pointless but interesting math puzzles](https://boards.straightdope.com/t/pointless-but-interesting-math-puzzles/760745/16):
>
> Here’s an interesting math puzzle of the Monty Hall genre. It actually isn’t “pointless” — Expert bridge players need to know the answer. (And if you already know the answer, please let non-bridge players tackle it first.)

To avoid hijacking this thread I’ll Spoiler the problem statement.

[SPOILER]The puzzle arises in the game of contract bridge, but non-players should be able to understand the setup. You and your partner (the dummy) have nine hearts missing only the Queen, Jack, Trey and Deuce. You cash the Ace; LHO plays the Trey, RHO the Jack. You lead toward dummy’s King, LHO following with the Deuce. _Should you play for the Queen to be with LHO or RHO?_ (Your opponents are indifferent in their plays of Trey vs Deuce, or Queen vs. Jack. However, as the play has proceeded they would not play a picture card when a small card still available.)

There are only two possibilities that remain for the original holdings:

LHO: 3 2 RHO: Q J  
LHO: Q 3 2 RHO: J

The cards were shuffled randomly to begin with and, with nothing else to go on, the _a priori_ chances for these two cases are about the same. (1st case is slightly more likely than 2nd.)  
_What is the percentage play now?_

[/SPOILER]

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