Who can figure this puppy out?

[TwoCatSam]

I have not peeked at the answer.

[TwoCatSam]

One hundred thirty six views and not one of you has taken a crack at it.

I have not been able to solve it either.

OR do a thousand push-ups when no one is looking!

Samster

[Colbster]

Despite having the fewest of "high" numbers, the 2-2-2-2-6-6 has the highest expected value of 3.333.  All of the other die have expected values of 3.000.  My take is that you choose 2-2-2-2-6-6.  I haven't read the answer either, that's just my estimation of the math involved.

[dennisbelle]

I would chose 333333

[TwoCatSam]

Colbster and dennis

Thanks for weighing in.  I am still working on it.

Sam

[TwoCatSam]

I am trying to math or logic this out...................

If you pick the 111555, you know you have a 50% chance of losing.  Why?  You opponent knows what you chose and he knows you have a 50/50 chance of rolling a 1 and anything but 444400 would be guaranteed to beat you.  He would not chose that die.

However, if you roll a 5, he would have to roll a 6 to beat you.  You have a 50% chance of rolling a 5 and he has a 33.33% chance of rolling a 6, so what are your actual chances of winning if you chose the 111555?  Is it 66.66% of 50%? 

I'm leaning toward the 333333 also.  If you chose that, you know your are a 3.  If he chooses 111555 he has a 50% chance of beating you.  You have a 50% chance of winning.  If he chooses the 222266, you have a 66.66% chance of winning.  If he chooses the 444400, you have a 33.33% chance of winning.  If you chose 333333, he would---being smarter than the average bear---choose 444400.

I do not understand how we can have a 3.0% chance of winning.  My math is not that good.

I do know Marilyn chooses these things because what you think is right seldom is.  Just once I'd like to win one of these challenges.

Come on, people.  Play along. 

Sam

[TwoCatSam]

I do not understand how one die can be stronger and it makes no difference which you choose.

DO NOT READ THIS UNLESS YOU'RE READY!  I WENT TO THE ANSWER AND IT IS MIND BOGGLING.  I EXPECTED IT TO BE.

[Colbster]

There are 3/6 where you get the 5 on the 5-5-5-1-1-1 and that beats the 4/6 2's on the 6-6-2-2-2-2 die.  However, 3/6 of the results are 1 which lose 100% of the time to the 6-6-2-2-2-2.  It comes down to the expected value as I thought.  The 6-6-2-2-2-2 is the strongest of the group.