I have not peeked at the answer.
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
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.
I would chose 333333
Colbster and dennis
Thanks for weighing in. I am still working on it.
Sam
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
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.
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.