plasmid

It's not impossible.

Yes, you're more likely to win if your tie is cheap and more likely to lose if your tie is expensive. That's why, even if you go into the problem thinking you have a 50/50 chance of winning if you don't have any prior knowledge of the values of the ties, you in fact have a greater chance of losing if your tie is expensive than if it's cheap. So the outcomes are really not equal and are dependent on the value of your tie.

Wait, does the driver have to have apples in his truck and be eating them in order to drive? If so, then I'll have to change my answer in post 6. I was thinking that he only ate apples if there were any in his truck, but he could drive without eating apples if he wasn't carrying any.

The most intuitive way (well, only intuitive way) I can think of to explain why the logic "I have a 50/50 chance of winning/losing" and "if I win then I gain more than if I lose" is faulty is because, particularly if this were to happen in the real world, the wives would not spend some amount of money on a necktie that could like anywhere within the range of positive real numbers. There would have to be some probability distribution of how much money they could spend on a tie. As soon as you create a probability distribution from which the two ties are drawn, it becomes clear that the more valuable your tie is, the more likely you are to lose the bet.

Thanks for getting this one started, PG. Not a bear trap, lines 5-6 are pointing toward something else.

When playing alone, the house's odds of winning $1 might be 125/216, but they also have non-zero odds of losing money to the player (and more than $1). So expected winnings by the house would be lower than 125/216.

How did you get 58 cents from that? Using the same numbers, I came up with 50 cents also. Just to make sure, since I'm getting the same answer, is the net outcome for the player: Lose $1 if no dice are your number Break even if one die is your number Gain $1 if two dice are your number Gain $2 if three dice are your number? It could still be in the house's favor if all of the non-losing options net the player $1 more; that is, they get their ante back and the number of dice they match is the number of dollars of profit.

I haven't watched Dr. Who since the really old episodes when I was just a lol-kitten, but this makes me think of

Hollow's my skull, think that I'm dead? Conclusion untrue, from burrow loft Union maintained, steel our thread It's straight as a brick is light and soft Recognize me? Better inspect A fraudulent claim shall not get through Handshake select one I reject In Soviet Russia, teeth brush you!

Maybe six hundred-ish. More if you like to write dates out like "August twenty-third, nineteen ninety-seven" instead of using digits. Less if you included some math riddles in the memoir. Possibly thousands if the page numbers were written in Roman numerals and weren't the source of the digits.

I see two. They are larger than the smallest equilateral triangle that could be formed from the white points in TSLF's post.

Does the driver start off with 3000 apples and need to deliver as many of them as possible to his destination, or does he need to end up with 3000 apples at his destination while starting the delivery with as few apples as possible?

Never underestimate the Dude. Hopefully the imagery of the riddle is obvious to all after seeing the answer.

With a little bit of magical sleight-of-letter:

Not a ship, that would take this too close to what the title says I'm not. Neither yoga nor the stocks. As you say, there are key clues that wouldn't fit with those and are pointing elsewhere.

Bloodthirsty tongues, coated sweet Welcoming mats on the floors Lost in their dream, thus I greet Then wake with a crack at the boards Metal and wood, right and left Crashing, they pray to take flight Fully renounce plan of theft For life or for death clinging tight

I had been considering the scenario where the amount of money in the envelopes could be any real number. In that case, if you have no information about the probability distributions, both an integration of your post 13 over the entire range of possible values in the envelope and the experiment of making random probability distributions shows that there is no gain for switching. However, I'm still not sure I can make an adequate math - to - english translation of those results; in particular showing how this is fundamentally different from a game where you are given $1000 and asked whether you want to flip a coin to either double or half your winnings (which is a no-brainer) in a way that makes intuitive sense. If the amount of money in the envelope is restricted to integers, that's a whole new can of worms because being even or odd gives information. I'll have to mull over post 7 again and decide which of those two conclusions I like the best.