Ask the Wizard #218
Edition Date: Nov 17, 2008
I need help with a puzzle called Eternity II. The prize for solving the puzzle is a staggering $2,000,000, a considerable amount of money to me. Here's a link to an interview, including the game maker himself, Christopher Monckton (former adviser to Margaret Thatcher, among many things). The game is obviously not really about gambling at all, but despite this fact, maybe you could add a word or two on your web page about it.
The game maker brags about the puzzle to be insolvable, in that link given above. I'm starting to think that he's actually right, and that he himself is the only one who will eventually become rich from selling that (ridiculous but fascinating) game. How would you, being a mathematician and all, go about solving this type of puzzle?
I hope you’re happy; I’ve been obsessed by this puzzle for the last month or so. I was lucky (or perhaps unlucky) to find the 256-piece puzzle at the local Borders book store, but I had to buy the four clue puzzles on eBay, from a guy in Australia.
I wrote a program that can easily solve the four clue puzzles. It solved the 72-piece clue puzzle #4 in less than a second. The way I did it was with a simple brute-force recursive program. I mapped out a path on the board, starting with the border. At each position, the program looped through all the unused pieces, looking for one that fit. If it found one, it moved to the next square, if it didn’t, it moved back a square.
I have had two computers crank away at the 256-piece $2 million puzzle for weeks, and neither have come anywhere close. I tend to agree with what the creator said in that video, that if you hooked up ten million of the world’s fastest computers, they still might not find the solution by the death of the universe. You would think I would have heeded his warning before starting, but in the face of a good puzzle, all consideration for practical use of my time goes out the window.
I have lots of ideas for shortcuts, but even if they sped up my program by a factor of a billion, it still probably wouldn’t help. I’m going to be extremely impressed if anybody solves this thing. What really nags at me is I feel there is some undiscovered branch of mathematics that could solve puzzles like this easily. Until then, I think glorified trial and error is the best we can do to solve it. Today’s computers are simply too slow, and the number of combinations too vast, for that to have much of a chance of success.
My question is on craps. I know that the Fire Bet is a lousy bet, but I bet it anyway, when I am rolling. Well, I got lucky and hit my four points, and was on the fifth point. I had won $75, and was on my way to winning $750, if I hit the 5th point. My other bets were $5 on the pass and $20 to win $30 on the 5. Having established the 5th point, which was a 5, I realized that I had a 2/5 chance of hitting it, for a net win of $785. I also realized that I had a 3/5 chance of not hitting it, for a net win of $25. If I wanted to hedge my bets, what is the largest win I could lock in? Also, what are your thoughts on this strategy.
Reason #4 why the Wizard likes Bovada:
Bovada offers the triple crown of gambling: casino, poker, and sports. Many other casinos have tacked on poker as an afterthought, and many poker rooms have tacked on a casino as an afterthought, and the lack of attention shows, sometimes painfully. And very few of these sites let you make sports wagers.
But Bovada doesn’t just offer all three, they do each one well, and everything’s integrated. It’s easy to play all three off one deposit, off just one account.
Another nice thing about Bovada is that you don’t need a separate account to play casino games with fake money. In fact you do not even need an account for that at all, you can just click over there and play. Finally, Bovada usernames are only six or seven characters long making them possible to remember. By contrast some competitors’ usernames are extremely long and cumbersome.