Solitaire Klondike: Math Whizzes, Get Cracking

Standard old Klondike solitaire has been getting my play lately. I have recently gotten into the habit of discarding bad starts since that is so easy to do on the computer, and even with doing that my win percentage still has been around 10% over 106 games tallied. I was wondering how good that was but only seem to find opinions instead of facts searching for that. Anybody know what is really good?

Theoretically, it seems, maybe 2 out of 3 Klondike games have solutions. But at various places like wikipedia found this surprising statement: "... the theoretical odds of winning a standard game of ... Klondike are currently unknown. It has been said that the inability for theoreticians to calculate these odds is 'one of the embarrassments of applied mathematics' " A challenge for the Wizard or someone else in this group ?

I just read a few of the linked papers. The rollout strategy Yan they used is similar in concept to the strategy used to analyze video poker or Pai Gow. The difference is that in these casino games, after the player's one decision, the game is over. In Klondike, there are dozens of decisions, all of which affect later decisions. So the problem becomes exponentially difficult from a computational standpoint. The Oregon State paper is pretty interesting too.

But divining an optimal strategy in a multi-step strategy game is a terribly difficult task. Just ask the Wizard - he did a game with two player strategy choices, where the first impacted the second, and that took quite a while. And that's just going from 1 choice to 2. Going from 2 to a larger number (like the number of plays in Klondike) is beyond the capabilities of closed-form analysis at this time. You have to use heuristics or you'll never come close to finishing.

I read a piece once about a guy, last name started with a C, that offered soliare. $52 bucks a game, $5 for every card peeled off, single draw, one time through. They said the odds couldn't be figured, but he made a fortune. I believe that particular variation is named after him. Anybody know of this, or did I have another dream???

I'm pretty sure this is how they offered it in casinos, back in the day. Klondike is one of the statutorially-defined gambling games in Nevada. See NRS 463.0152.

Quote: avargov

I read a piece once about a guy, last name started with a C, that offered soliare. $52 bucks a game, $5 for every card peeled off, single draw, one time through. They said the odds couldn't be figured, but he made a fortune. I believe that particular variation is named after him. Anybody know of this, or did I have another dream???

Canfield. Evil, evil game.

Quote: MathExtremist

I'm pretty sure this is how they offered it in casinos, back in the day. Klondike is one of the statutorially-defined gambling games in Nevada. See NRS 463.0152.

I'm pretty sure too. I think it was back in the fifties. Every time I get into a conversation with a real Vegas old timer I ask them about it. Usually they are not old enough to remember it, but sometimes they recall second-hand stories of it. I think they followed the 52 units to play and 5 units per card rule. Same as at Cryptologic Internet casinos.

Agreed, this is one nut on the gambling tree that has never been cracked.

Quote: Wizard

this is one nut on the gambling tree that has never been cracked.

Regarding the solution, why is it that modern computers don't help? If it is a problem of tediousness of examining all possibilities, could a program written for a computer [a super computer?] get that job done for this problem or other such problems?

I asked a related question about a year ago: http://wizardofvegas.com/forum/off-topic/general/530-solitaire-vegas-version/

Basically, I wanted to know if any casino currently offers, or ever offered, Vegas Solitaire.

Quote: odiousgambit

Regarding the solution, why is it that modern computers don't help? If it is a problem of tediousness of examining all possibilities, could a program written for a computer [a super computer?] get that job done for this problem or other such problems?

For a variety of reasons.

First, there is the very large number of starting positions.

Second, there are times when a decision has to be made. I.E. A spot opens up, and you have a choice of two cards/piles to move. Which you move affects the rest of the game. The supercomputer would have to compute the remainder of the game for both possibilities before deciding which way was better. And, in the interrum, additional choices come up. While it's easy to picture the factorial tree being formed, it is also a chaos situation.

It is not just tedious from a multiple options of play point of view, but from a programming standpoint as well.

It quickly gets staggering to the point of being impossible.



Maybe if HAL took a crack at it....

But since HAL is already 14 years behind schedule (or 19 years depending on your point of view), don't hold your breath waiting for the answer.

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