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wordcross

 Posted: Wed Feb 24, 2010 5:25 am    Post subject: 1 I think this counts as a puzzle, but it's one to which I don't actually have the answer (although I'm sure that a definite answer exists). So, like many people, I play far too much solitaire on my computer. I play the built in solitaire game that comes with windows (Still XP by and large, yet) I usually play the game as a something to distract me while I'm in the process of doing something else, so I play easy. I have it draw a single card at a time, untimed, with standard scoring. For the purpose of being as clear as possible, let's adopt the following conventions for describing gameplay elements: -The "Draw Pile" is the stack of 24 cards that the player can flip over one by one as he/she attempts to put them into play -The "Stacks" are the 7 columns of cards where the majority of the gameplay takes place -The "Ace Piles" are the 4 stacks of cards that end up at the top of the gameplay area (Ace on the bottom, King on top) The scoring for the game is as follows: -Start at Zero. -Turning over a card in a play stack is worth 5 points. -Pulling a card from the draw pile and playing it on a stack is worth 5 points. -Putting a card up on the ace piles is worth 10 points. -Taking a card off of the ace piles to use on the play stacks is -15 points -Using an "undo" is -2 points. -Hitting the end of the draw pile and starting over is -100 points (subtracted when the cards are turned facedown once more) -The score never goes negative. It will stay at zero until positive points are attributed. There are a few gameplay rules in effect as well: -The cards in the draw pile are *not* shuffled when turned over. -When moving a single faceup card off of a facedown stack, the top facedown card is not automatically turned over. That takes another click. -Undoing the flip does not bring the moved card back to position. -Only one undo is allowed between moves. -Putting a card from the draw pile directly onto an Ace pile is still only worth 10 points. Putting it on the stacks and *then* onto the Ace pile is preferable if possible, as it nets a total of 15 points. -The draw stack only goes in one direction. Once a drawn card has been covered by another drawn card, you must go through the entire stack again to reach that card again (thus accruing a -100 point penalty) So using this system, I was able to figure out what the maximum possible score is. As far as I can tell, that's: [745] In addition, I figured out what the lowest score is that a player can get if he/she is attempting to get the highest score they can. [520](Since the score doesn't go negative, just bring all 52 of the cards down to the stacks before putting them all on the Ace piles. At 10 points apiece, that's 520 points) The question I haven't figured out yet is a hypothetical that negates one of the rules: If it were possible for the score to go negative, what is the lowest score possible if the player plays perfectly* and finishes the game? This includes the possibility that the cards have been shuffled such that it is necessary to go through the Draw Pile multiple times. *to play perfectly means to use every opportunity to play necessary cards in order to win and get the highest possible score. _________________Has anyone really been far even as decided to use even go want to do look more like?
bonanova
Daedalian Member

 Posted: Sat Mar 06, 2010 9:31 pm    Post subject: 2 Although this sounds like an interesting problem to simulate it sounds like you've been able to prove the answers. Kudos.I may try a simulation. Re: sig. It's been tried. For another opinion see Rom. 6:1,2._________________ Vidi, vici, veni.
wordcross

 Posted: Sun Mar 07, 2010 3:50 pm    Post subject: 3 I have the answers to the first couple of questions, but not the last one. I'm not so good at mathematically assessing the issue, but I've been trying to decide what I think would cause the most runs through the draw pile. Something where you're only able to use a card at a time to help reveal cards on the play stacks, so it goes back and forth. I'm not sure how plausible it is that this could happen without other choices becoming available, but I'm sure there could be quite a run._________________Has anyone really been far even as decided to use even go want to do look more like?
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