I never learned the name of it, and it was suprisingly difficult to google for it, but it’s a simple game, so it doesn’t really matter.
Shuffle a deck, draw the last four cards from the bottom, and flip them over on the top. The first and last cards of the four card set are the only one that matter. If the SUIT matches, discard the middle two cards. If the NUMBER matches, discard all four cards. If there is no match, draw another card, and check it against the last three in the series. Repeat until you’re drawn all the cards.
It’s an alright game, in a mindless sort of way. However, after playing it a few times, it rapidly becomes apparent how impossible it is to ‘win’ the game with zero cards remaining. Basically, the first card you draw has to be the same number as the last card you draw. As it happens, after a year and a half of moderate, but consistent playing, I ‘won’ the game. I’m curious if I got lucky, or if it was a matter of time by this point.
So what are the chances of winning this game on any given day? I lack the knowhow to even approximate an answer, so I leave it in your hands.
I have played that game and I know it as Accordian. You are right in that there isn’t much to it, but I think I won it a little more often than once every year and a half.
You can work the deck better if you do not immediately remove cards when there is a number or suit match. Keep pulling a few more cards to get the lay of the land, then choose your path.
I wrote a quick program to play these games (assuming that multiple plays per draw are possible, as in Achernar’s example). After playing one million games, here are the percentages of games with N cards left:
And indeed there was a bug… I should have noticed this: since you’re always removing an even number of cards from the deck you must end with an even number. Here are my new values, again with one million runs:
I think off hand, the game’s name is accordion. I also want to reference Idiots Delight… but I am way less sure on that one. In any case, I am sure www.Pagat.com
will help you. (Playing Card Games Website, unafiliated with any card company, as far as I can tell.)
Rules clarification needed:
When cards can be removed, must they be removed instantly? In the week I spent on this, I would lay out all 52 cards, and work from the back so I could plan what would be left. In other words, I gave myself the option to take out the 2 or 4 cards sections in order I wanted, which gave the ability to go down different paths. I recollect winning over 10%. Someone else mentioned looking a few cards ahead, which seems a weak version of my strategy. Omph seems to assume that this is not legal. What are the rules?
Yes, I assume that any move which can be made must be made immediately. This makes the game a no-brainer (the rules completely determine your actions) and therefore easy to program. Your variant sounds like more fun to me though.
I do like that game. It’s good when you’re sick, and can’t really sit up. Getting sick of not winning, I added a rule of removing all four cards for a 4-card flush. Adds to the “excitement”.
In my family, we call this game “hand solitaire”, since it can be played with all of the cards held in hand, without a table (great for long car trips). We used exactly the rules that Marlow set out, with “chain moves” allowed. And like Munch, we toyed with removing all four on a “flush”, but while this decreases the expected number of cards left, I think it actually decreases the odds of winning.
Omphaloskeptic’s Monte Carlo numbers seem to agree with my experience, by the way: It seems to be fairly common to end up with 2, 4, or 6 cards left, but nigh impossible to get zero.
.7% eh? I guess that corresponds with my playing experience, although I would have thought it much harder, just based on the fact that you have to be pretty luck from the start to even have a chance of winning the game.
As for the game, you must take any moves that you can, but you can ‘chain’ discards together. I might play around with the variations.
Omphaloskeptic, I’ve always called this “One-Handed Solitaire,” and I too wrote a quick program to give almost identical output to yours. It’s been over a year, but your numbers look right; I especially remember thinking “if I can get down to twelve cards, I’ve done better than average.” And just for your own satisfaction, I originally wrote my “print” line to list all 52 possibilities too–but I had a fencepost error, and the program listed every even number as “impossible” an every odd number as having a positive probability.
I’ve played this game ever since I was a little girl. I never knew the name. It’s great for brainless, I have no table to lay out solitarie times. The rule that I always wondered about is: What happens when you use all the cards you have flipped over? Now all the cards are face down. Do you draw four from the back again? Or even if it works out to where you only have one or two left, can you draw to get back up to four? I’ve had people tell me I’m cheating when I do that, but I don’t understand why.