Gin rummy as a game is so easy to explain and play that all you really need is someone to play it with. If you can't even muster that much—and I know how this feels so I have no right to berate anyone—don't worry about pretending to be two people. You've heard of poker-based solitaire, now get ready for rummy-based solitaire.
Gimlet Rummy is based on gin rummy where you try to knock your hand in a limited number of deals. You don't really have an opponent that has its own hand, but this phantom still scores and the goal is to score 100 before he can and ultimately score more, just like in gin.
Starting with the usual ten-card hand you play each turn by drawing a card and discarding a card on a discard pile sorted by suit. You must hit with at most 5 points of deadwood (instead of the standard 10) before a pile contains six cards, if this happens your opponent scores. Along with the standard knock and gin(in this case a gimlet), there is also a double gimlet where you go out with a fully-melded 11-card hand.
The card discarded when going out doesn't go to the discard piles, but the deadwood cards do, and you can't go out if any discard pile exceeds six cards. Scoring when going out depends on how many cards are on the discard piles, with an extra 20 points for a gimlet and an additional 40 for a double gimlet. If a discard pile does reach six cards your opponent wins and scores 30 plus whatever deadwood remains in your hand.
Your only real opponent in this game is yourself. Cliché aside you don't have a lot of turns to make a valid hand; you have at most 21 discards before you go sour. Discarding decisions are between risking busting soon or breaking melds in strategic discards. A bonus dilemma from this is deciding between rushing a quick score or taunting the pile for a gimlet or a double, the 20 or 40 point profit a great reward to those who dare.
You can only lose at most four times, but more often you are allowed three losses. Your opponent isn't really clever, but it sure is a good scorer, so every knock is a cheap shot while every attempt at gin is almost an all-or-nothing battle.
A decent solo rummy implementation, this game has a unique balance of skill and chance that foundation-based solitaires lack. This still plays differently from actual rummy games as you aren't fighting against someone with the same goal as yours.
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Appendix: Rules summary
Gimlet Rummy by John Burton
Played with a 52-card deck. Aces low. A = 1, 2-10 face value, J-K = 10.
Shuffle the deck and deal yourself 10 cards.
Melds consist of at least three cards and can be a run(consecutive cards of the same suit) or a set(cards of the same rank). Cards can only belong to one meld at a time.
In every turn draw a card then discard a card by placing it in a discard pile matching the card's suit.
When you go out your base score is based on the number of cards in each discard pile:
0 cards = 10 points
1 card = 8 points
2 cards = 6 points
3 cards = 4 points
2 cards = 2 points
5 cards = 0 points
Your final card when you go out goes to the draw pile instead of the discard piles.
Knock: You can knock if you have 5 points in unmelded cards or less. These cards go into their respective discard piles and you score the final base score. You cannot knock if adding deadwood will lead to a discard pile having six cards.
Gimlet: All 10 cards of your hand are melded after discarding. You score the base score plus 20 points.
Double Gimlet: All 11 cards of your hand are melded without discarding. You score the base score plus 40 points.
If any discard pile reaches six cards your opponent wins and scores the value of your deadwood plus 30 points.
Play continues until someone reaches 100 or more points, this is the winner.
