Punk and Gin Rummy scoring

These posts are not related directly to Ambition, but to other games. Still, I receive a lot of questions on them, and should put them up there.

The first item is a card game I wrote, shortly before Ambition, called Punk. It's a fairly simple game, and I'm not sure how skillful it is, but it's fun and easy to teach. It was inspired by the Smallest Unique Integer (SUI) game. It's also adaptable to any number of players between 3 and 10.

The rules are available here: http://www.pagat.com/invented/punk.html

My Gin Rummy scoring rubric is a little more complicated. (For the rules of Gin, go here.) My opinion of Gin is that, while an excellent game, luck plays too prominent a role. I blame this on the scoring system. It tends to reward "early knock" hands, where one player is able to form a knocking hand (10 points or less of deadwood) within a couple turns, and the other is stuck with a high deadwood count (sometimes 50+). This isn't a skillful victory, but a lucky one, and yet it can award a player half the game (if played with a winning score of 100).

As a remedy, I developed what I call the "square root system" of Gin Rummy scoring.

In a knock (non-Gin) round, the knocking player scores for the round according to the square root (rounded down) of the difference in deadwood counts, with an upper limit of 5 points. Therefore,

* if his deadwood count is better by 1-3 pts, he scores 1 point for the round.
* if his deadwood count is better by 4-8 pts, he scores 2 points for the round.
* if his deadwood count is better by 9-15 pts, he scores 3 points for the round.
* if his deadwood count is better by 16-24 pts, he scores 4 points for the round.
* if his deadwood count is better by 25+ pts, he scores 5 points for the round.

In an undercutting round, the undercutting player scores the square root of the difference in deadwood counts, with a bonus of 3 points affixed. This means that an undercutting player can score anywhere between 3 and 6 points; the former in case of a tie, the latter in event of a 9- or 10-point difference between the scores.

In a Gin round, the Gin player scores the square root, rounded down, of the opponent's deadwood count, plus 4 points. The Gin player is thus guaranteed at least 5 points, and can theoretically score as much as 13 (if the opponent's deadwood count were to exceed 81).

The game ends when a player reaches a total of 20 points or more.

This scoring system has two marked effects on Gin Rummy, both of which I consider to be positive changes to the game. The first is that it increases the weight for Gin rounds (skillful) while decreasing that of early-knock rounds (lucky). Using this scoring system, any Gin is at least as good as the maximum score for a knocking hand. The second is that it increases the weight of small-margin rounds, which under the usual scoring system were practically insignificant. The longer a round progresses, the more likely the victory is to be skillful rather than lucky, but also the smaller the difference in deadwood counts will usually be. A round where the knocking player wins by a margin of 4 points is almost insignificant under the traditional method of scoring (4 points out of 100) while much more significant (2 points out of 20) under my system.

Having played using both systems extensively, my judgment is that the square-root system of Gin Rummy scoring simply plays much better.