July 28, 2005

More considerations

So, after further thought and testing, I'm definitely revising Nil downward, most likely to 20 points.

Two other considerations lie on the board for me:

First among them is the Hold round, where no passing occurs. On the passing schedule given in Rules of Ambition, I have the 4th and 6th rounds set as Hold rounds. I'm considering getting rid of them. They're more chance-driven than the other rounds, and I don't see what they add to the game (if anything) justifies the increased role of card-luck.

Many of the early rules of Ambition were inherited from Hearts, and discarded when found not useful in the new game. For example, there was a originally a rule against playing the K, or spade honors (the 6 was not introduced yet) on the first trick. In November 2003, I discarded this rule. The analogous rule in Hearts was useful; in Ambition, it was not. Likewise, I feel that the Hold rounds are more useful to Hearts than Ambition.

If I'm going to remove the Hold rounds, the question remains: With what, if anything, shall I replace them? I'm in the process of testing out a "Request" mechanic, and may introduce that if successful.

My second consideration concerns Slam. I'm considering making an even more drastic scoring revision: Slam scores 25 points. However, other players score no points for the round (but no strikes). Since this eradicates any difference between a 57-point Slam and a 75-point Slam, the round might as well be ended (in this case) as soon as Slam is achieved.

This revision won't alter, by much, the value of a Slam to the Slamming player. What it will do is eradicate some of the pesky complications Slam introduces for the other players. Consider a round that splits 57-29-5-0. Three players get decent outcomes (36 for Slam, 29, 20 for Nil) and one gets the shaft: a 5-point understrike. We must ask the question: why does he (or she) get punished especially? After all, the Nil player contributed as much to the Slam as the 5-point understriker. My view is that, if a Slam is made, the three other players ought to share equally in the punishment.

It's not completely "fair" for a person to score an understrike during a Slam round. A Slam usually happens when, near the second half of a round, one player is able essentially to take total control of the round. This means that the understriking player failed to take enough points, but effectively had half a round in which to do so. Moreover, it seems dubious to reward Nil in this case, when it is (from this perspective) only the accomplishment of having taken no tricks in a partial round. For these reasons, I feel that those things happening in the round aside from the Slam, in truth, are not always representative of how well a person played.

A Slam changes everything about a round of Ambition: cards that might normally be end-of-round winners become losers, for example. This means that a hand that could usually be played for ~20 points can become a 5-point understrike. This adds to the risk of taking one's first points (and forfeiting any opportunity for Nil). So, the threat of a Slam encourages Nil. This is not what I want. That Nil facilitates Slam is desired; that aspect of the game seems to work as designed, but that Slam encourages Nil is somewhat problematic (for no other reason, because said Nil further facilitates Slam). For this reason, I feel that it's overall for the best that, in the event of Slam, players share the same outcome: a 25-point loss relative to the Slammer.

So I am likely to implement these changes in the future.

July 23, 2005

Results on Nil tweakage + miscellaneous prestige whoring

So, after my post on 15 July, suggesting that Nil should be revised downward, I received several positive responses. I later determined 20 to be the appropriate value for Nil, based on two objectives. Keep in mind the concept of relative score, which is a person's score, for a round, minus the average of all four players' gains, and is the best measure of a good or bad round. My first objective was that, if Slam is not achieved by any other player, Nil should provide a positive (or zero) relative score. This is true if the Nil bonus is at least 20. The second objective was for it to be at least 3 points better, from a relative-score perspective, to take 11 points and stop a Slam than to make Nil and allow it. In a relative-score perspective, conceding 3 points is equated to losing 1, which means that, according to this objective, Nil should score no more than 20. So 20 seems to be the perfect value for the Nil bonus. It also played very well in some testing last night.

Secondly, yesterday I scored the most prestigious strike in known history. At the time, I was 20 points in the lead (0/79 to 1/59) after four rounds. I was playing the hand to keep Nil open, but holding the king of clubs in a 5-long suit with the intention of taking it if the opportunity arose.

In the middle of the round, the player at my opposite led the 6, followed by a ruffed A. Holding the five and king of clubs, I had the option of declining the trick, but knowing I probably wouldn't probably be taking any more, I figured it was safe. I followed with the K, knowing the ace and 2 had already been played, expecting a 0-point club to follow, giving me a solid, probably 24-point trick. Wrong. Matt Davis, on my left, had run out of clubs and ruffed the K.

The resulting trick, 6-A-K-K, was worth 29 points, the greatest total possible. There are six possible 29-point tricks, but this was the highest-ranking of them, making it the single most prestigious trick possible. I took no others that round, and still struck (the split was 29-26-19-11) because of it, but because I had not yet seen a 29-point trick, and because I'm a prestige whore who wanted to be the one getting the first 29-pointer, it was well worth the strike.

I did, however, lose the game because of this strike, with 1/136 against 2/139.

July 20, 2005

Some basic FAQs

I'm going to take this time to answer some questions I regularly get regarding Ambition. Anyone with more questions should feel free to send them to me.

1. What happens when someone takes all the points/tricks?

This is very rare; I've seen it once. There are several ways I can see playing it. One is to give it an even higher bonus value (50, 60, or whatever). Another is to allow a player accomplishing this to negate a strike. I generally leave this to the discretion of the players, but when I saw it happen we counted it as -1 strike. I've also heard the suggestion that, since it results mainly from a lucky hand, it shouldn't be rewarded especially at all.

2. What about when someone gets a negative score, by scoring 5 or fewer points, then taking the -6 LT option? Does that count as a Nil?

Ah, you got me. This is the one thing I didn't address in the rules. It rarely happens. Yes, I would count it as a Nil.

3. Why is Nil worth 24 points?

Nil is intended to give a fairly average round to a player without other options. While 24 might seem to be an excellent round, consider that when 3 players split the 85 (or 91) points, it's quite likely that at least one non-striking player will exceed it. That said, I'm strongly considering reducing Nil to 21 in my next revision of the rules, which will be issued "officially" around 23 November. Of course, unofficially, you can play however you want.

Before Nil was introduced, there was too much of a luck element in the game: players could get stuck with weak hands that didn't allow them much control over anything. Thus, the Nil bonus was introduced. Originally, Nil was worth 11 points. This didn't make it much of a bonus, so I upped it to 28. This was too high, so I reduced it to 24 (and only 16 if two people get it). Now, I'm considering taking it down to 21 or even 18, undecided on whether or not to continue penalizing double-Nil.

In assessing how good a round outcome is, it's important to note that the nominal score isn't what's important; it's the relative score that counts. The relative score is a player's score, minus the average of all four player's scores. For example, if a round splits 33-26-21-5 (the corresponding scores being 0-28-21-6), the average of the four scores is 52/4 = 13, and the relative scores are -13, +15, +8, -7.

In a "normal" (no Nils, no Slams) round, the "model split" is something around 29-24-19-13. The player with 13 has a slightly negative round (-1), the other non-striking players get +5 and +10. We infer that an average "good round" is somewhere around +4 to +8. The model split for a single-Nil round is 37-28-20-0. Originally, Nil was set at 24 to give the player a middle position between the two non-striking players. That gives him a relative score of +6. In truth, I've come to feel that this overrates the accomplishment. Reducing Nil to 21 would scale the relative score back to +3.75, which seems more in line.

Nil is, I believe, still somewhat overrated as a strategy, only because of its obvious defects. (On the other hand, that is partly my fault as designer for over-rewarding it.) The biggest danger of Nil is that the strategy is essentially passive, leaving a player unable to clear suits, stop a Slam, or control the round in any meaningful way. It's also quite possible that the Nil will fail late in the round (a 6D against a 5D when two are out of the suit, for example) and leave the player with an understrike. Finally, Nil allows many more Slams to happen than otherwise would.

The other liability of Nil is that it becomes more difficult with another Nil player. This has not proven, however, enough of a drawback to act as a deterrent, as collisions between two Nil players happen quite often.

4.Why is 57, and not some other number, the threshold for Slam, and why is the bonus set at 36?

I think the biggest question I get in this regard is why Slam is a constant bonus, instead of increasing with higher Slams. The reason, simply put, is that often the 57- to 60- point Slams are more skillful and interesting than the 70-point Slams, which often just result from unusual hands.

As for the threshold, 57 is what I call a "research constant"; it seemed to work best according to playtesting, I like it, and I probably won't change it. 54 is definitely too low. I've considered raising it to 60 or 63, but am leaning strongly toward keeping it as is.

5. What's the highest-scoring game you've seen?

I've been in games that have approached 700, but the highest-scoring game I'm familiar with comes from Al Hahn. It was a 940-point game, in July 2005, where the winning player scored 257 (!) points.

How high- or low- scoring a game will be depends completely on the players; how often they aim for Nil and Slam. Some tables routinely break 600; other groups rarely get above 400.

The lowest-scoring game I've seen was a 120-point three-rounder. I won it with 70 points. However, this was in November 2003 before Nil was introduced. I doubt you'd see a game under 160 with the new rules.

6. What's the lowest overstrike you've seen?

24, mine. I believe the split was 24-23-21-17.

In 3-player games, I've seen splits of 29-29-27.

7. Has it ever happened that the strike-out player also had the greatest point total?

It's rare. I've seen it happen twice; both times, to me.

Once I was in a game where, after four rounds, I had a clear lead: 0/84. Second place was 2/22. I struck in each of the next three rounds. No one overtook me in points, but the third-place player managed to move up from 2/14 to 2/72 and win.

In a tournament last spring, which was played as an 8-person rotation game (with people rotating in and out of tables with each round) I struck out, in the final round, ending with 3/239. The winning player had 2/238.

8. How many people play Ambition, worldwide?

As the number grows, I have less and less track of it. I would estimate that between 500 and 3,000 people play it regularly, 2,000 to 10,000 have played it, and that around over 150,000 people have heard of it (but probably most of them know nothing other than that a card game with the name "Ambition" exists.)

The doubling time for Ambition's popularity seems to be about 9 months.

July 15, 2005

Nil tweaks

First of all, I'm now in Madison, so anyone who's interested in setting up the Ambition scene in Mad-town should contact me.

I should admit at this time that I'm considering a minor, but important, change to the rules centered around Nil scoring.

Currently, Nil scores a 24-point bonus normally, but only 16 in the case ("double Nil") where two people achieve it. The "double Nil" rule was included to use Nil as a check against people going for Nil too often. The problem is that it didn't work as I expected, and therefore it's an extra rule that doesn't seem to do much good.

Instead, it seems better to revise Nil as follows: It's a 21-point bonus, in all cases. In the double-Nil case, this is still a pretty sorry round outcome (one opponent will always do at least 13 points better) and in the single-Nil case, it still does as I had hoped: provides a fairly average round outcome to the player achieving it.

Anyone with thoughts regarding this change should contact me: ambition_game@yahoo.com .

July 03, 2005

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.