Ambition S*

This is a variant I developed called "Ambition S*". It may supplant standard Ambition among some players, because it's designed to further reduce the role hand-luck plays in the game.

It's no secret with Ambition that I had a specific aesthetic mission: to reduce the role of pure chance, in the form of hand-luck. I figure, based on some statistical analysis I've done, that hand-luck contributes to about 3-8% of the game's variance, most likely 4.2%, or 95.8% skill, strategy, and "flux" (more on flux later). Also, the 4.2% figure does not account for "strategic luck" (which is inevitable in strategy games of 3 or more players) nor table position.

While 4.2% luck may sound high, chess is about 1.7% luck if you randomize the white/black determination. It's very tough to get a game above 90% skill-and-strategy, without iterating it a bunch of times (e.g. Poker, which converges to 100% skill in the long long run).

Here's Ambition S*, or Ambition for the purist.

Ambition S*

This variant involves two alterations:

1. Randomized seating (*)

Seating arrangements change with each round, randomly. The deck is shuffled once or twice, then each person draws a card from the middle and places it face up. Cards are ordered by Rank (A high, 2 low) then suit (♠ > ♥ > ♦ > ♣). The person with the highest-ranking card stays put. The person with the 2nd-ranking card sits to that person's left, 3rd-ranking across, and 4th-ranking person sits at his or her right.

Motivation: Simply-put, table position matters a lot in trick-taking games. It's obviously not "hand-luck", but in trick-taking games, table position is an active source of "strategic luck". Being on the left of an aggressive player means that one will be in 2nd position a lot, and 2nd position is strategically much weaker than 4th position.

2. Scatter passes (S)

This follows, at least in an aesthetic sense, from the first alteration. If the standard passing cycle were used, one could possibly pass to the same opponent multiple times, and even in succession.

Scatter passes are used in every round of Ambition. For those unfamiliar with the term, a Scatter pass is a pass where each player sends one card to each opponent.

Motivation: Hold rounds, while challenging, add quite a bit of hand-luck to the game. My models (based on some research I've done on the game; I don't get much sleep) represent hand-luck as a normal random variable (in terms of contribution to relative score) with mean 0 and standard deviation around 1.5, but Hold rounds have a standard deviation of about 2.0, maybe a little more.

Also, there are rare "sure Slam" hands that are clear outliers to this normal model. These hands can become common after bad passes. For example, a person with 5 spades might be passed 3 more, by an opponent trying to clear the suit, leading to a slammable 8-card spade suit. This effect is partly "strategic luck" (seasoned players know mono-suit passes are a bad idea; poor players always add "strategic luck" factors to the game) but also part hand-luck. In fact, it's mostly hand-luck.

Finally, a common offender in terms of hand-luck is the usually abysmal "straight-flush" configuration, consisting of 3 or more cards of a suit in sequence (8-9-10-J♠). Some of these configurations are good (slammable) and others are harmless, but as a general rule, straight-flushes are bad: they involve a set of equivalent (for trick-taking purposes) cards that are hard to get rid of. We can't eradicate the straight-flush entirely-- sometimes it just happens-- but a common "screw-pass" will involve 2 or 3 cards in sequence, possibly creating a straight-flush in the passee's hand.

Scatter-passing also gives players more liberty in terms of their available pass options. For example, mono-suit passes are no longer dangerous, since the cards passed will all go to different opponents. It makes it "safe", in that regard, to clear a 3-card suit; on the other hand, it is more difficult to keep that suit cleared, since the cards received all come from different opponents.

Comment or write me: What do you think of this variant, Ambition S*? Good idea, or not so hot?

28 January 2005: Game Report

I'm not going to post game summaries often, because so many games happen per month that this blog would drown in them, but here's one, from earlier tonight, that was quite enjoyable.

Before I begin, let me clarify some terminology. In email, someone pointed out that I had, in the past, overloaded the term "points"; I would use it to describe both "points" taken in a round (in tricks) and points scored in the round's resolution. We'll resolve this ambiguity by henceforth referring to the first sense of "points" as chips, since they are recorded publically, usually using chips. That is, you might take 34 chips in around, strike, thus score 0 points.

The players were myself, Peter Antonov, Zach Hyman, and a girl named Sky. We began around 9:45 pm in a coffeeshop called "Goodbye Blue Monday's". Zach and Sky were new to the game.

Round 1

This was my first strike of 2005, and boy was it painful. I was playing for Nil, but held on to some rooks (jargon for 9-J; in this case, 10♥, 10♠). I saw Peter (slightly crazy) as a Slam-threat, and kept those 10's for "just in case" counter-Slam purposes. This was a bad idea. I got stuck eating 3 chips on the trick, 10♥-9♥-7♣-2♥. (I led, having taken a 0-chip club trick. Under the latest rules you may take tricks and get Nil so long as you score no chips.) I got no more tricks and had a round score of 3, an understrike. This just shows that one cannot play to screw other people. (I could have totally Nil'd that hand, but I feared that Slam.) On top of that, Sky did a fine job of denying Peter his Slam, taking 22 chips which, along with Zach's 18, fed Peter the strike instead of Slam glory.

The scores: Mike, 1/3; Zach, 0/18; Peter, 1/0; Sky, 0/22.

Round 2

I was dealt a reasonably powerful hand. While Peter went Nil, Sky took 16 chips and I got 28. Zach struck. Sky had a 7-point lead over me, I was in 2nd place. Throughout the game, Sky played very well for a brand-new player, I was impressed.

The scores: Mike, 1/31; Zach, 1/18; Peter, 1/24; Sky, 0/38.

Round 3

Zach went Nil, the round itself was very tense. Peter opened aggressively, taking 22 chips in the first five tricks. He tried to work a red-suit Slam, getting up to 33, then losing the lead. I held the A, 2♣. Nil was not an option for me. I had about 10 points, feared a limp round and Peter's slam. Peter led the Q♣ and the 10 followed from Sky. I played the A♣ in third position. Zach played the jack, so I won another useless 0-trick. We all wanted to bust Peter's Slam (who doesn't?) so this meant Sky couldn't have had the Bad Boy, nor Zach. Peter had it; there were 5 clubs left, 3 in my hand. Adrenaline pumping, I led the 2♣ in the hopes of forcing the King. (The odds were in my favor, but my heart was racing.) I, indeed, took the King-- 13 chips for me, no Slam for Peter. Peter's reaction was priceless; he accused me of counting (guilty, but still lucky.) Sky had 28, and Peter, 33, so I just took everything and landed at 30.

The scores were: Mike, 1/61; Zach, 1/42; Peter, 2/24; Sky, 0/66.

Round 4

I made several errors of judgment. With the right pass, I could've had a Nil hand, but I had seen two Nils at the table already and figured they were in fashion tonight. So I kept the A♠ and A, 2♣ instead of passing them. They were both well-protected (3-5-7-A♠, 4-8-9-A-2♣ and I didn't see any harm in keeping the boys around.

My first mistake was to grab the King, with the 2, around the fifth trick, not seeing that the Six was in there as well-- 19 chips, bringing me to a very premature 24. On the tenth trick, I ate a 6-point red and had only two apparent ways out of the lead: the 4♣ and the 3♠. I also held the A♠ . If I had done my counting homework, I would not have led the 3, but I did. The 3 met the only remaining spade, the 2. I got screwed on the three of spades. (The ace, on the other hand, would have triggered the 2's high/low and fed Zach a hearty diet of chips.) Doomed at this point, I played the sure-winner Ace (it's always better to strike hard than strike soft; evenly-split rounds are the worst falls for the striking party) then lost the final trick on the 4♣; it turned out that 3 people had clubs. I ate a very bad strike: Zach got 19; Peter, 27; Sky, Nil for 24. My relative score (RS = personal score - average of all 4) of -17.50 tasted sour beyond description.

At this point, I was tied for a distant second place; Sky had a 29-point lead.

More specifically, the scores were: Mike, 2/61; Zach, 1/61; Peter, 2/51; Sky, 0/90.

This was a time for me to reflect and reconsider: I play unambiguously for 1st, and the only way I could see to a win was a Slam. With 2 of us "on the wire" (jargon for having 2 strikes) the game was almost over.

My counter-Slam efforts had ruined me in Round 1, reiterating the point that Ambition's not a game where one can play against a specific player. The game's designed to screw at least one person each round, but anyone who tries to exert control over who that person is, is playing with fire and often gets burned. Then I just totally botched round #4.

I resolved that, in the final round, I would play strictly for my bottom line. This meant I wouldn't give up a perfectly good Nil to play counter-Slam, as fun as it is to bust a Slam.

Round 5

I drew a no-brainer Nil hand and got two pawns (jargon for 3-5) in the pass (Scatter, this round). Peter, sending me the 3♣, told me he was giving me a card that reminded him of me. I don't know what he meant-- I'm not a Nilaholic-- but I didn't mind the gift in this case.

About 40% of hands can be played, with the right group of players, for Nil. Even still, I only play about the bottom 15-20% that way. Nil provides an average nonstriking round, but has several flaws: it's an inherently passive strategy, it facilitates Slam, and getting busted on a small trick just hurts.

If I'm going to set out for Nil, I pretty much need to know that I have the weakest hand, and be fairly confident that there won't be another successful Nil on the table. Double-Nil is the pits-- it's only 16 points when 2 people get it-- and it's also very easy for one of the other players to Slam (57, or 5/8 of the deck) when two players are racing for the bottom. Ambition's check against the overuse of Nil is Nil itself.

Zach was limping for a while, but in this case I knew I could out-Nil him. I had no power anyway, so Nil was about my only option. I just wanted him to eat something, to fail and let me have the Nil glory all to myself. He got a 4-chip diamond trick, and nothing more, taking an understrike.

The rest of the chips? Split 44/43, but Peter got (and used) the -6 LT which dropped him to 38. Sky struck, finally. I actually dropped to third place (from tie-second) but on much better terms. Peter, from last place, got a monster round-- relative score of +21.50, putting him 1 point from the lead.

The scores were: Mike, 2/85; Zach, 2/65; Peter, 2/89; Sky, 1/90.

[Ed. note: At the time, we believed Peter to be in the lead at the end of round #5, with 95. I miscalculated Sky, who struck, to have taken 45, in which case Peter would not use his -6LT. Later review showed that she had taken 43; Peter did need his -6LT after all.]

Round 6

Ambition is, always, anybody's game. It's 96% skill-and-strategy (about 4% of the game's total variance results from hand-luck; however "strategic luck" accounts for a bit more). Yet as late as game's end, every player has the chance to win.

Part of this results from Ambition's uncertain endgame: it's usually not clear until near a round's end that it is, in fact, the final round; the variable length of Ambition (game-ends-at-3-strikes losing condition) was built-in for exactly this purpose.

The 6th round sure felt like the end-- unless Sky struck, or someone Slammed, the game was over... and two opponents had a red trick's worth of high ground on me.

I wish I remembered more detail about this round: it was very intense. As for me, I was dealt a nice, 20ish hand-- a first-round blessing, an endgame nerve-wrecker. It wasn't a Slam hand (of course, I love Slamming, but I don't try with long-shot hands since I'm pretty risk-averse) and it wasn't a Nil hand (just as well; I like controlling the late rounds).

Any Nil intentions were shot by about the sixth trick: we'd all taken points. This was also good because it meant that Slam danger was low (Slamming w/ 3 competitive players is hard). At some point, Peter shot ahead into the teens or low-20s when I had a chance to drop the 6♣. I must've spent 30-45 seconds on the decision. I really wanted to save the Six for Sky, seeing her as more of a threat, also not wanting to end the game just then (I was behind Sky) but finally decided: OK, I'll let Peter have his strike. Some combination of my Six and other stuff got him to 31. Two tricks later, the round got to a point where I could take everything and still be OK, and this I tried (I'm pretty sure I lost the last trick; I don't remember). I got myself to 26. Zach got 19, and Sky, 15. (Sky didn't take any more chips; if I had saved the Six for her, I would've lost the game. Speaking of which... damn.)

The game-end totals were: Mike, 2/111; Zach, 2/84; Peter, 3/89; Sky, 1/105. Totalling 389, this was a relatively low-scoring game, but definitely one of my favorites.

Conclusion

That was the most fun game of my year. It re-iterated just what makes Ambition, in my opinion, so fun to play. It's almost purely a game of strategy and skill-- hand-luck doesn't dominate as in Bridge or Hearts, there are myriad strategies and every hand plays well for at least one-- but it's not rigid like some skill games. I consider myself a late-intermediate player (I don't know if Ambition has any advanced players yet) and can vouch that a group of 3 promising beginners gave me quite a challenge. Late-novice and early-intermediate players do beat me sometimes (my most recent loss, 30 Dec 2004, was a second-place finish; 146-145 to a late-novice).

Ambition's not a rigid pure-skill game so much as one of strategy, flux, and spirit. The interactions of players' objectives, the role of intuition about others' intentions, and the very human element of making costly mistakes, all create the uncertainty, notso much hand-luck. In my opinion, the psychological element of Ambition is as strong as that of Poker. As Ambition evolves and as advanced, World Series of Ambition type play emerges, I suspect that the psychological and flux elements of the game will be the most pronounced and decisive game aspects.

A concluding thought is this: there's something obviously very weird about any game that, while definitely one of strategy and skill, allows the lowly 6♣, in the 6th round, to decide the outcome.

Getting started

Library

The most recent rules. (Post #5; cardschat.com)

23 Mar 2004 set of rules. (Out of date, but containing some cool variants/history. This is probably where most people hear of Ambition.)

Anatomy of the hand. (11 Sept 2004; still relevant-- no major rules changes. I intended to do more essays like this, but then the homework and the grad school apps invaded.)

Troll crossing. (27-28 Jan 2005. This is provided for amusements' sake; at least I found it funny when I first read it. Ambition is attacked by anon troll, defended by loyal-- in some cases, new-- friends.)

About Me

I am indeed Mike Church, a 21-year-old mathematics major at Carleton College. On the side, I do writing-- poetry, short story, faux-news. One of my 2,000 dream jobs, in high school, was one day working for The Onion.

I was an avid Magic player in middle and early high school. Some of the design in that game is beautiful, but the implementation is awful. Who can earnestly like a game where who has the most money is a decisive factor in available strategies and game outcomes?

Among my favorite teas are English Breakfast, Darjeeling Bop, and Cherry Vanilla. My favorite macro beer is probably Newcastle Brown Ale or Yuengling, but the Appalachain Brewing Company (PA microbrew) makes some amazing stuff.

My favorite band, currently, is probably the Finnish rock group HIM; they've produced some of our generation's best music and are huge in Europe, yet unheard-of in the U.S. (Figures, huh?)

I developed Ambition in late September 2003, to play with friends during the Budapest Semesters in Mathematics program (which I highly recommend). It grew out of Hearts, but I could quickly see that it was an entirely new game, and developed it as such. My aesthetic mission with Ambition was to create a trick-taking game where hand-luck played as small a role as possible. I believe I have been successful; Ambition's very instructive; every time you strike, you know you made a strategic mistake, and normally where that mistake was made. I taught the game to some Budapest expats and Hungarians who, apparently, still play the game.

In March 2004 Ambition was published in Japan's Nikoli magazine. Since then, Ambition has traveled to (at least) the following countries: Australia, Canada, France, Hungary, Japan, United Kingdom, United States. I could not achieve this without ample support and assistance, so I issue thanks to all of you who have helped me along the way.