Ambition: version 8♦ is now out.

The latest rules for Ambition are here. Mostly, the changes are simplifications to the scoring system in order to increase the game’s mass appeal and, hopefully, virality. I don’t believe that I’ve compromised on the game design in doing so; the intrinsic strategic complexity remains, but the cognitive overload associated with the scoring system has been trimmed back a bit.

I’m planning, after years of delinquency on this matter, to release an online version late this year, but I’ve wanted to get the rules to a steady state before doing so. This iteration, I am pretty sure, is or is near the final one, at least as far as the core rules go. There are a few unresolved questions that I have about the scoring system, but I’m going to wait until I have real data (from players, not simulations) before making those calls.

The roadmap from here looks like this. Currently, I’m working on a command-line console version– an embarrassing minimal viable product (“MVP”)– that I plan on releasing this August. The source code will be on Github and open-source; card games themselves are rather trivial to implement, so there’s no point in hiding that code. The first iteration will be a tutorial (with players making random legal moves) more than a game, designed with the intent of helping people learn Ambition interactively rather than from a dry rules document.

After “launching” this MVP, the next project will be to create real players for a single-player version. As for AI, I have a machine-learning approach in mind that I think will work. That might take a month or two (since this is purely a weekend side project) to implement and run, but I’d like to have that together by mid-autumn. This means there should be real AI players. I have no idea whether they’ll be any good at the game. I may crowd-fund this by creating a KickStarter project to solve the AI problem and giving a percentage away to the person who writes the best player.

After that, I’ll start working on the front-end (like, a real app) of the game, noting that most people are not interested in downloading a command-line card game, and also that people prefer to play against real people rather than AI. I’ve been doing back-end software for my whole career so I have no idea what that will entail or how difficult it will be, but I look forward to the learning experience.

Ambition and what it taught me: the 4-factor model.

Nine years ago, I came up with a card game called Ambition in which I attempted to remove card-luck from a trick-taking card game. This turned out to be a surprisingly difficult (and very fun) design problem. To give a 50,000-foot overview, the original game was one in which the goal was to get a middling score each round, making the objective more about manipulating the flow of the game (and the players) rather than trying to take (e.g. Bridge) or avoid (e.g. Hearts) tricks. The original game had only the middling objective, but as with Hearts and it’s “shooting the moon” reversal, I had to add high-risk, high-reward strategies for very strong (Slam) and very weak (Nil) hands. What I ended up building was a game where card-luck has a very small influence, because every hand has a credible strategy.

I’ve estimated that card-luck produces about 5% of the variation in a typical 2-hour game. (This could be reduced to 3-4% by reducing the Slam bonus, but that would also make the game less fun, so what would be the point?) For a trick-taking game, this is rare. Now, Bridge is an immensely skillful game, but it’s got a lot of card luck in the short term. For this reason, Bridge players duplicate the game in serious settings, which means that they play the same hands as everyone else in the club and are scored on their relative performance. A typical Bridge tournament might have 20 teams– or 40 people. I don’t think there are 40 Ambition players in a given state at any time, so duplication’s not an option.

Why’d I want to eliminate card luck from a trick-taking game? The short version of the story is that I had caught that German board game bug, but I was in Budapest for a semester (at this program) and had only a deck of cards. But I’d fallen in love with the German design aesthetic. Also, experience had led me to conclude that the games regarded as being the most interesting, and the ones that become culturally important, tend to be skillful games. Go, Chess, and Bridge are all very deep and skillful games, which makes their outcomes meaningful and indicative of genuine skill (or decisive). Poker becomes skillful with enough patience; viewed as one game played over a person’s life, it converges, as most games well. This led down the rabbit hole of “luck/skill balance”. What is it? Oddly enough, I concluded that it doesn’t exist, at least not when framed as a linear dichotomy.

The idea of “luck vs. skill” places Go (a very deep, skillful game) at one end of a continuum and Bingo (which is pure chance) at the other. As this ideology goes, luck games are cotton-candy junk food, and skill games are, if a bit dry, respectable and rewarding. Supporting this is that the culturally successful and long-lived “mind sports” tend to be highly skillful, which seems to imply that if you want to design a “good” game, you should be aiming to get rid of luck. The problem with the luck/skill dichotomy is that there are a number of game mechanics it fails to model. For a trivial example, Rock, Paper, Scissors contains no randomizer but (at one iteration) is effectively “random”, because it presents simultaneous decision-making with a perfectly-symmetrical strategic shape (i.e. no strategy is functionally different from any other). Rock, Paper, Scissors at one iteration can be considered to be effectively a luck game, so what about the iterated version. Is the long-term, iterated game luck-driven or skillful? That’s a surprisingly hard question to answer, even theoretically. For a more practical example, consider multi-player German-style favorites like Puerto Rico, an excellent game sometimes criticized for the influence of table position (i.e. the difference between sitting to the left vs. the right of the best player can have a measurable affect on one’s outcome). There are almost no random elements to this game, but play order becomes an influence. Is that aspect– knowing where to sit– luck or is it skill? (Answer: it’s meta-game.) But the biggest problem with the luck/skill dichotomy is that it breaks down completely when there are more than 2 players. In a 3-player game, an unpredictable, nonconventional, or outright incompetent player can make strategic choices that favor one player over the other– an effect deriving neither from a truly random element of the game (such as dice or a deck of cards) nor from those players’ individual levels of skill. This “interaction term” element is strategy: a mix of luck and skill inherent in simultaneous, poly-agent decision making.

The difference between a demonstration of skill and “strategic luck” is that the former will generally affect opponents’ outcomes in a non-biased way. If Alice does something that gives her an advantage over Bob and Eve both, she’s playing skillfully, not getting lucky. If she does something that unintentionally or chaotically gives Bob an advantage over Eve and Bob wins, that’s strategic luck favoring Bob.

In two-party games, there is no strategic luck. If the opponent’s strategy causes one to lose, that was (by definition) skillful play, not strategic interference. Likewise applying to two-team games (like Bridge) it is accurate to say that friendly “strategic luck” is skill.

However, in games of 3 or more players, it’s pretty much impossible to eliminate strategic luck (not that I’m convinced that it would be desirable to do so). This is reminiscent of Arrow’s Impossibility Theorem, which state that it’s impossible to design a “perfectly fair” voting system, where “fair” means that the presence or absence of a candidate C should not affect the relative performance of A and B (i.e. no “Nader effect”.) Games with three- or more players face an inherent trade-off between (a) restricting interactions between players, making the game less fun, versus (b) encouraging them but introducing strategic luck. So with large groups, it’s often better for a game designer to just own the strategic luck and make the alliance-forming (and -breaking) aspects a core element, as with Diplomacy or Apples to Apples.

This may be why the games that develop the mind sport culture always seem to be 2-party games. A game of 3 or more players without strategic luck would have to be structured too much like “multiplayer solitaire” to be fun, but one with strategic luck is unlikely to develop a tournament scene, as the cultural purpose of those is to determine “the best” player. (When there’s strategic luck, the best player can be undefined. Alice may be superior to Bob when Carla sits at the table, while Bob is better than Alice when Dan is playing.)

As for Ambition, I removed the card luck but I introduced some strategic luck. A “bad” hand can lead to a great outcome based on unrelated prior decisions by other players. Strategic luck is noticable. Which made it not quite like Go or Chess where a superior player can expect to win 95+ percent of the time, but more like a German-style game where pure chance factors are uncommon (you rarely feel “screwed” by the cards) but strategic luck is tolerated. And that’s fine. It adds to the fun, and it’s a casual game, after all.

Luck, skill, and strategy are 3 factors that determine players’ outcomes in a game. Pure chance elements can be isolated and assessed mathematically. Skill an usually be quantified, by observing players’ outcomes and adjusting, as with the ELO system. As for strategy? It’s completely impossible to quantify this element in a general way, because the strategic variables within a game are, in some sense, the spinal shape of the game itself. Pure chance elements can be analyzed through statistical means, but there’s no general-purpose way to measure strategic luck. I’m not sure if I can even precisely define it.

I said there would be 4 factors, so what’s the fourth? The most interesting one, which I call flux. To explain flux, consider one important observation pertaining to supposedly “purely skillful” games: they don’t have the same outcome every time they’re played. If they did, they’d actually be frustrating and boring, even for nearly exactly matched players. Thankfully, that’s not the case. Alice defeating Bob does not mean that Alice will always beat Bob. What this means is that there’s something subtle– an energy– that makes the game a real contest when it’s played between players who are close in skill level.

Flux is minute-to-minute variation in a player’s skill and strategic effectiveness. Positive flux is being “in flow”– the state of consciousness that makes games (and programming, and writing, and many other things) fun. It’s a state of mind in which a person has above-normal concentration, confidence, ability to assess risk, and effectiveness in execution. Negative flux is the opposite, and it’s described by poker players as being “on tilt”. It’s being out of flow. When players of equal or near-equal skill compete, it’s often flux that determines the winner. And that’s what makes such contests exciting– the fact that the game is skillful and decisive (so the outcome actually matters) but that, because the contestants are close in skill level, the end-of-game binary outcome (winning vs. losing) is going to be determined by minute-to-minute fluctuations in animal energies. Flow. Flux. “The zone.”

Luck, skill and strategy are all important tools in a game designer’s arsenal as he pursues his design goal (which is not to land at a targeted point on some bullshit “luck/skill continuum”, but to design a game that’s fun to play). Luck gives more players a chance at . Skillful elements make the game decisive and more . Strategy, on the other hand, is what makes multiplayer games interactive and social. All of these elements can be quite effective at making a game fun. But it’s the tense real-time drama of flux as players go into and drop out of flow that really makes a game interesting.

Lottery design: how I’d do it.

Here are some thoughts I’ve had on how I would design a lottery if it were my job. I find computer programming and real game design to be more fulfilling than the design of these sorts of mind-hacking gambling games, which is why I would consort with a cactus before I’d ever work for Zynga. That said, someone has to do that job. Here’s how I’d do it if it were mine.

A toy example is the mathematically interesting, but impractical, “no-balls lottery” driven by “strategic luck” (to use a game-design term). It works like this: at each drawing, players choose a number between 1 and N (say N = 60). It costs $1 to play, and the payout for choosing the winning number is $N. Where’s the house edge? The winning number is not chosen at random; it’s the one chosen by the fewest number of people (with ties either split or resolved randomly). What’s cool about this lottery is that it has the appearance of being “fair” (zero expectancy, no house edge) but it produces risk-free profit for the house no matter what, because the winning choice will always be chosen by less than 1/N of the players. The more uneven the distribution of choices is, the better the house does. Game theory (Nash equilibrium) predicts that we’d see a uniform distribution of choices over time; I have no idea how it would actually play out. The house edge would unlikely be enough to cover administrative costs, but it’d be an interesting social experiment.

At any rate, the press loves lotteries. Not the small, reliable, boring kind, but the big ones. The $640 million jackpot for the MegaMillions has been a major news item of late– it’s the largest U.S. jackpot lottery in history. I even chose to play, mainly for epistemological reasons related to recent and extremely unusual events in my life that lead me to suspect supernatural trolling. Let me explain. There’s somewhere above a 99.999% chance (call this “prior” p) that the universe acts the way we think it does, and that there’s no correlation between balls drawn at a lottery and personal events in my life. It’s actually very likely that the correct value of p is much higher than 99.999%. I can’t put a true probability on it for the same reason I can’t put one on religious questions: probability enables us to reason about uncertainty of known structure, and this is about uncertainty of unknown structure. That said, there’s a 1 – p chance that the universe is deeply weird, that it has the tendency to troll the fuck out of people, and that playing the lottery right now (only right now, because this is a singular moment) might lead to profit. I don’t know what this “1 - p” is, but I’m willing to pretend, for the moment, that it’s high enough to buy a few lottery tickets.

(Technically speaking, the MegaMillions already has positive expectancy. This is practically irrelevant, as it is for the notorious St. Petersburg lottery. Almost all of that positive expectancy is concentrated in the extremely-low-probability jackpot and, between taxes, split jackpots, discount rates applied because lottery payouts occur over time and, far more importantly, the extreme concavity of the utility curve for money, I don’t know that it has a meaningful expectancy. I’m buying because, despite my scientific training, weird events cause lapses into superstition.)

A lot of people think the way I do, and the vast majority of them never win lotteries. People are very bad at managing low-probability events. Cognitive biases dominate. What actually ruined my interest in the lottery, as a child– my dad played about once a year, and let me pick numbers– was realizing that a Super-7 outcome of {1, 2, 3, 4, 5, 6, 7}, which “would obviously never happen” was precisely as likely as for me to pick winning numbers. (Actually, {1, 2, 3, 4, 5, 6, 7} is a bad play because of split jackpots. Dates are common fodder, so pick numbers 32 and higher if you want to minimize that risk.) Moreover, this type of magical thinking tends to surround the largest lottery jackpots, which appear “historic”. Of course, I know how silly it is to think this way, because large jackpots are nothing more than an artifact of Poisson processes and very long odds: it would be possible to build up a $5 billion jackpot (assuming people would play) just by designing the lottery so that the odds of winning are very small.

So if I were designing a lottery, how would I do it? Let me say that I’m ignoring the ethical question of whether I think gambling and the lottery are good things. I’m assuming the position of a person who thinks lottery gambling provides a social value. (My actual position is more uneasy.) I would not be happy to design some small scratch-off game. I’d want to build the lottery responsible for the first billion-dollar jackpot.

First, 7 balls is too many; the ideal number seems to be 5 or 6 (short-term memory). Two-digit ball ranges are also desirable, with 50 to 60 being typical. Numbers in the 50s seem moderate on account of the “inverse Benford effect”, whereby numbers with leading digits of 5 and 6 seem “moderate”. (Falsified financial figures tend to lead with ’5′ and ’6′ digits, although log-normally distributed real-world variables should lead with ’1′ over 30 percent of the time.) A typical 6-ball lottery, with 50 balls, gives odds of 15.9 million to 1. That’s clearly not enough. It might produce a piddling $30 or $40 million jackpot on occasion. Congratulations: you’ve earned ten months’ salary for an upper-echelon corporate scumbag (and by waiting in line for 3 minutes for that ticket, you’ve had to do more work than that well-connected blue-blooded shit has done in his whole life). Since it’s long odds that produce large jackpots, how do we push those odds into the billions?

The idea’s already there. Consider the 6-ball lottery that I described. The odds can be made 720 times longer by distinguishing or ordering the 6 balls. This is how the Powerball and MegaMillions work. One ball is distinguished as “special”. This makes the lottery more “fun”/engaging, and it makes the odds of choosing a perfect ticket longer. My target, in designing this lottery, is going to be to aim for odds in the 1- to 2-billion-to-1 range.

First, I think we’re ready for two distinguished balls, one red and one green. In fact, we’ll need that to get the kinds of long odds we want. The range for each is going to be 1 to 31. Why 31? Because, from a design perspective, it fits. One of the most common sources of lottery numbers is dates, so why are we cluttering up the card with these higher, less useful, ungainly numbers? For the other four balls, however, we need a wider range: 1 to 80. Yes, 80 puts us afoul of the “inverse Benford effect”, but we’re selling a premium product, so 80 is appropriate.  How many possible tickets are there? 80!/76!*4! * 31 * 31 = 1,519,898,380. With 80% of ticket revenues going into the non-discounted dollar amount jackpot (which means we’re actually only putting about 50% in, because we’re paying an annuity over about 25 years) we’ll be seeing billion-dollar jackpots on a regular basis. Not only that, but we’ll be seeing $1-billion non-split pots on a regular basis. For the first time ever, we’ll be minting billionaires from a lottery.

Of course, it’s the jackpots that bring ticket-buyers in, but it’s the small prizes that keep them coming back. The prize is a free ticket if you hit either the red or green ball (16:1), $100 if you hit them both (961:1). (A $100 payout on 1 in 1000 tickets, for jackpot lotteries, is unheard-of.) We’re paying 16 cents on each ticket there, but I think it’s worth it to keep continued engagement. We also want to make the second-to-top small prize large: $1 million for a ticket that matches the 4 white balls and one of the colored balls. The odds of that are 25 million to one, so we’re paying 4 cents per ticket there. We can shave expectancy on the middling prizes, which will be low compared to the odds against them. No one really looks at those, anyway. It’s the frequently-won small prizes, the second-best prize, and the jackpot, that actually matter.

Here’s why I think we should do this. Here’s the real ideology behind what I’m suggesting. I don’t care much either way about lotteries. Nor do I have a need to make that kind of money off people who, in general, need it more than I do. I do think Instant Games are a bit unethical (pathological gambling, and the fact that winnings almost always go into buying more scratch-off tickets, often on the same day) but also I think that, compared to alcohol, tobacco, and trans fats, lottery tickets are one of the less harmful things sold in most convenience stores. This said, the lottery I described is a starter in giga-lotteries: 1.5-billion-to-1 odds, three-digit millionaires and billionaires being made out of random people on a regular basis. Sure, the odds are very long, but most lottery players don’t give a damn about the odds: they’ll play as soon as they see $500-million jackpots, for the novelty. I do it, just to see the huge numbers. It’s gossip. But to paraphrase Justin Timberlake, a billion dollars isn’t cool (or won’t be, after it becomes commonplace). You know what’s cool? A trillion dollars. Or, at least, $85 billion or so. U.S. lottery revenues are about half that, but I think we can do more. Way more, once we establish a lottery where billion-dollar jackpots are the norm.

I don’t care here, as I said, about revenues. My goal isn’t to make money off of peoples’ cognitive biases with regard to low probabilities. It’s not to get rich. (Since I can’t legally implement this idea– only governments can– I never would.) Making money isn’t the goal. We should shove as much of our ticket revenue into the jackpot as possible. Rather, the goal is to make huge fucking jackpots. Two distinguished balls (one red, one green) is just the start. For the real act, we can have six different colors (white, red, gold, blue, green, and silver). This colorful lottery will be so engaging and so well-hyped (once $10-billion jackpots are old hat) that we can charge $5 per ticket. The ranges on each ball will be 1 to 84. We’ll need a lot of high-profile small prizes, and a two- or even three-tier jackpot system will be in order, as the odds of a perfect ticket will be 351 billion to 1. Top-tier jackpots will swell and swell and swell, building for months and growing exponentially. We might have to make this a world lottery to get a winner a couple times per year or so. But at some point, however, someone out there will win a huge amount of money. It will take a long time to get there, but a trillion-dollar jackpot will, at some point, happen.

What’s the redeeming social value of a trillion-dollar jackpot? Complete and total humiliation of the world upper class. Mockery of the world’s most destructive dick-measuring contest. A person, chosen completely-the-fuck at random, being catapulted to the top of the Forbes 500 for no fucking reason whatsoever. So fucking awesome. I would buy $1000 of these fucking lottery tickets every month and hand them out to the most undeserving randoms, solely in the quixotic, long-shot pursuit of the noble goal of humiliating every single private-equity asshole on Park Avenue at once by having a lottery player out-win all of them by orders of magnitude.

Is this evil? I’m not sure. I don’t actually want to see this experiment happen. I fully support humiliation of the existing upper class, but this sort of extreme lottery would just create a new upper class. The only difference is that this would be an elite made for no reason, as opposed to our current elite, which exists for mostly bad reasons. Moreover, I just don’t think it’s the best use of my time and talent to encourage mathematically naive people to pump trillions of dollars into a process of no social value.

The objection I have to it, again, isn’t gambling: we gamble all the time. Every blog post I write has an effect on my career– mostly positive, in that I can establish myself as knowledgeable about technology, progressive management, mathematics, software engineering, and computer science– but potentially negative, as well. This post, in which I describe the application of game design talent to an extremely perverted social project, is probably riskier to me than buying a few hundred lottery tickets. And this blog post, unlike the MegaMillions, has no chance of ever earning me $640 million.

There is another problem with this trillion-dollar lottery (TeraTrillions, and I am fucking trademarking that name). I am afraid that someone would fucking Occupy that shit.

Fscking Ace: a simple, depraved gambling game.

Fscking Ace is a simple game of cards. It’s not highly skillful or deep, but it’s fun and twisted. As this is a gambling game with wide swings, I’d recommend not playing at the specified increment of $1, unless one has an appetite for risk. For low-stakes “fun games”, divide dollar amounts by 100, playing with pennies instead of dollars, or decide that they are “points” that count for bragging rights only.

Disclaimer: I’ve never played this game for money. I probably never will. I’m not much of a gambler and, at any rate, a good dealer doesn’t taste his own poison.

Number of players: This can be played with 3 or more players. Use a double-deck if there are 6 or more players, a triple deck if there are 11 or more, and so on.

The deck: The pack contains 48 cards: all diamonds, clubs, and hearts, the Ace, 2, 3, 4, 5, 6, and 7 of spades, and two jokers. The colored joker is the $10 joker; the other is the $5 joker. (Mark one if they are identical.) If a double deck is used, then remove one Ace of Spades, leaving 95 cards. Remove two Aces of Spades from a triple deck, forming a pack of 142.

Optional: when using multiple decks, players may wish to remove the extra 2′s, because these “doublers” magnify wins and losses. With more than one deck in play and lots of doublers, the potential for catastrophic loss or enormous gains (each being the other, given the game’s zero-sum nature) is substantial.

Starting a round: Choose first dealer using the most distasteful mechanism you can come up with (highest or lowest salary, who can tell the most offensive joke, highest or lowest number of previous sexual partners). Or just draw lots. Whatever works. Dealer shuffles the pack and places an unused card (such as an unused spade) under it, making it impossible for any player to see, by accident, what’s on the bottom.

Playing a turn: Turns begin at the dealer’s left and progress clockwise at the beginning of the round. (Play order may be reversed, as described below.) Each player, on his turn, must turn over at least one card. If it’s a spade, his turn ends. Otherwise, he may keep turning over cards, until drawing a spade, or he may decide at any point to end his turn. If he chooses to end his turn, he scores the cards turned up. Most cards are worth $1, but the jokers are worth $5 and $10. If he draws a spade, he scores nothing for that turn and it ends.

For example, a player who drew, for his first four cards, 7♦-4♣-K♣-$5Jo, would score $8 for that round if he decided to stop. The joker is worth $5 and the other cards are $1. If he drew again and caught a spade, he’d score $0 for that round. The cards drawn by him that turn would be discarded, and his turn would end.

The red twos, if drawn and scored, are worth $1 base but also double the values of regular (non-Joker) cards that one has scored (from $1 to $2, $2 to $4, and so on). Twos of clubs are worth $1 but double the values of jokers that one has scored. (If multiple decks are used, they compound. For example, three 2♣’s makes a $10 joker worth $80.)

If a player’s turn is ended by a 2♠, he keeps it (as if it were scored) instead of discarding it. If he loses the round, his losses will be doubled. Also, when a player’s turn is ended by a 7♠, the order of play reverses (from clockwise to counter-clockwise, or vice versa). The 3, 4, 5, and 6 of spades have no special effect.

Ace of Spades, ending the round: If a player turns up the Ace of Spades, the round ends immediately. That player becomes the loser of the round, hence the name “Fscking Ace”.

The loser pays each player for the cards they have scored, plus an additional $1, to each player. A bonus of $5*N, where N is the number of players, is given to the player who scored the most cards. (In a tie, this bonus is divided among the tied players.) Due to Jokers and doublers, this is not necessarily the person who scored the most money.

The person who would have played after the one drawing the A♠ will open play in the next round. There is no ending condition other than peoples’ continuing willingness to play this evil, evil game.

Balls, a 3-player trick-taking card game

I’ve been looking for a great three-player trick-taking card game for a while. I designed Ambition, a four-player trick-taking card game, back in 2003. I believe Ambition’s one of the best playing card games out there, but it scales quite poorly. It works best with exactly four players, but not well with three. So, if nothing else, I need something to play when a fourth for Ambition is unavailable.

Skat I found appealing in concept, but loaded with a bit of cruft. I wanted to improve it or, better yet, develop a brand-new three-player trick-taking card game. Throughout December 2010 and January 2011, I spent much of my spare time play-testing a brand new (and, in my opinion, quite good) game of cards. It’s called Balls, and the rules can be found here.