Beyond Poker: Liar’s Dice
Beyond Poker reviews games which are not poker, but which scratch the same itch or exercise similar strategic muscles. In this series you’ll find games which involve hidden information and bluffing, probabilistic thinking, risk-reward estimation, or which simply apply poker concepts like the hand rankings in a novel context.
So far in Beyond Poker, I’ve stuck to commercial games: first a couple of digital games like Reiner Knizia’s Deck Buster, then some of the sort that are played with cards and tokens, like Coup. Now, I’d like to change things up and take a look at a traditional game, one which some readers may in fact have played themselves.
As is often the case with traditional games, it goes by many names and has a huge number of variants and house rules. For convenience, I’m going to call it Liar’s Dice and describe the most common version I’ve encountered, which can be played in any size of group.
All that’s needed to play is a collection of six-sided dice, plus one opaque cup per player. It’s standard for players to start with five dice apiece, but there’s no reason a greater or lesser number couldn’t be used, based on preference or the availability of dice. You could even start with unequal numbers of dice, as a handicapping mechanic if some players are more experienced than others.
Each round of Liar’s Dice begins with all players shaking their dice up in their cups, then slamming them face down on the table such that the dice are concealed. Players then peek at their own dice. The starting player for the first round is determined randomly, while in subsequent rounds, the player who lost the previous rounds starts.
The starting player announces a bet, consisting of a die face and a quantity, for instance “five Threes,” or “eight Ones.” What is being declared here is a guess (or a bluff) as to the total number of dice showing that face, among all players’ cups. Proceeding clockwise, each player must either make a higher bet or a challenge the previous bet. This continues for as many orbits of the table as are necessary until a challenge is made.
In determining whether a given bet is a valid increase, quantity counts first, followed by the die face being called. For instance, if the previous bet is “five Threes,” then valid options include: “six Threes” (increasing quantity); “five Fives” (increasing die face while keeping quantity the same); and “seven Ones” (increasing quantity while changing die face). Examples of invalid bids include: “four Fives” (as decreasing quantity is never legal); and “five Ones” (as when quantity remains the same, the die face must be increased).
Once a player challenges a bet, the cups are lifted and the dice revealed. If there are at least enough dice showing the face in question to cover the bet, the challenger loses the round. If there are not, then the bettor loses the round. The player who lost removes one of the dice from their cup and a new round begins.
A player with no dice remaining is eliminated, and the last player left wins.
The similarities between Liar’s Dice and poker are fairly evident. Each player has her own bit of hidden information, and must then attempt to make inferences about other players’ knowledge based on their actions throughout the round. Meanwhile, when it is her turn to bet, she must weigh the relative safety of betting based on her own dice, versus the need to bluff occasionally to avoid allowing opponents to glean too much information for her bets. A lot of the game comes down to studying opponent tendencies and tells, while mixing up one’s own play enough not to be predictable.
More than this, though, the negative-sum nature of an individual round creates some interesting parallels with the play of a final table in a tournament. Obviously, chips in a tournament form a zero-sum rather than negative-sum game, but the payout structure of a final table creates ICM issues which resemble a negative-sum game. Since chips won are worth less than chips lost, players want to avoid all-in confrontations unless they expect to be way ahead; similarly, in Liar’s Dice, it’s always better to see two other players get involved in a challenge than for you to be involved in one yourself.
This creates the interesting principle that if the players are playing well, the majority of challenges should go against the bettor. When, based on one’s own information, it seems the bet is close to 50/50, it’s far better to bluff than to challenge. This is because, when challenging, there is only one way to avoid losing a die, which is to be right. When raising the bet, however, there are two ways to emerge unscathed: if the next player elects to keep betting as well, you can hope a challenge happens before it comes around to you again, while if he does challenge, you can still hope to win.
This is very similar to the semi-bluffing principle in poker, that the value of betting comes from a combination of fold equity and showdown equity. There too, the principle is that in most situations, the calling player can be expected to show a stronger hand than the bettor.
Even before the bets get to the point that you’re considering making a challenge, it’s good to play aggressively. Beginners at Liar’s Dice tend to make the mistake of making the most conservative bet they legally can, because they want to maximize the odds of being correct if challenged. And yet, as long as the opponent doesn’t challenge, the dice don’t actually matter. Meanwhile, a conservative bet means that there’s a greater likelihood that the betting will go around the table without a challenge. By making a bet that’s just below the threshold you think the next player will challenge, you maximize the changes that someone will be forced to challenge before the action is back on you, which is really the goal of the game.
For something as minimalist as it is, Liar’s Dice is a surprisingly fun game. It also serves as a good fundamental mechanic on which to base more complex games; I did so myself, in fact, with my game Cash or Crash, which adds a commodities market theme and replaces the dice with a set of cards for each player. The design goal I had in mind was to expand on the bluffing elements of the game by allowing players a degree of control over their own holdings, even mid-round, rather than leaving them at the whim of a die-roll.
Despite its resemblances to poker, Liar’s Dice has one serious flaw when it comes to playing for money: it is extremely susceptible to collusion. The advantage of signalling holdings between players is significant in poker, but in Liar’s Dice, it’s essentially insurmountable. It’s also impossible to avoid, as there’s not even a need to signal physically; the betting structure itself lends itself to the development of conventions similar to those in Bridge, so enforcing a rule forbidding communication between players at the table is hopeless. Of course, that ceases to be an issue in heads-up play, but the game dynamics there are not quite as interesting as in a group.
Overall, then, it’s a game best played for fun, or for small stakes with friends. Compared to many other such “beer & pretzels” games, it has one distinct advantage, which is that it is free and requires no special components. Dice are easy to come by and portable, so all that’s needed are some cups or, failing that, impromptu cardboard screens. It’s probably not even that hard to come up with a variant using a standard deck of cards, if dice are not available. It’s also exceptionally easy to explain, thus good for groups which include both experienced gamers and novices.
Finally, with some adjustments, minimal implementations of the concept can serve as convenient exercises in game theory. For instance, give two players each a single coin, rather than dice. Treat heads as “higher” than tails, so that one can respond to “one Tails” with “one Heads” but not vice versa. As the first player, what is the optimal strategy when having flipped tails? When having flipped heads? Are they both pure strategies, both mixed, or does it depend on the flip? What is the first player’s edge?
Alex Weldon (@benefactumgames) is a freelance writer, game designer and semipro poker player from Montreal, Quebec, Canada.