Game-Defining Concepts – The Doubling Cube

Written by Alex Harkey

doublingcube

This month we’ve looked at numerous games which show off game-defining concepts; brilliant mechanics and noteworthy ideas which share identity with a game. Later this month we’ll be looking at how to identify opportunities for creating a game-defining concept in your game and how to actually get started implementing it.

To emphasize our monthly topic we wanted to analyze one example to demonstrate how a simple solution can truly define the strategy of a game while resolving weaknesses.

This week we’re looking at one of the greatest game concepts ever created: the Backgammon doubling cube.

A Brief Introduction

Fear not if you are unfamiliar with Backgammon, I’ve included a brief description of the game and the doubling cube. Feel free to skip to the next section if you are already familiar.
A Brief Overview of Backgammon

Backgammon is a 2-player abstract racing game that can be traced to the oldest known board games. On a turn, players move their playing pieces (often referred to as checkers, stones or counters) by rolling dice and allocating results to move their checkers. The primary objective is for a player to be the first to move all of their checkers off the board. In order to complete this goal players will be moving their checkers toward their opponent’s side of the board, making decisions on when to attack, block and pass their opponent’s pieces.

Dice showing double sixes

Despite Backgammon’s advanced levels of strategy and the recent emergence of a professional tour, it is and has always been a game associated with luck. As with Poker, skill and strategy play a more important role over time but can frequently be overshadowed by significant swings in variance and the luck of the dice.

One important aspect of Backgammon is that when doubles of a number are rolled, a player gets the equivalent of four moves; one way the dice can quickly begin to swing the game to favor one player over another.

A Brief Overview of the Doubling Cube

Many people who have played Backgammon may not have played more than a single game at a time. Since one game heavily decided by dice isn’t the best evaluation of player ability, Backgammon can also be played as a series of games in which players compete to be the first to a certain number of games/points. As an example, let’s say players are playing to eleven points. While this may seem like an excessive number of games, this is also where the beauty of the doubling cube comes into play.

Each game begins with a value of one point. The doubling cube is placed in the middle of the board (called the bar). As the game progresses, if a player feels they have an advantage, they may choose to offer a double. The resulting decision facing their opponent is to either:

  • Accept the double, increasing the value of the current game to two points.
  • Decline the double, but concede the game immediately (along with the one point).

As this decision is generally faced by a player at a disadvantage it can frequently be an agonizing choice. Fight an uphill battle or surrender and fight another day? If a player decides to accept the double, they gain control over the doubling cube, which can even be offered back to the opponent if the game swings in their favor.

The Genius of the Doubling Cube

While the idea is simple, what does the doubling cube provide Backgammon that the game didn’t have before? Let’s look how the doubling cube affects some of the potential deficiencies of Backgammon. Afterwards we’ll examine several of the enhancements the doubling cube brings to the game. Keep in mind this article is geared toward gamers and game designers rather than Backgammon enthusiasts so advanced strategy and analysis will be absent.

Remedies to Backgammon

backgammon
It solves the elongated game problem –

One downside of a game of Backgammon is that it can in practice become longer than reasonably necessary. Frequently the tension and excitement of the game turns into a drawn out affair to bring the game to a completion. The doubling cube provides both the option and the incentive for one player to press a do-or-die decision on the other player.

While there are several scoring situations that can provide greater benefit to play to completion rather than double, many of the tedious and ordinary endings can be eliminated. The doubling cube allows an opponent who is quickly outmatched to respectfully accept defeat in one battle while resetting the board to continue the war. This is a nice alternative to forfeiting in Chess after losing your Queen due to a careless mistake on turn six, or even worse, playing out an inevitable defeat for far longer than necessary.

It mitigates luck – 

dice

You can’t control the outcome of a roll of dice but you can control when to offer to double or whether to accept. The cube allows strategically sound usage of the doubling offer to all but eliminate the potential of losing after gaining a significant lead. Does your opponent really want to double the value of the game when you’re sitting with a 80% likelihood of winning? If they take the offer, celebrate as you’ll come out way ahead in the long-term. If they decline the offer, you just turned a 80% likelihood into 100% victory. Strategic use of the doubling cube puts control into the hands of players, rather than fate of the dice.

For all the criticism people place on games with an ounce of luck to them, isn’t this precisely what we want in games? Unpredictability, upswings and downswings, a chance for an opponent who is behind to come back and most of all: the ability for skill to ultimately decide the outcome if players execute their decisions effectively.

 

Enhancements to Backgammon:

It magnifies strategy –

magnifyingglass

The doubling cube adds an entire level of strategy to Backgammon that didn’t exist prior to its creation. Backgammon without the doubling cube is kind of like poker without the betting – deal out the cards and seeing who ends up with the best hand.

With the doubling cube, the better player wins more often and is less susceptible to the variance of dice. The most skilled cube players extract significant points from opponents over effective checker play alone. The biggest takeaway here is that the doubling cube naturally complements standard backgammon play; it adds a strategic variable that can affect current and future decisions once it is realized.

It is remarkably simple for anyone to pick up

If you have never played Backgammon with the doubling cube, give it a try. You’ll find that initially nothing really changes; you’ll roll the same dice and you’ll take many of the same turns. The cube doesn’t interfere with the previous structure of the game.

patreon2Using almost the minimal increase in complexity, the proportional level of strategic depth the cube adds is astounding. Now the cube does increase the number of strategy miscues. Beginners are often found to accept an offer to double when they probably should not and intermediate players are commonly cited for declining the offer when they should probably accept.

The best part is that these are very forgiving mistakes. There are no “gotcha” situations involved in which a player didn’t realize their whole strategy would fall apart (because they failed to realize their opponent’s would collude to buy out the resource market in Power Grid – not that I’m still bitter about it or anything). In any case, a player still has the chance to overcome their mistake and has a fighting chance. Long-term they may bury themselves with poor cube play but they can dig themselves out as they climb up the learning curve.

Even the basics of the doubling cube are friendly to new players. Are you unsure whether to offer the double or not? Put yourself in your opponent’s shoes – if you feel uncomfortable with their impending decision then it sounds like a great time to offer to them the double. If you receive the offer to double, estimate if you have a 25% chance of winning, if you do – accept.

It raises the stakes.

Poker

There is something special about playing a series of games that can’t be encapsulated in the “one match only” approach of many traditional board games. One downside might be that a game 7 in sports carries significantly more weight than any of the six before it. The doubling cube ensures there is never a situation of “I’m so far behind I’ll just autopilot the rest of game 3 and try to do better in the next game.” The doubling cube can at any time make an otherwise uneventful game into an enticing one.

Let’s say I’m behind 4-3 in a series to 7 points. In the current game my opponent offers to double and while I’m once again behind in the game, I’m in a situation where it is worth it to accept, taking possession of the cube. Now the game is worth 2 points which would catapult my opponent toward the finish line with 6 points if I lose.

Not only are both my opponent and I far more interested in the outcome of a game that would otherwise be a run-of-the-mill game in the middle lull of a bigger series, but I’ve got several critical strategy choices to make. I need to evaluate my overall strategy and just how aggressive I’m willing to be in order to try to win this game.

It is a strategic double-edged sword

doublingcubebar

Continuing the previous example, what if I take some calculated risks and reverse the situation, taking a significant lead in the game? I can now offer to double the game to 4 points and press my opponent to make this the potential deciding game of the match.

And so my opponent now faces one of the most agonizingly simple decisions in the history of games. They must either:

  • Decline the double, giving me 2 points and a 5-4 lead in the series.
  • Accept the double, putting the entire series on the line at a notable disadvantage.

Choose wisely.

This is what I find the most incredible part of the doubling cube: it isn’t a one-time gimmick in a game. Backgammon is thrilling because a game can swing back and forth and the doubling cube isn’t something you take lightly. There is suddenly a very haunting feeling when you’ve doubled a game prematurely followed by your opponent gaining the upper hand and offering to double it again. Accepting an initial double and taking the cube into your possession carries a conflicting range of emotions. You’re back is against the wall but you’ve got the launch pad to rise from the ashes. Like a Phoenix.

Obligatory Phoenix

Obligatory Phoenix

Conclusion

There are plenty of detailed examples I wasn’t able to include but If you’re not convinced by these words, play a few games with the doubling cube. It seems ordinary at first but if you give it an honest try you’ll soon see it is one of the most elegant and game-defining mechanics in existence.

Oddly enough, the doubling cube seems to have limited application in other games. Since its inception it has become critical to the identity of Backgammon in much of the world.

It is difficult to imagine a single idea solving several problems while enhancing the best parts of any game design. In our next article we’ll lay out a framework that may help you create a game-defining concept in your current design. Thanks for reading!

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12 comments on “Game-Defining Concepts – The Doubling Cube

  1. Patrick

    I’m not getting it.
    If you are on the loosing side, why would you ever choose to not accept? If you’re loosing, the chances of winning and getting those 2 points are low, while the chances of your opponent getting 2 points are high.

    If the luck-factor in the game is high enough to actually have a change to that comeback, it all turns into a betting/luck based game again. You’re just betting on the fact that your opponent will have less luck than you do. Which is also silly.

    I really don’t see a good mechanic here, just a way to add another luck based layer on a luck based game.
    Note: I don’t play backgammon, so I could be completely wrong here, but I’m not getting it.

    1. Alex Harkey

      Great question Patrick! The decision comes from a calculation called expected value (EV). If two random players (ignore skill differences as Backgammon has such a high degree of variance involved) begin a game of backgammon initially worth 1 point they each have an expected value of 0.5 points (50% chance of victory multiplied by 1 point).

      As the game changes one player may get to a 70% chance of victory and offer to double. The opponent with 30% chance of victory now has an expected value of 30% x 1 point = 0.3 points.

      If they decline, their expected value of winning is -1 point (100% x forfeiting 1 point to their opponent).
      So declining has an EV of -1 point.

      If they accept their expected value of winning is 30% x 2 points = 0.6 pts
      Their expected value of losing is (70% chance of losing x losing 2 points to their opponent = -1.4 points)
      The overall expected value of accepting the double is 0.6pts (winning) + -1.4pts (losing) = -0.8 points

      So in this case accepting the double is 0.2 points better than declining the double. Over the long-term that is a winning play. Now there are many other factors in play but this is why you would accept even though you’re behind in a game.

      Breaking down the math really doesn’t demonstrate the elegance of the doubling cube as it makes it sound like a formula. In reality it is a judgement that a player must make entirely independent of dice or variance. The timing of the doubling cube, board positioning, match standings and the style of play by your opponent would all be factors a player would evaluate in order to make the decision.

      This is a bit like facing a large raise in the final stage of a poker hand and being asked to call or fold – math is essential but player ability is also a very important factor.

  2. Raul

    Very interesting analysis of this mechanic. As I see it, the idea of allowing players to force a concession or risk higher losses is a way to make play more agile.

    I have actually seen similar ideas introduced in some modern board and card games. For instance, the first Magic:The Gathering sets were designed with the idea in mind that players would bet cards at the beginning of the game and the winner would take them. Under that approach, some cards were designed that allowed to tamper with the trophies (add or substitute cards), and the opponent would be allowed to stop that by forfeiting the game.

    In the board game Titan, at the start of any combat players can negotiate defeat, accepting a reduced amount of losses in exchange for the risk and the time of playing it out.

  3. Eric

    Thank you for this article. Indeed, the doubling cube makes Backgammon a much more interesting game. In addition, I think that a wager (even a token amount) spices things up considerably.

  4. Jayle Enn

    It’s been many years since I last played backgammon, and I never understood the use of the doubling cube– I thought it was some weird mechanism for setting odds. I never realized the game was intended to be played multiple times in a session, and now it makes a lot more sense. Thank you for explaining that!

    1. Alex Harkey

      Jayle, it’s actually an incredible experience and it doesn’t really last as long as it might seem. I hope you have the opportunity to try it soon!

  5. Ian Scot

    I’ve seen those things over and over again since childhood and knew the belonged to backgammon but never knew what they were for (I always thought they were rolled) great article!

    1. Alex Harkey

      Ian, I always had the same thought. Its such a simple component I dismissed it until I found an explanation for it. Give it a try next time you get the chance. Thanks for the kind words!

  6. alanleduc

    I’d never heard of the doubling cube before. Very cool concept. Thanks for sharing.

  7. Aegar

    Having never played Backgammon, this article was a fascinating read. Another mechanic to stash away in my toolbelt. Thanks a ton for this well-written piece!

    1. Alex Harkey

      I’m so glad to hear that, Aegar! I was concerned I’d be writing to only those who had played Backgammon before and I’d miss all the game designers I really hoped to reach. Thanks for brightening my day!

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