Removing Luck

Today’s post is a thought experiment: Can we take a game that includes a degree of randomness and remove all luck? Does doing so improve it? What does this mean for game design?

Let’s start by simplifying the problem: We’ll make the assumption that our original game is entirely deterministic except for die rolls and that we are going to remove those. We’ll consider three games: Something simple, something that adds a social element and something that adds some complexity. Let’s go with Snakes and Ladders, Liar’s Dice and Titan.

Alright. Our first attempt to remove randomness with be the simplest: Let’s assume continuous average rolls. The dice always come up 3.5. Actually better call it 4 because none of these games is going to handle a 0.5 particularly well.

Snakes and Ladders just became even more predictable. Depending on the layout of the board it’s now either an infinite loop or victory will go to the first player. Assuming we lay out the board to avoid the infinite loop – what happens to the game?

Well the dominant strategy didn’t change. The odds of any particular player winning didn’t change (assuming we don’t know who’s first player before we start). The quality of the game changed though – its easy to get snobby about games and say “Well it had no quality in the first place” but let us be honest: Generations of children have at some point enjoyed the game. Despite it being the same in terms of most metrics we might consider important as gamers – something has been lost.

Liar’s Dice is laughably broken. The opening bid is always “4s equal to the number of dice remaining”

Titan behaves strangely. There’s a bit of novelty in working out how best to maneuver piles in four step jumps to obtain the best creatures and when to move to stop your opponent doing the same. The capacity to plan several moves ahead adds something to the game and makes predicting and interrupting an opponent’s path of movement more interesting.

The combat system has totally fallen apart though. A system that determines whether you need 2+, 3+, 4+, 5+ or 6+ to hit doesn’t survive everything being 4s very well. A single high skill monster is now a match for infinity lower skill monsters. The diversity in the pool is completely undermined and so any advantage that might’ve been gained in the strategic layer is lost when most strategic advances do nothing at the tactical layer.

New plan: We’ll replace the dice with cards. Each player gets cards marked “1” through “6”. Whenever they need to roll a die, they play a card to indicate its result, when all six are played they recover their hand.

Snakes and Ladders becomes a different sort of game. It remains as strategically trivial as it has always been but asks for a slightly different type of thinking, which might have some novelty for its intended audience. Particularly given clever board design that ensures that taking the fastest possible route to the biggest ladder leaves you with the wrong cards in hand not to inevitably hit a bigger snake. Not a lot of replayabiltiy of course once someone has seen the trick, but it’s doing better than the “All fours” version.

I’m not sure what happens to Liar’s Dice. In the first round you know that each player has rolled five different numbers – but not which one is missing. It’s particularly important that you don’t know that it’s a wild card – since that gives a lot of wiggle room for the total around the table. Is this a game that benefits from there being more information that’s available to players?

There are certainly lucky and unlucky rolls in Liar’s Dice. Having a roll of all the same number is like mana from heaven, so smoothing that out and making it more of a game of skill seems like something that’s got a place. I think whether the extra complexity justified the improvement would depend a lot on the individual player – but for the average player it probably doesn’t work out.

So what about a more complex game like Titan? It’s very much not a trivial problem to determine what the optimal move pattern is to maximise gains over the first few turns. There’s also the emergent property that if you want to do a move of the same value twice (For instance to repeatedly use “2” in order to back and forth on the same useful space) then you can do so by engaging in a fight and managing your hand so that the right card is left to you at the end. You could even see a strategic conceed made in order to leave an opponent with only a strategically poor card for their next move.

The battles are likely to be very regular. Due to the fact that you roll a handful of dice at a time you’re likely to use more than one hand of cards on a roll. So a monster that rolled 8D6 is now rolling 1, 2, 3, 4, 5, 6 and 2D6. On the other hand those last two can distort an effect quite strongly. If that monster needs 5+s to hit then you can double your effect by using your 5 and 6 twice at the expense of knowing the next hit is going to go badly. I’m not sure if this would lead to interesting play and counterplay in which you’re trying to force fights that let you get optimal use out of your cards or if it would be degenerate. Possibly the “Player whose turn it is chooses which battles are fought in which order” would need some refinement.

So removing randomness causes us to pretty much break Snakes and Ladders whatever we do with it, we’d need to modify the game so heavily that it would be unrecognisable compared to the original to do otherwise (except for the theme of course).

It could do interesting things to liar’s dice if we wanted to, but the chances are that the method that replaces dice winds up adding complexity to a game which presently benefits from an elegant simplicity. There may be more refined ways to remove the random element, though again they end up changing the game. Arguably if you take removing randomness from liars dice and replacing it with choice far enough and are willing to change enough rules in the process you wind up playing Skull (or something like it).

The approach generates a lot of emergent properties when it’s applied to a more complex game. I can do all of the theory crafting I like, but without actually trying it I’m not sure how a deterministic Titan would come out. It would be interesting to try this sort of approaches on a lot of games designed at a time where “games have dice because that’s what they do” and see what falls out. While it might not work for a game wholesale there are likely a lot of novel mechanism combinations waiting to be discovered there.

I always like it when game design comes to resemble mad science. Keep experimenting and happy gaming 🙂

5 thoughts on “Removing Luck

  1. I can’t comment on the other two examples, but regarding Snakes and ladders:

    I’ve just simulated a few million very simple games of snakes and ladders (actually with no snakes or ladders, but with ‘bounce-back’ for overshooting the destination), and the winning distribution is dependent on board length – for a 100-square board the first player wins about 28% of the time in a 4-player game, or about 53% of the time in a 2-player game.
    This is less biased than the result for a 6-square board (about 32% 1st player wins for 4-player, and 54.5% for 2-player) – which is equivalent to “first to throw a six” – but still not really ‘fair’.
    I doubt that reasonable numbers of snakes and ladders would affect this much.

    There is a reason it’s easy to be snobby about S&L, and I would say that it’s fair to describe it as “not so much a game as an activity”. The issue is not the randomness, rather the lack of agency. It occurs to me that it would be possible to add things to the game to salvage it, while still retaining something of its character. Which seems like a tempting project.


    I think the main argument for randomness in games, other than adding variety, is to add some dither to the result. If a game is 100% skill, then a stronger player may always beat weaker ones. That being so, it would be hard to say anything other than who is the strongest. There’s no indication of closeness, and weaker players have little indication of whether they’re improving – and all would likely become disheartened. In sports, a handicap is a recognised solution, but that really only works for a dedicated player community with much repeat play (such as exists for Go).

    The question then is how much dither should there be? At one extreme, all players win at 1/n frequency and no skill is required. At the other, the best player always wins. Obviously, somewhere in the middle is generally preferable – but I suppose that where exactly is optimal may depend on the expected skill range of competing players.

    • Hi Loris,

      Good thoughts. I didn’t really think about what I was replacing randomness with in this post, but looking at it I suggest two possibilities: One is to reduce randomness by replacing it with determinism (every roll is a 4) and the other is to replace it with agency (choose a card 1-6 and decide which to play, redraw when all cards are gone). In looking at a game that has literally no agency replacing randomness with agency significantly changes the character of the game and arguably what’s being added is more important than what’s being taken away.

      I’m not sure that I agree that a game needs a competitive scene (to enable handicaps) or a dither rating. How does a highly rated game with no random factors but that doesn’t see competitive play fit into that view? Something like “Hey that’s my fish”

  2. I’ve not played “Hey that’s my fish”, but from the bgg description I think I have the idea.
    If people are playing each other widely then it presumably wouldn’t matter, no matter how ‘knife-edged’ the game. You’d know where you stood from who you could beat.
    And if a regular group are playing routinely then they might be able to handicap amongst themselves. But if they didn’t, and the game was particularly knife-edged, and one player had a definitive skill advantage, then I don’t think it would last as a game for the group to routinely play.
    Then again, if multiple players can gang up on the typical victor, I suppose that may contribute to balance. I’m not sure that’s a good solution, though.

    Incidentally, I think you’ve overlooked a source of random. Just because a game doesn’t have random factors ‘on the board’ doesn’t mean randomness isn’t important. Some games (e.g. scissors-paper-stone) are entirely dependent on the quality of the internal random-number generators the players bring to bear.

    • I think you’ve just given me my topic for today’s blog (If I get time to make one today).

      I was a psychologist before I was a board game designer – I almost never think of human input as random. Rock, Paper, Scissors is not about having the best random number generator – it’s about having the best capacity to figure out what non-random behaviour your opponent is exhibiting. In a repeated rock paper scissors tournament with players demonstrating several strategies “Choose a true random outcome” players finish in the middle, not at the top.

  3. Absolutely – scissors paper stone and variants only work competitively because people are so hilariously bad at being random, and the skill is in reading opponents.
    I imagine though that high level players in these tournaments need to be able to feed some decent randomness into their game.

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