The Paradox of Catch Up Mechanics

Playing Power Grid the other day I thought “I could build an extra house, but I don’t want to, because then I’ll buy resources later and that’ll cost more money than the extra house would earn”. There’s a mechanic that penalises the player who’s ahead so good play becomes – in part – about fooling the mechanic so that the game thinks someone else is in the lead.

Fooling the Game is Good Play

There are a lot of games with catch up mechanics where a bonus is offered to a player who’s losing or a penalty is applied to one who is ahead. Playing these games well often involves manipulating the metric that the game uses to determine who’s winning so that it does a poor job at detecting your progress.

This is true even of “soft” catch up mechanics that have no formal implementation. When Munchkin was popular with groups I played with people very quickly realised that the first player to level nine almost never won. There’s no formal catch up mechanic but players are obliged to draw cards of the form “Play when another player tries to do something, it goes horribly, sucks to be them.” so inevitably the first person to nearly win would face a slew of these. The single skill most consistently correlated with winning was an ability to fool other players into believing that you expended all of your ‘screw you’ cards on the last player’s near victory so that they squander theirs on the current player, you can stop them and there’s nobody left with resources to oppose your final fight.

Whether you’re fooling people or systems, convincing them you’re behind improves your chances.

The Paradox of Catch Up Mechanics

A catch up mechanic needs to determine which players are winning and losing to be effective.

Who will benefit from the catch up mechanic is a factor in determining which players are winning and losing.

I’m convinced that a truly accurate catch up mechanic would find itself in a paradox really quickly. I can see it being of the form “Jeff has the least stuff so we’ll let him buy the cheap resources but if Jeff gets the cheap resources their value exceeds that of the difference between how much stuff he and Sally have. So really Sally is losing so we’ll let her buy the cheap resources, but if Jeff doesn’t get the cheap resources…”

So What’s the Point?

Honestly, I don’t know. We’re all going to die in the end anyway.

But in terms of catch up mechanics they might not achieve “Find weakest player, help them catch up” but they’re still doing something valuable.

If a winning player determines that their best move is to use their advantageous position to break some of their things or trade away useful resources inefficiently in order to get the catch up mechanic bonus – they are still breaking some of their things or trading away useful resources inefficiently.

Consider the following:

We’re playing a game and I’m winning.

I have 8 points and the option to add or subtract 2 from my score

You have 7 points and have used up all of your options for this turn

At the end of the turn whoever has the least points gets a 3 point bonus

If I add to my score I go up to 10 and you get the bonus, also hitting 10 – we’re tied!

If I subtract from my score then I go to 6 but then claim the bonus shooting up to 9, while you’re still on 7 – I’m two points ahead!

So in the surface because I’m winning and have more effective options I can manipulate the catch up mechanic so it benefits me and not you. Leaving me 2 points ahead by abusing a mechanic that was supposed to help you.

Digging a little deeper however, consider what happens if we delete the catch up mechanic: In that instance I add 2 to my score and am leading 10-7 – I’m three points ahead!

So despite the fact that I got the bonus from the catch up mechanic and it didn’t change your score one iota, the mere fact that it existed meant that I’m leading by 2 points rather than 3. Just be encouraging me to make the otherwise suboptimal move of subtracting two from my score.

Catch Up Mechanics as Incentives

The problem that I’d identified was not in catch up mechanics themselves but in how I’ve been conceptualising them.

“A catch up mechanic is a mechanic that identifies the losing player and gives them a boost allowing them to catch up” was the wrong way to think about them.

“A catch up mechanic is an incentive for a leader to make moves that would otherwise be suboptimal to allow others to catch up” seems a better way to conceptualise it.

This way of looking at them leads to some differences in how they’re designed. It seems naïve to go “We’ll assume our players play the same way as if the mechanic didn’t exist and offer people who are behind a leg up” when players are generally pretty good at games and taking advantage of the rules in order to win.

Instead respecting the players capabilities and going “Everyone will try to use the mechanic, including the current leader, who may even have a greater ability to access it if their position has given them more options. The goal is to make sure that when the leader is encouraged to use it the price of doing so is smaller than the reward, but the net effect is that they can’t be a runaway leader because they’re still paying those prices.”

A Good Catch Up Mechanic

Viewed through this lens a good catch up mechanic has these traits:

Stratified: If there are multiple players having the mechanic be effective at each step means careful thought needs to go into when to use it and when to pull ahead. If there’s no advantage in dropping from 1st to 2nd place it won’t work because the boost won’t be big enough to justify dropping 1st to 5th

Positive: If a catch up mechanic is adding to a players progress then each round everyone will progress, even if some players are deliberately losing progress to access the mechanic they wouldn’t bother if the boost didn’t outweigh the loss. A negative catch up mechanic risks creating a game that will never end if the penalty for being ahead is high enough then someone who deliberately backs off and someone who gets hit by it are both behind their starting point and the game may never end.

Manipulable: Players should be able to manipulate the thing that the catch up mechanic is assessing in a timely fashion. If the leader can’t deliberately lose some resources to access it then either it doesn’t propel people past the leader or it was inevitable that someone will be propelled past the leader. In which case they were only ahead on some metric that failed to capture winning since their being surpassed was inevitable.

Costly to Manipulate: There’s no sense in offering a catch up mechanic to whoever has the least cash if players can buy gold, get the mechanic and sell their gold to have the same amount of cash in the very next turn. To work there needs to be some friction in how the mechanic is accessed.

Incidentally you might notice these are all attributes shared by the mechanics of Power Grid and are weak to completely absent for Mario Karts Blue Shells. So I feel like they work for at least those two examples 😉

3 thoughts on “The Paradox of Catch Up Mechanics

  1. “I’m convinced that a truly accurate catch up mechanic would find itself in a paradox really quickly.”

    I think you’re conflating strength with accuracy there.
    Suppose we say that a catch-up mechanism is accurate if it selects the weakest player(s). It doesn’t necessarily have to give them the exact amount of benefit which would put them level with the leader.
    If it does have that much strength, or greater, you get a bucket of crabs (probably the reason people hate Munchkin so much).

    In general, I think I want to see a catch-up which “brings up the rear” – that is, everyone is kept in the running, in essentially the same order, with no strongly gameable cut-offs.
    I think the leader should be striving to get further ahead, not fuddling around blocking off the opposition by sponging up benefits intended for those behind them.

    • I’m not convinced that a player will do something because the designer thinks they “should” be doing it if the game awards more victories to a different strategy.

      Certainly on an individual turn an accurate catch up mechanism can avoid being in paradox if the gap between the players is larger than the bonus the mechanism grants. However for it to never to be in the situation of “Boost should go to A, but that puts them ahead of B so boost should not go to A, but that puts them being B…” the boost would have to be smaller than the smallest possible deliniation between player A and player Bs position. It’s hard to imagine the game in which such a mechanism could ever be meaningful.

      • Let me try that again, because I think I am misunderstood.
        I mean, I think a game is better if it is designed such that the leader’s best option is generally to try to get further ahead, rather than staying ahead by blocking all attempts at overtaking.
        If it’s much harder to overtake than to stay ahead, what you have is a very frustrating game for everyone except the leader, and perhaps a boring one for them.
        Blocking doesn’t have to be impossible, it just should be a tactical decision based on specific conditions, rather than a general strategy.

        Secondly, you are assuming the ‘boost’ is constant. It doesn’t have to be, because it could change in magnitude or application.
        A simplistic (made up) example : a racing game, players have a hand of cards carrying movement values (plus other effects), and play one a turn to move that many spaces.
        Catch-up could confer one optional space of movement to vehicles which would otherwise end their turn two or more spaces back from the leader.
        I recognise and agree that manipulating the metric is important – in this example what you have in your hand is not considered by the catchup. But the ‘leader’ doesn’t get the option to access it at all.

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