On Kingmaking…

A very interesting situation came up on Saturday night, as I was enjoying a game of “El Grande” (a board game) with Baditude, Iwan, Little Buhr, and Maja (pronounced “Maya”… those wacky Germans).

The specifics of the game are unimportant, but it involves scoring points. After a set amount of turns, the player with the most points at the end of the game wins. Points are good.

About two-thirds of the way through the game, I was in the lead, with Iwan not too far behind, and Little Buhr and Eryn mixing it up a little ways off behind him, and Maja trailing the pack. A specific card came up that would give me seven points, and give Maja four points. Maja had the option of veto’ing this play, or letting it stand.

Her options amount to this:

1) Let the play stand. In this case, I would get 7 points, she would get 4 points, and every other player gets 0 points. My lead would be extended, by 3 points relative to her, and by 7 points relative to everyone else. She would make up 4 points worth of ground on every other player. So while she decreases her (slim) chances of winning by extending my lead, she greatly increases her chances of not coming in last place. Those 4 points don’t get her out of last place, but they certainly let her get closer to the pack. It also makes me almost unbeatable.
2) Veto the play. She would remain in a relatively distant last place, but my lead wouldn’t be extended. Perhaps the next rounds of play could bring her better luck and she can make up ground, but her chances of winning remain the same – slim. I still hold the lead, but my victory is far from ensured.

The other thing, dear reader, you need to be familiar with is a term called “Kingmaking”. Kingmaking, as I understand it, is when a player that has no chance of winning a game is still able to affect who will win the game. Let’s say it’s Alice’s turn to play, with Bob going next and Charles going after that. Alice is presented with a choice that will prevent Bob from winning, but if she does that, Charles will win. Alice can effectively choose who she wants to win. The situation is compounded when Alice happens to be sleeping with Charles. (Not the case in this game, obviously).

I lobby for Maja to not veto the action. Clearly I want those 7 points, but I also know that Maja has been playfully whining about being in last place for most of the game. She’ll do what it takes to NOT finish in last, and I use that to my advantage.

So Maja makes her play, and decides NOT to veto the action. I take my 7 points, extending my lead and eventually winning the game (by less than 7 points). Maja gets her 4 points, and ends up still coming in last place by a single point.

After the game, Baditude is unable to contain his frustration at Maja’s choice, and grumbles something about “kingmaking”. I immediately get defensive. At the time, my impression of kingmaking is more like collusion, where a husband and wife team make poor plays to intentionally help the other person win. Clearly this is unfair to other players, and in my book, ranks a small step above cheating. Maja and I have no special relationship, and she has no vested interest in me winning, so at the time, I consider the “kingmaking” comment not only offensive but flat out wrong. (I understand now that kingmaking is more about a non-contender choosing an arbitrary winner, regardless of their relationship, so it makes a little more sense).

I’m reluctant to speak for Baditude, but my impression of his argument was that any play that reduces your chances of winning the game is a inexcusably “bad play”. Maja’s play clearly increased my lead relative to everyone else, including her.

I disagreed with Baditude, feeling a bit defensive that my hard-won victory was just going to be chalked up to an arbitrary choice by another player. I didn’t have a lot of time to think about it, but I was thinking that a play that reduces your chances of coming in last place can’t necessarily be a bad thing, can it? Baditude said that he respected my opinion, but disagreed. Well, that’s what his mouth said, at least. The actual message was a very clear “I hear your opinion, but you’re clearly wrong, and possibly insane.” I admit that made me bristle a little, too.

It was 1am, and I was getting up early the next morning, so I headed home, my head still spinning.

On the drive home, I thought a lot about that play. Was it “kingmaking”? Was she arbitrarily handing me a victory? Was it a “good play” – one that benefitted her position? Or was it a “bad play”, one that made it harder for her to win?

I thought about it mathematically. She gained +4 on three players, and -3 to me. If we were playing a two-person game, this would clearly be a bad play. If she did that move every time, she’d never catch up to me. However, in a multiplayer game, I became more and more convinced that this was a good play from a “long run” point of view. If she had somehow made the same play twice, but targeting two DIFFERENT players, she’d end up with two players up +7, and the other two players +0, and find herself in the lead at +8.

But in the short run? You can look at aggregate points scored. She went up +4 points relative to three players, for a total of +12, and -3 points to me, for a total of +9.

I will grant that her play made it harder for her to win. However, I don’t think that that, in itself, is enough to write it off as a bad play.

Baditude, as I knew he would, posted the topic to boardgamegeek.com, a hugely popular hangout for boardgame enthusiasts. I was hoping he’d post it, because after such a strong disagreement, I was curious to hear what others would think. It’s been a lively discussion and interesting reading. The majority opinion appears that Maya made a good play.

So, in the end, Maja’s play certainly helped me win the game. In that regard, I guess it could be considered kingmaking. However, I think it was kingmaking as a side effect. The motivation of her play was not to arbitrarily hand me a victory, but rather to increase her position to avoid coming in last place. And I think I’ve convinced myself that it was an outright good play mathematically, and it’s made me reconsider how I think about gaming strategy, and as a result, real life “strategy” as well. Good stuff.