Sunday, June 17, 2012

Playing For Second

I was playing a game of Through The Ages in the 3 player league this week (against the Mons of Mons' Goblin Raiders fame) that had an interesting conclusion. I'd played an early Genghis Khan to build up a bit of  a point lead but he'd since died. The score was something like 70-20-16 but I no longer had a material advantage in any real sense. I felt like I was in a good position to win but it wasn't guaranteed. The player with 20 points had in his hand the International Tourism card. This is a pact you can propose to another player as your political action for the turn. If they accept then both players score points each turn equal to the number of wonders the other one owns. The guy with 16 points had 2 wonders and the other two of us had 3 each. There were probably going to be around 3 more turns in the game to score points off of it. Who should he propose the pact to?

If he proposes to me then I rate to score 9 points and he rates to score 9 or 12 points (depending on age IV timing). If he proposes to the other guy then other guy will score 9 points and the proposer expects to get 6 or 8 points. Which should he do?

If he's looking at purely maximizing his own score then he should propose the pact to me. If he's trying to win the game he has to propose it to the other guy. Realistically the only way I'm going to lose is if the other two guys focus on taking me down together with big military plays or by throwing points to each other. If instead they throw points to me it's going to be all over. If he's playing for second place then he should absolutely propose it to me. He can give up on passing me and just work on powering beyond the other guy.

So really it comes down to what should you do in a game when you probably can't win. Do you maximize your individual score, do you maximize your individual placement in the game, or do you go for broke and take the slim lines to try to win anyway? Ultimately he proposed the pact to me, I accepted, and both other players stopped even trying to hit me with anything. They went after each other instead and I coasted to a very easy victory.

Along a similar vein, I played some (for fun) games of Hold'Em at Andrew's birthday party last night. We ended up playing 4 times and I finished with a record of 1st, 1st, 3rd, last. Sky had 1st, 2nd, 2nd, 3rd. Sky mused about which of those records was actually better? Clearly both are very good and would be +EV if we'd been playing for money no matter what the payout scheme was. If it was winner-takes-all then I'd be better off. If it was a 'double up' format where half the people get the same prize then Sky's would be better. So really which is better depends on what sort of weighting function we assign to the different places.

I watch poker coverage on tv when I notice it's on and often they talk about playing for a specific position. Someone with a smaller stack will try to avoid confrontation in the hopes of surviving while a couple other people lose out. Especially when they're 'on the bubble' where all but one of the remaining players is going to win money. A lot of people tighten up and do whatever they can to survive while someone else loses out. Playing passively in this way has to give an advantage to the bigger stacks at the table who can now have an easier time bulling people around and stealing pots.

If it's acceptable in poker shouldn't it be acceptable in board games? There are board games where you're often making plays to give other players points or to hurt other people's positions. (Think El Grande, Diplomacy, or Advanced Civilization.) A game of El Grande with all people playing solely for first is a very different affair than one where people are happy with second place. In the first game getting an early lead is very dangerous since everyone else is going to gang up on you. In the second game an early lead is game winning. People who are playing for second will just keep feeding you points because you simply don't matter anymore in their utility function. They have to give points to someone, and they're allowed to lose to someone, and they're probably going to lose to you anyway. So they might as well give any points to you instead of to one of their competitors.

I donno. I hate the idea of playing for second place. But if what I'm content to come 6th in an event and someone gets out to an early lead in the semis shouldn't I switch focus and start playing for second? Even if it's not a sand plaque on the line... In 2010 when I came 2nd in Tigris and Euphrates you could say my line of play was for second. There was an obvious leader and it would have taken a coordinated effort from the rest of us to take him down. We really could have done it if we'd been willing to spend a blight each. But none of us were willing to be the first one to use our blights and kept fighting amongst ourselves instead.


David Nicholson said...

It just kind of bothers me that in your example of the score being 70-20-16 that you will only lose if they gang up on you that it is quite likely that even still you place second. This would mean that someone has to play a strongly anti-Ziggyny strategy and still end up last.

It doesn't seem right to play to change if A or B wins but come last either way.

Robb said...

Ya, but both other players probably don't know which of them comes out on top if they both start taking Anti-Ziggyny lines of play. It could be that whoever draws more wars, or the last war, comes out on top, which is unknowable, but they both only have a shot if they build military and play aggressions in the mean time. So it isn't really a "kingmaking" line of play, it's a "keeping yourself in it" line of play.

Also, what I really like about WBC is that it rarely, if ever, rewards anything but firsts, removing a lot of this dilemma. And it also obviously (but only slightly) rewards playing for place over playing for maximum score, giving you a good idea as to how your opponents will play if they truly cannot win.

Sthenno said...

In many board games if you walk in playing for second it is very easy to achieve. I think in our group at university the most common strategy in a game was to figure out the play that maximized your own score while minimizing everyone else's. If players 1, 2 and 3 use that strategy while player 4 maximizes his own score and only worries about minimizing the score of players 1 and 2 then the odds that player 3 comes in first and player 4 comes in second really go up (depending on the game - but I've tried this in Puerto Rico and wow does it work there).

Of course players 1 and 2 might feel kind of annoyed that player 4 basically gave the game to player 3. On the other hand, if all players are of equal skill then this might be the highest EV for player 4 depending on tournament structure and payouts. It's an even better strategy if players are not of equal skill and player 4 knows he is one of the weaker players. If you think you are the worst person at the table and you think you know who the best person is, then letting the best person win to try to maximize your own score is probably your best option (again, assuming there is some reward for second).

If you are playing for no rewards, just for fun, then the optimal strategy is probably to practice mindfulness meditation and enjoy the present regardless of your outcome - but that's another thing entirely.