Wednesday, August 27, 2014

Knowing you have won

I saw a quote from a recent Mark Rosewater column about Magic's new direction today that struck me as very important.

"I explain that if the game ends while the players are still invested they end the game excited and wishing to play it again.  If the game ends after they wanted to stop, though, it makes them leave the game with a negative impression, which decreases their chance of playing again."

This is, I suspect, a hugely important reason why the last few turns of my game Fantasy Monster Beatdown (FMB on the sidebar) haven't been as engaging as I would like.  The trouble is that the game is over when someone reaches 45 points and because the entire score a player has accumulated is visible at all times people give up when it becomes clear they can't win.  It is hard to be invested in a game when you know that the outcome is already decided regardless no matter if you are winning or losing.  Perfect knowledge of who is winning exists in plenty of other games but it is obscured by having complicated calculations to figure out the final score.

For example, you could easily count a player's entire score in Vegas Showdown to determine exactly where they will end up but people don't do this - they look at the points scored on the track, make a rough estimate as to how well the player seems to be doing on the board, and go with it.  Even though a player who is losing could be aware of that in theory they don't know it in practice and they can play without any certainty of the outcome.  This ensures that veteran players can have a very good sense of who is the front runner without explicit counting but newbies get the excitement of playing the last turn without knowing that they have already been defeated.

There are a few ways around this.  The usual one is to keep much of the scoring on the board and make it complicated to add up as Agricola, Le Havre, or Carcassone do.  New players just can't penetrate all of the scoring details so mystery remains.  There is also the solution employed in Puerto Rico where points that are scored are kept hidden so that newbies only have a vague sense of what a player has scored but in theory all point totals are accessible via memorization.  One of the requirements of any of these systems is that the game have a fixed end condition that is not dependent on the number of points scored and as it is currently designed FMB does not have that as an option.

One interesting option that comes from a game the name of which escapes me at the moment is having scoring be slightly random.  Each time a player scores they get a token which has either a 1, 2, or 3 on it indicating how much it is worth but the number stays hidden.  That way a player who performs better overall almost always has the higher total but you can't actually be sure just what each player's hidden total is.  This does introduce additional randomness into the game but it also functions to keep people who are just a few points behind in expected value interested because with a little luck they could still claim victory.

I can't change FMB to have a scoring system where a lot of the points rest on the board because it just isn't that sort of game.  I also don't like the partially hidden mechanic that Puerto Rico uses in this case because people would feel obligated to try to memorize their opponent's scores and that is tedious and not fun.  Making the optimal way to play also a fun way to play is a key component in good game design.  What I do like is the idea of knowing how many point tokens an opponent has but not knowing the exact score they have as a result.  It would be pretty easy to change the scoring system such that every point scored is a chip with a value of (1,2,3), (0,1,2), or (1,2) without changing any other mechanics and I could neatly avoid a lot of the issues the current game has at endgame.

There would be some small issues that need resolving - I would need to establish the game end conditions based on the game turn rather than point total but that is very trivial since the game tracks the game turn passively anyway.  There would also need to be consideration of how to balance going first vs. going second but I have a few easy dials to turn in that regard like preventing the first player from picking up spells or an artifact card on their first turn.

The thing I like most about this solution is it changes the actual tactics and gameplay very little aside from the last turn.  The game always had a situation where the last turn or two involved crazy maneuvers to gain points while surrendering territory and this changes that just a little but in a way such that anyone who is already good at the game will remain so.


  1. The game you're thinking of may be A Brief History of the World.

    You can still have points be the end condition even if they're hidden since a player can always count up their own score and announce that they've won. Or have it so they announce that they've broken a certain threshold and the game ends in X turns from that point. Or you could have the game end once X chits are collected (either by one player or the table as a whole).

  2. Yeah, it is possible I could use either of those conditions. However, since in FMB players collect one artifact token each turn I can just end the game after each player has had 11 turns (game ends when a fourth artifact would come into play). It is simple and doesn't require people to keep a count of their points or chits which is nice for simplicity.

  3. Another approach is to regularly increase the stakes.

    Then add in a system for a player to activate the endgame (at a cost), switching to a new mechanic at that point (that isn't 100% predictable).

    If you are ahead in the early game by enough that activating the endgame still keeps you ahead, this is a good move, as otherwise the increased stakes means other players can catch up (your lead means less).

    Ie, suppose you can "try for a killing blow" on your turn. The cost would be some fixed amount of points (say 10). You then roll off against the highest-except-you (random number+your score, vs random number+their score). If you win, the fight ends. If you lose, you either just pay the cost, or you pay the cost **and** skip your turn.

    If you are 10 points ahead at any point at the start of your turn, "trying for a killing blow" would have a 50-50 chance of ending the game with you winning. Which is a pretty powerful option. If you fail, you are now back in the pack (tied, **and** lost your turn).

    So now, each time a player falls behind they risk losing. But this loss doesn't snowball -- the other side gets a chance to exploit it, and if they fail their advantage fades.

    The "increasing stakes" matters, as otherwise once you have a reasonable advantage the right move might be to try to solidify it rather than risk it. You could also go with the "racing car game boost", where players sufficiently behind in total earn points faster/easier, all in an attempt to encourage players who are ahead to try to end the game.

    Or you could make "try to end the game" a mandatory thing that happens if you get too far ahead. On success, the game ends and you win. On failure, you lose some of your lead (lose a turn, or just lose some points, whatever).


  4. The game is purely a two player game at this point so some of what you are saying wouldn't really work. There isn't a pack, just one opponent.

    The trick with making the endgame come at an inconsistent time is that a well matched game could last for a tremendous amount of time if neither player is in a position to spend a lot of resources to win. I want the game to have a consistent and short playtime so I am looking at a fixed end point.

    I do like the ideas, but I don't think they fit how the game works at the moment.

  5. So I personally am not a huge fan of the "pull chits from a bag" mechanic, as it is often implemented. Either there is a large variability in points from the bag (1,2 - one of those chits is worth twice as much!), in which case often the game is decided by pulling better chits, or there isn't (9, 10) in which case why have different values at all, other than obfuscation. The "excitement" of an uncertain outcome only comes at the expense of randomness, and since you also can look at your own chits and have a good idea of the EV of your opponent's chits, anyone willing to do a little math won't find it very exciting.

    (Eclipse does the system well - you pull X chits out of the bag based on how well you did in the fight, look at them all, and keep only 1 of them - but it also combines this with many other methods of scoring points, and caps the total number of chits you can hold, and there is a small bag, so often players who fight early are rewarded with the high-valued chits. )

    If the last couple of turns aren't engaging, can you cut out the last couple of turns? Maybe introduce a random endgame mechanic, similar to Evo's? Or claim that the game is over if a player is ahead by 35 points on turn 5, 30 points by T6, etc, otherwise it ends on T11? You're saying that players lose engagement when the outcome is basically decided - that's probably going to be true even if obfuscated a bit with chits - why not just have the game end if the outcome is decided.

  6. I agree that 1 and 2 are pretty different. My current idea is to have an even mix of 0,1,2 in the bag and those are even more extreme! However, I do expect people to draw about 20 chits each over the course of the game so their scores will generally be reasonably close to EV given that they are going back into a bag with only 50 chits in it.

    I think you would find that your argument that if people can calculate who is winning that things aren't exciting doesn't work if you look at other games like the ones I listed - Le Havre, Agricola, Carcassone, and more. People *could* calculate those out but they don't so much. I think that the very fact that the score is obvious is the big problem, not that the winner is possible to derive. Of course that will vary with how competitive and skilled the players in particular are.

    The 'pull many, keep best one' would work for the phase of the game where you get points from Mines at the start of your turn but wouldn't work for other sources of points. I could have two different systems there I suppose. However, given that I expect people to only need to take 1 chit at the start of each turn on average and 1 more chit during their turn for other reasons I don't think it is an unreasonable number of chits to deal with overall.

    The thing about the last few turns that isn't engaging is only that you can often tell who is going to win. The actual play is usually very interesting - probably the most interesting part of the game, really. In every case that I can think of if the players both knew that the game was very close and either could take it then I expect they would love the endgame. The only thing I am trying to get away from is the level of certainty they have about who is ahead and by how much.

  7. I did a bit of simulation to see how random this is I assumed 51 chits evenly distributed between 0, 1, 2 and that player A drew 20 and player B drew 25 from the same bag.
    A wins: 15946 B wins: 79293 tie: 4761
    This does mean that when A and B are playing for who gets to draw the last chip it matters who draws it.

    On the other hand if you just want the players not to know who's winning, you could have all the chits be worth 1, and have the player hide them in bags.

    1. For this particular game it is *far* too easy to keep count in your head.

  8. Sthenno is right that counting the chips your opponent has is not terribly difficult. Pounder's simulation also shows way more variance than I am really interested in, so I think I will have to find some other way of accomplishing my goal.

    I had another idea that might bring me to the same end but with much less in the way of play changes:

    At the end of each turn the player draws a Fortune of War card (a deck of cards equally distributed between (-2.-1.0.1,2.3) that is already used to randomize other results) and apply that value to their current score. If the total is 45 or more, they win. This way it is totally possible to win even if you are down a few points, but you will have to get somewhat lucky at the end. You would still know your opponent's score but there would be some unknowns in terms of exactly when they will win the game.

  9. Do you still have ways to remove cards from your deck or your opponent's deck? Knocking out their 3s is a big deal if they're being used in scoring.

  10. There are a number of ways to modify the decks and I would definitely look at them again if I implemented this. One artifact lets you always see your top card. One turns your minus 2s into plus 1s. One turns enemy plus 3s into 0s. They are all useful for sure but the amount they alter your win percentage overall isn't huge. They only rate to affect a single draw in this way, usually dont proc on that draw, and only

    1. Only give you three gold in that case. Relevant for sure but not an issue I think.