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For games in which it is not possible to take simultaneous turns, as the number of players increases, so does the wait time between a player's turn and their turn again. It becomes a balancing issue with the game's design to keep the game the same or introduce elements that help speed up game-play.

  • What is the maximum downtime between turns that I can expect players to be ok with?
  • What steps can be taken to mitigate downtime between turns (examples from games, and your opinion of their effectiveness, are appreciated).

For example, Settlers of Catan, when expanded to 5-6 players, allows all players to make purchases during any player's turn. This is done to mitigate having too many cards if the robber comes up between your turns, but it also increased engagement on other people's turns. MtG and other CCGs have instants that can affect your opponent's turns. Even games like Monopoly allow trading between players to keep them engaged.

What other design approaches can be used for larger numbers of players if simultaneous play (like Roll Through the Ages) isn't possible?

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I think the main points have mostly been hit. A few strategies:

  1. Direct interaction during other players' turns. For example, if there is a combat element, if the defending player has interesting choices such as playing cards from hand to gain advantage. As mentioned, Magic is a good example as the defending player has plenty of decisions to make and cards to play. Counterpoint is Risk, where defender just rolls dice doesn't work as well for keeping interest.
  2. Indirect interaction during other players' turns. In a recent game Eminent Domain, player gets to piggyback on the decision the current player makes. Or in a game like Battlestar Galatica, there is so much meta-game discussion that regardless of whose turn it is, all players are engaged and invested even if the game mechanism doesn't allow them to interact with the "game" at that moment.
  3. Pre-planning while avoiding Analysis Paralysis. Player can more or less make all decisions about their turn while other players are doing their own. A key part of this is avoiding adding new information during current player's turn. For example, if the player must draw a card, have them draw at end of turn rather than beginning of turn. This will give them more time to internalize their choices.
  4. If there really is no way to do any of the above, then you need to find a balance in length of turn. Perhaps make really short turns, but if the player only has a few actions each turn they may be all the more frustrated because they feel like they can't get anything done on their turn. If you instead give them lots of actions, you can make the player's turn feel really beefy, but that's going to make the wait for next go-around that much worse.

I don't think there's a golden rule for amount of downtime. Instead, it's all about perceived downtime. My "turn" may only come up every 15 minutes, but as long as I am thoroughly engaged in what my opponents are doing during their turns, and I have true decisions and actions to take during their turns... it doesn't matter.

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By the way, this is all a matter of preference. Check out Andrew Looney (Fluxx, Chrononauts) in his principles of game design -- he actually prefers no engagement when it's not his turn. I don't think most people are like that, but for some casual/conversational games (think light card games like Spades, or even drinking games) it may not be appropriate to have lots of engagement outside of a player's turn. wunderland.com/WTS/Andy/Games/DesignPrinciples.html –  Daniel Richnak Mar 2 '12 at 18:51
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The maximum acceptable downtime will depend primarily on how much analysis is required (and possible) for a player's turn. For example, downtime in Power Grid can get quite high during the final few turns. I've had to wait as long as 20 minutes in one 6-player game. Yet, that didn't bother me, because the game state wasn't going to change dramatically before it got to me (that is, options will not open up for me, they will only be taken away) and there's a good amount of mental arithmetic involved in figuring out the optimal placement. To contrast that with, say, Carcassonne, I once had to wait close to 5 minutes for a turn due to one analysis paralysis prone player, and that was torturous. Even though we draw our tiles at the end of a turn to speed play, there just weren't that many options, so it was extremely boring. This would also be true for games where the board state will change dramatically between turns, so foreplanning is not worthwhile (Fluxx is a good example of this - any downtime that's not measured in seconds feels long for that game, because there's not anything worthwhile you can do when it's not your turn).

Along those lines, my personal experience is that the best way to mitigate downtime in a game with indirect interaction is to give players enough to think about when it's not their turn, either about the current turn or planning ahead for the future. Recognize, however, that not every game is (or should be) a deep, brain-burning game, so this is not to say that the answer is to add complexity; perhaps a better way to state this point is to ensure that the downtime is proportional to the depth of the game. You don't want people to run out of game-related things to think about, because you lose them once their minds start to wander.

If your game has any kind of direct interaction (e.g. negotiation, trading), then there's really no such thing as downtime, since all players are involved at all times. If downtime is a concern and your design would lend itself well to a direct interaction mechanic, that would probably be the way to go. Even something like a bluffing component can go a long way toward helping keep players engaged; for example, in hidden money games like Power Grid or Imperial, I greatly enjoy trying to project more (or less) wealth than I actually have, getting inside my opponents' heads to try to get them to do what I'd like.

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Good comparison between Power Grid, Carcassonne and Fluxx. The nature of the game really does matter as to how much down time can be tolerated. –  Pat Ludwig Feb 28 '12 at 7:45
    
An excellent analysis. Especially that last paragraph; Settlers is an example of an almost-no-downtime game for that reason. –  Tynam Mar 2 '12 at 19:32
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You've already hinted at the most successful method, at least in my experience.

I'll relate it by an example. In Supremacy, the original was "On your turn, do steps 1 and 2, then any three of steps 3-8" (I might have the numbers wrong; I sold my Supremacy set years ago) The revised sequence of play in the revised and expanded game is everyone does steps 1 & 2 simultaneously, then in each of the other steps, those doing that step roll for initiative, and act in rolled order.

This sequential play of each step reduces the wait between players, and preserves a sense of simultaneity, without actually having simultaneous play.

Star Fleet Battles, and the Impulse chart is another variation on this mode, as is Civilization/Advanced Civilization.

The other common ways include limiting which steps can be taken on one's turn, and some form of timing mechanic.

In Galaxy Trucker, you have only a couple minutes to finish building your ship after the first person declares theirs done; first one done flips the egg-timer... and calls stop when it runs out.

In chess, it's often played with a chess clock, and the game is lost if one is in check or one has run out of time on the chess clock.

In the original Supremacy rules, you don't get to do all the steps. This limited your turn time by reducing how long it took to resolve your turns.

One other useful tool for reducing down time is useful rules summary cards with the most common information on them. The biggest factor in slowing down many a game is rulebook referencing; by elimination of the need to go to the rulebook by an effective and clear summary card, one reduces the tendency to look in the rules.

One other item you hinted at in the question is the "reaction" effect. By having something that you get to do during the opponent turn, one tends to be more attentive to the opponent's turn, and not notice the downtime as much, despite not actually reducing the downtime.

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+1 nice answer. As you've mentioned Supremacy and SFB, I'd also point out the Puerto Rico / San Juan solution somewhere between the two - players do bookkeeping steps at the start and end of turn and then rotate taking single actions rather than entire turns. –  Tynam Feb 25 '12 at 16:52
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Another game that takes the phase approach is 7 Ages. All players secretly decide which two or three actions they'll take, and then the actions are run in order -- everybody who's doing maneuver does so, everyone who's buying units does so, etc. Especially for longer games this frequent intaraction is important. (I actually get bored with SFB, though I'm not very good, because every step takes what seems like forever to resolve and if it's not mine I'm not engaged.) –  Monica Cellio Feb 27 '12 at 15:14
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