The Tao of Gaming

Boardgames and lesser pursuits

Race — Random thoughts on number of players

A while ago someone asked if it mattered that a game was four player vs 3 player. I didn’t really have an answer then. One thing that I realized (later) is that I take ‘swingier’ actions with more players.

[This idea is based I read many years ago in the Bridge World, but I can’t find it online)].

Assume that your opponents will score in a normal distribution. Now say you could wave your hands and magically score the same each time. A bit above average (say, 1 standard deviation). In a (generic) two player game, you’d win fairly often. But as more players are added, you’d do poorly. Let’s make this concrete. You always score 13 points, and your opponents roll 3d6. With one opponent, you like your odds. With 2 or 3, you are doing ok. Anyone who thinks they’ll win against six opponents has never rolled up a D&D character.

Single-session Matchpoint bridge tournaments take this to an extreme (which is why the article was published). With dozens (or hundreds) of pairs, skill gets you so far, but swinging for the fences is useful too. (Longer games and other forms of scoring change that).

So consider a “New Sparta needs a military world” opening. Do you explore +5 or +1/+1? With more players, I feel more strongly that Explore +1/+1 is correct … Even if the +5 gives me a good card 100% of the time, I’d rather take my chances getting a good card and some spare cash. With three opponents, the safe 35 points isn’t as tempting as shooting for 45 (but often getting 20).

As Race is often 2-4 players, this isn’t a huge effect … yet.

With more players you can also swing for the fences by calling speculative trades (produces), and other tactics.

What else? With more players I’m slightly more worried about releasing good cards for opponents (since 4 players tend to go through the deck two full times, while less players usually peter out at 1.5 or so), but that’s a minor concern compared to other issues.

I haven’t really thought of other issues relating to # of players…

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Written by taogaming

March 26, 2008 at 10:50 pm

5 Responses

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  1. The game this is kind of interesting for is Take it Easy. I have a friend who occasionally recounts playing in a very large (50+?) player game of Take it Easy at The Gathering. Obviously, that’s a game that you have to play totally differently if you’re playing with a very large number of players, because you’ll need an awesome score to win.

    I find the argument somewhat less convincing for Race, though. There are good risks and bad risks – risks where the payoff is worth what is risked, and risks where it isn’t. Maybe the calculus of what is a good risk change a little bit with additional players, but personally I don’t see it changing so much with additional players that it changes how you might approach the game. Maybe playing a consume/trade becomes a better risk because you’re more likely to see a Settle played to feed your windfall world, but it’s still situational.

    For me, fishing for a military world with +1/+1 is always a bad risk, whether you have 3 or 4 players. Unless you have a backup plan and two extra non-specific cards are helping you to buy something else anyway, picking 3 cards does not seem likely to deliver anything particularly useful, in my experience. I suppose I should run the numbers.

    Chris Farrell

    March 27, 2008 at 1:20 am

  2. The game this is kind of interesting for is Take it Easy. I have a friend who occasionally recounts playing in a very large (50+?) player game of Take it Easy at The Gathering. Obviously, that’s a game that you have to play totally differently if you’re playing with a very large number of players, because you’ll need an awesome score to win.

    I find the argument somewhat less convincing for Race, though. There are good risks and bad risks – risks where the payoff is worth what is risked, and risks where it isn’t. Maybe the calculus of what is a good risk change a little bit with additional players, but personally I don’t see it changing so much with additional players that it changes how you might approach the game. Maybe playing a consume/trade becomes a better risk because you’re more likely to see a Settle played to feed your windfall world, but it’s still situational.

    For me, fishing for a military world with +1/+1 is always a bad risk, whether you have 3 or 4 players. Unless you have a backup plan and two extra non-specific cards are helping you to buy something else anyway, picking 3 cards does not seem likely to deliver anything particularly useful, in my experience. I suppose I should run the numbers.

    Chris Farrell

    March 27, 2008 at 1:20 am

  3. One of the other advantages of +1,+1 with 4 is that the chances of a develop and a settle go up with 4. This means it’s more important to have both a Develop and Settle plan, and a +1,+1 is more likely to give you both without discarding cards you want to hold onto. As you add fifth and sixth players this concern increases.

    Alternatively if you think only one of Develop or Settle is likely I’d probably favor the +5. It gives you more cards to react appropriately to either phase. This assumes all of the cards in hand are nonstarters, far too costly in the short term and you have an appropriate number you are willing to spend.

    frunk

    March 27, 2008 at 12:18 pm

  4. But, as the odds of seeing both a Develop and a Settle go up, so do the odds of seeing someone else doing an Explore, therefore getting you one card without doing anything, and significantly devaluing the +1/+1 in my opinion (but not so much the +5). If you can count on someone else to do the Explore more reliably, you can get that one extra card you need to make a Develop or Settle more viable.

    Chris Farrell

    March 27, 2008 at 2:01 pm

  5. To me the big difference between 3 and 4 players is your ability to react to someone who sets up a strong, early produce/consume threat (at least 6-8 VPs plus good card income along the way) when the leading tableau player has 6 cards in tableau. Is the producer going to be able to run the cycle two times (for, say, 6 &8 VPs) or three times (for, say, 6, 8, &10 VPs plus a nice 6 development due to the extra income)? This will often decide the game.

    With only three players, if one or the other of them is always exploring or trading each turn or if they both call Develop or Settle on the same turns, then they can’t run the tableau fast enough (a single player can’t end the game in less than 6 turns). If there are four players and only one player is doing Produce/Consume, then the odds of getting three cycles in goes way down as, among the non-Producers, there will probably be enough Develop and Settle calls for someone to run the tableau fast enough.

    Similarly, with three players, if two players are doing Produce/Consume, it is very hard for the third player to run out the tableau to stop them in time. However, this is partially mitigated by the 36 VP chip pool for, depending on leeching and how many VPs got taken early on, there may not be enough VPs left to run the cycle more than twice (and using Deficit Spending to tip the balance can be important).

    With four, there is no VP brake against two Produce/Consumers, but there are two players to try to run the tableau out. In addition, only one of the Produce/Consumers typically needs to call Produce, so the other Consumer might help build tableaus (as this player is presumably getting fewer VPs per cycle and would like to increase this by adding more production or consumption). (There can also be a slow-down in the Produce/Consume cycles when the two Producers (implicitly) disagree about which one should be calling Produce.) With three Produce/Consumers in a 4-player game, the VP brake discussed above comes into play, and so on.

    These dynamics extend as the numbers of players increases, but, overall, the speed of tableau growth goes up with more tableau-building actions being called, due to both fewer players needing to call Produce and decreased odds of collisions from all the non-Producers choosing Develop (or Settle) on the same turn. As a result, experienced players in 6-player games tend to swing into Produce/Consume mode slightly later and in a bigger fashion (8 growing to 10 VPs per cycle and greater card flow) because they expect to be able to run the cycle only two times, not three. This adjustment in playing style can take some getting used to.

    The larger player effect are a bit tricky to disentangle from the other effects of playing with the expansions: the implications of various new expansion card powers, the increased “streakiness” inherent in drawing from a larger deck, and a larger pool of 6 developments from which several efficient “interlocking” ones be placed; all of these things will also affect play styles and some of these effects do interact with the number of players in the game.

    For example, as Brian points out, while the deck does grow in size, with 6-players, the increased reshuffling means that the odds of finding “interlocking” 6s goes up, which of course means that 6-hoarding across a reshuffle becomes a more important player tactic…

    Tom_Lehmann

    March 27, 2008 at 10:23 pm


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