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[TiGD] Delta influencing choices with varying # of players

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zaiga
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Joined: 12/31/1969

Here's a Random Thought [TM]. Just to get it out of my system. Feel free to add your own thought and comments on the subject.

Some two-player games feel very interactive and confrontational, whereas some multiplayer games can feel as if you are playing a solitary game. Indeed, sometimes when you play the same game with more players it may feel less confrontational. With more players it becomes more important to focus on your own plans, and it become less importnat to focus on hindering your opponents' plans. More players -> less confrontational. Isn't that a strange paradox?

Not if you understand what my playing group calls the "delta". The delta is the total relative difference (in victory points, or resources, or what have you) between one player and the other players. This is easiest to explain with an example. Suppose it's your turn in a game and you can choose between taking either action A or taking action B. Action A gives you 2 victory points. Action B gives you 3 victory points, and another player 2 victory points. Which action should you take?

The answer is: it depends on the number of players. If there are only two players in the game (you and your opponent) you should take action A, because that creates a relative difference of 2 victory points. Action B would only create a relative difference of 1 victory point.

Now, suppose there are four players in the game. Taking action A would now give you a relative difference of 2 victory points per opponent, for a total delta of (3 opponents x 2 VP =) 6. However, taking action B would give you a difference of 1 victory point when compared to one player (the one who received the 2 victory points), and 3 victory points relative to the other two opponents. This creates a total delta of (1+3+3=) 7, which makes taking action B the better move.

What about three players? Then action A would give you a delta of (2+2=) 4. Action B would yield a delta of (1+3=) 4.

Five players? Action A yields a delta of (4x2=) 8. Action B yields a delta of (1+3x3=) 10.

As you can see, in a two player game you would choose the action that helps your opponent the least (action A), whereas it is the better plan to take the action that also helps someone else in a multiplayer game (action B), and the latter action becomes even more lucrative when you add more players to the game.

Let's do another example. Action A gives you 2 VP. Action B now gives you 3 VP, and another player also 3 VP. How many players does the game need to make action B better than action A? The answer: five players.

Four players. Delta action A (3x2) = 6. Delta action B (0 + 2x3) = 6.
Five players. Delta action A (4x2) = 8. Delta action B (0 + 3x3) = 9.

Now, I know that games aren't always that simple. Often actions don't just yield bare VPs to players, but it is a complex thing of shifting different kinds of resources and possible ways for scoring VPs. Diplomacy and psychology come in as well, making actual analysis during a game a lot harder than my simple calculations above. Also, players will need to factor in a player's current standing. It's a much better idea to help the player in last place a little than giving free VPs to the player who's leading, for example. However, I do think it is important for a designer to understand how the delta works, and how it can alter changes in a game with a varying number of players.

Zzzzz
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[TiGD] Delta influencing choices with varying # of players

First off thanks Rene, for some reason my mind sparked when I read your post! I have been just having the hardest time getting my mind thinking games again... anwyays

Quick question: Was one of your assumptions that the player had to choose one of the options, A or B? What if the player just decided to pass (lets say passing is option C)?

Ok ok, I know passing results in a 0 delta, but I would argue that is not true. It only results in a delta of 0 for this turn. Maybe the player was setting up for a *big bad* delta move (option D), but needed to gain a few more "resources" before the player could make the move. The player might still have options A and B, but choosing either of those might make option D (which is really just one of the A or B options from their next turn) impossible.

One final thing I wish to toss out there for fun. The delta concept with your example seems to base delta solely on the concept of one player’s perception of the delta gain from options A or B. Is this not a false sense of delta? I think it is unless the player is the last player in a given game round. And for the first player of a round it is really a perceived delta since they have no idea what the other players will do this round.

This brings up another thought for discussion, should all options available to a player be assess from just their perspective of getting the most delta without thought of what their opponents will do? For that matter, should the player also attempt to assess what other players will do, thus altering their thought about what maximum delta options they choose? (hmmm not sure this sentence makes sense... well I will let you all decide!!)

zaiga
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[TiGD] Delta influencing choices with varying # of players

Zzzzz wrote:
Quick question: Was one of your assumptions that the player had to choose one of the options, A or B? What if the player just decided to pass (lets say passing is option C)?

The player has to choose between A or B, there's no other option.

Quote:
This brings up another thought for discussion, should all options available to a player be assess from just their perspective of getting the most delta without thought of what their opponents will do? For that matter, should the player also attempt to assess what other players will do, thus altering their thought about what maximum delta options they choose? (hmmm not sure this sentence makes sense... well I will let you all decide!!)

The examples I gave are purely theoretical. Think of it as your first turn in a game, with many more turns yet to come, and where your decisions do not affect what other players can do.

Of course, in a real game you won't make decisions in such a vacuum, they will be based on your current standing in the game, the standing of other players in the game and how your choices affect the choices of other players, etc. I haven't taken a decision tree into account here, that would be food for another Random Thought[TM] ;)

Zzzzz
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[TiGD] Delta influencing choices with varying # of players

zaiga wrote:

The examples I gave are purely theoretical. Think of it as your first turn in a game, with many more turns yet to come, and where your decisions do not affect what other players can do.

Ok.... but I still would say that your own decisions may influence your future decisions. So with that in mind, the player may choose the lesser delta of options A or B during one turn, just to allow for a larger delta option A or B in a future turn.

This of course assumes that one turn choice can influence and impact another turn choice. Such as building 2 armies now (option A) or saving resources (optoin B) to allow for say 10 armies to be built next turn (assuming one of my second turn options is building 10 armies).

So basically if my first turn can result in a delta of 3 for option A, or delta of 1 for option B. The delta for my second turn options A and B might be better if I choose option B during the first turn.

For example:
First Turn:
Option A yields delta of 3
Option B yields delta of 1

Second Turn (after choosing option A in first turn)
Option C yields delta of 2
Option D yields delta of 3
Thus my max delta over turns one and two could be as high as 6 (option A in first turn, option D in second turn)

Second Turn (after choosing option B in first turn)
Option E yields delta of 7
Option F yields delta of 5
Thus my delta over the two turns could be as high as 8 (option B from first turn, and option E from second turn).

Though as I stated this assumes that your own choices can influence what your future choices can be, which in a vacuum I might not know, so I would assume most players would choose optimally for each turn not caring about how they influence their future turns.

Ok... again Rene thanks, my mind is actually trying to think again!!!!

zaiga
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[TiGD] Delta influencing choices with varying # of players

Zzzzz wrote:
Ok.... but I still would say that your own decisions may influence your future decisions. So with that in mind, the player may choose the lesser delta of options A or B during one turn, just to allow for a larger delta option A or B in a future turn.

Of course, you are totally right. If your current action somehow influences your future options, you will have to take that into account.

Quote:
This of course assumes that one turn choice can influence and impact another turn choice. Such as building 2 armies now (option A) or saving resources (optoin B) to allow for say 10 armies to be built next turn (assuming one of my second turn options is building 10 armies).

So basically if my first turn can result in a delta of 3 for option A, or delta of 1 for option B. The delta for my second turn options A and B might be better if I choose option B during the first turn.

Exactly. This is a good example of the difference between tactical thinking (optimizing your current turn) and strategic turn (planning ahead for future turns).

Quote:
Ok... again Rene thanks, my mind is actually trying to think again!!!!

No problem, that was the intention of this thread!

Rick-Holzgrafe
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[TiGD] Delta influencing choices with varying # of players

Here's another question: when is the delta important?

Early in a game, I might want to choose high-delta moves, to improve my overall position relative to all other players. At this point I'm not concerned about being in the lead; I just want to stay in the hunt, so larger deltas are usually better.

But late in a game, I don't care whether I'm a mile ahead of the other players on average; what I care about is actually being in the lead, even by a whisker. I won't want to benefit any serious contender at all, if that would decrease my lead or increase his.

And as Zaiga pointed out, even in mid-game it matters whether you are granting VPs to the current leader or the biggest loser.

All of the above is an over-simplification, of course. Sure, I'll benefit the guy in second place, if by doing so I can cement my own win. But there again, it's not the delta that matters to me.

I'm not pooh-poohing the idea. I think it's a useful concept, and I'm adding it to my mental toolbox with gratitude! I just wanted to point out that it's not universally applicable -- as you did, Zaiga, in your original post; I just saw a different slant on it.

Thanks for the idea!

FateTriarrii
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Joined: 01/04/2009
[TiGD] Delta influencing choices with varying # of players

I have two things. One, another thing that might make play different is strategic planning. Wait, these tie into each other, so I only have one idea.

I think a tactic --> strategy game matter of things is another part of the tension relief. A game with lots of strategy (chess the obvious foremost example) means that there are many moves that all must go right and so the players spend every second at their disposal checking and double checking each part to get it right. Wereas with risk the player only has vague goals like "I'm gonna crush europe like a bug next few turns" because so much is decided by the dice (the great europe-crushing army might be blown away by two lucky defendants). And this may be part of multiplayer too.

I heard once that there needs to be some variation to keep people coming back. The easiest and most reliable way is either chance or "chaos". Chance is cards/dice, stuff no one controls. "Chaos" is the amount of difference one player makes. And the more chance/chaos the more tactical play becomes, the less strategic.

With chaos it must be remembered, though, that it goes up exponentially for every player has more on their plate. So a 2 player game you have a simple 1-->1 correspondence with one relationship to keep track of. With 3 players, though, you have three relationships (A-B, A-C, B-C). And four gives you six. And five gives you ten!!! So, for example, Diplomacy (the game of relationships) you have 21x the amount of chaos that you get in chess.

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