If you measure in meters and I measure in yards, but we both decide to call them Victory Points instead of their normal names, can you really compare the two and all it unambiguous?

No, I do not prefer linear games in your sense of a single path to victory. (I’m not convinced that _Multiple Paths to Victory_ actually has a discernable meaning but that’s a different debate) However I do however prefer games whose growth curves are effectively linear rather than exponential. but that’s a different matter.

In that case, 2 scores that are the same could be said to require a tiebreaker – and some would say it’s the designer’s responsibility to indicate which path is ‘harder’ (deserving of the +epsilon score) and therefore deserving of a tiebreak favor.

While I understand that some say and feel that, I do not agree and I don’t accept those views and feelings. I do not see any responsibility or any level of requirement for a game or a game designer. More specifically I view such epsilons as unnecessary cruft and fiddle to rightfully be avoided and (almost) always removed as a normal part of game development. (The always is for those games which explicitly require such patterns, like the above mentioned King of Siam).

In that case you cannot say “you need to beat the other player, not merely do as well” because there’s not necessarily a metric to compare the 2 scores against each other (except the score, which has turned out to be not enough information).

You lose me here. A method was provided. The method revealed a tie. All the information is right there: they tied. What else is needed? Why the mandate for an unambiguous winner? I see no need. The two players scored identically. They tied. They took different actions to reach that tie but their scores are tied. The numbers are the same. I see no lack of information. What is this missing information and why is that an insufficient metric?

In contrast, the games you seem to prefer have the VPs on the same axis, and therefore it’s enough to compare them to each other directly, and one can say “the score indicates the tied players did as well as each other”. In that case, your argument holds water, however…

When is scoring ever orthogonal? There is one measure with which to compare the players, no matter how scoring movement is accomplished. That seems like a single linear scale to me no matter what the game is.

One could argue that the purpose of the rules (with regard to win condition) is to determine a single clear winner. …

This may be the core of our disagreement. I find determining the winner uninteresting but I do find the competitive attempt to win interesting. The scoring method describes how winners are determined. It may or may not provide uniqueness in that determination.

If you want to win, then ensure you unambiguously win.

And in your later comment above:

In fact, the efficiency argument is not a restatement of the epsilon argument.

How so? It is just efficiency in making primary Vps and epsilon VPs.

It does not weigh any type of VP activity any more than any other. Instead it assigns value (an epsilon I suppose) to another item which has no VP value otherwise.

I see no difference among VPs or epsilon Vps. They’re all score values.

More applicably, in some game where the tiebreak is “the player with more resource cubes leftover” would essentially be rewarding a player for attaining the same score as another player, but doing so either by using fewer resources, or by using the same resources but gathering more resources over the course of the game. It rewards efficiency in this very, very small way (i.e. only in the case of a tie).

I dislike such patterns. They attempt to layer a secondary and unnecessary value set over the primary challenge (scoring method) of the game. That’s the sort of cruft that should be removed in development.

So while you could describe that as adding an ‘epsilon’ score to the resources, it’s distinct from increasing other established VP sources by epsilon.

You’re drawing a typing difference between items which are worth 0+e and those worth N+e (where N is non-zero). I don’t see them as that strongly differentiated, as fundamentally different in any degree. I just see score values with some bigger or smaller than others, just like any other score values.

In short:

• Tie-breaker as a game-balance factor
• Tie-breaker for efficiency
• Tie-breaker as incentive toward desired play-paths/patterns

The efficiency argument and even the game balance factor are a restatement of the epsilon argument addressed above.

In fact, the efficiency argument is not a restatement of the epsilon argument. It does not weigh any type of VP activity any more than any other. Instead it assigns value (an epsilon I suppose) to another item which has no VP value otherwise. A game like Caylus offers 1vp for every 3 resource cubes at the end of the game. That weighs the cubes even more than simply an epsilon, but it’s similar. The game rewards having leftover unused resources.

More applicably, in some game where the tiebreak is “the player with more resource cubes leftover” would essentially be rewarding a player for attaining the same score as another player, but doing so either by using fewer resources, or by using the same resources but gathering more resources over the course of the game. It rewards efficiency in this very, very small way (i.e. only in the case of a tie). So while you could describe that as adding an ‘epsilon’ score to the resources, it’s distinct from increasing other established VP sources by epsilon.

Real quick I’d like to address your comments on my view of tiebreaks. When I say “the player who wins should be…” I am in no way referring to any kind of moral high ground that one player’s game had over the other. Morality is something that you have appended to the word “should” – I was merely referring to the epsilon argument as you described it in the first part of your bit about my comment (above). If you and I both score 12 points, and your 12 points have that invisible epsilon attached (i.e. you scored 12.1 points to my 12), then you should win. That’s all I was saying. Not that your play was morally superior to mine and therefore you ought to be rewarded better. The “ought to be rewarded better” is just a reflection of the invisible epsilon.

Now on to the new thoughts on this topic:

The subject of ties and tie breaking has come up again in a 5 page thread about Dominion. That thread linked another thread about tie break rules in which you (JC) made a comment…

For the rest of the games I want no tie breakers. That makes the games more demanding: If you want to win you need to beat the other player, not merely do as well.

In reading that comment and remembering much of the discussion we had about ties at the time, I thought I’d note that you seem to prefer games that are linear, where in general players are all racing along the same line to victory.

The concept of “Multiple Paths to Victory” is a tricky one to explain, and some consider that it does not exist, but if for example it means there are more than 1 distinct approaches to the victory condition, it would not be trivial to gauge progress on any 2 of them compared to each other. In that case, 2 scores that are the same could be said to require a tiebreaker – and some would say it’s the designer’s responsibility to indicate which path is ‘harder’ (deserving of the +epsilon score) and therefore deserving of a tiebreak favor. In that case you cannot say “you need to beat the other player, not merely do as well” because there’s not necessarily a metric to compare the 2 scores against each other (except the score, which has turned out to be not enough information).

In contrast, the games you seem to prefer have the VPs on the same axis, and therefore it’s enough to compare them to each other directly, and one can say “the score indicates the tied players did as well as each other”. In that case, your argument holds water, however…

One could argue that the purpose of the rules (with regard to win condition) is to determine a single clear winner. Otherwise, why play the game? We could all simply not play the game, and rejoice in our shared victory with the tied score of Zero. The rules shouldn’t say “any player who scores at least 30 points wins” because that criteria does not indicate a single winner, and in a multiplayer competitive game the whole point is to find a single winner.

There are some who would argue that the point is not to find a solitary winner, and to those it would be enough to say “any player with at least 30 points at the end of the game has won.” A subset of those people would further say “therefore the point of the game is not only to get 30+ points, but to keep other players from doing likewise.” I think that a potentially interesting game could be built around that unusual win condition, but in general I don’t think that’s the purpose of games, nor the reason most people play games. It’s certainly not the reason I play games.

• Seth

Are you thinking of Arrow’s theorem? But I think it is a misconception that this is what it means. There are many election systems which are fair (for any fair definition of fair), and I think a Condorcet-inspired tiebreaker could work great for tournaments.

If 2 players have 3 strongholds between them and the opportunity for an alliance presents itself, they can share the win immediately by allying. It’s usually in the interest of the player with a single stronghold, but not necessarily in the interest of the stronger player. His choice may be difficult. Do I share the win (possibly an emotionally inferior result), or go for it alone?

Clearly, in this system, all 6 players could ally and end the game in a complete draw. 5 could ally against 1. Etc. I suppose my feelings on these kinds of results would depend on the circumstances during play.