22

Accurding to Zermelo's theorem, in finite two-player games of perfect information in which the players move alternately and no affect of chance, one of those three possibilities is true: First player can always win. Second player can always win. Both players can force a draw. For example, Tic-Tac-Toe is known to have a strategy by both players that will ...


19

One of the clearest examples of game theory in Dominion shows up quite frequently in 2 player endgames, and it's called the Penultimate Province Rule (PPR). Basically, you should avoid buying the second to last Province if buying the remaining Province would allow your opponent to win. Imagine a game where my opponent and I each have 3 Provinces, with 2 ...


15

Tl;dr: Players' meta-goals do affect gameplay. And unless all players have the same goals, the entire concept of "best player" isn't well defined, let alone "second best", etc. First a bit of game-theory framework. Let's say each player has a "utility function" which takes as input the game end-state and gives as output how much "utility" they get - an ...


10

Because if you're only ever going to call "cheat" when I play my last card, I'll cheat like crazy on every turn other than my last card and do everything in my power to make sure that I'm not cheating on my last card.


9

No - there need not always be a tie in the general case. Even in games of perfect complete information there may still be a bias towards one player. For example the game of nim cannot end in a tie, and depending on the starting position gives an advantage to either the first or second player - e.g. Size of heaps | Result with A | B | perfect play --...


9

You're correct in that it's usually better to let other people call cheaters out, since there's a personal risk but no personal reward. However, imagine the case where it's about to be my turn, there's a large stack on the table, and I have no option but to cheat. Here, it might be best for me to call "cheat" on the person who just played in order to clear ...


7

You can call "cheat" even when you aren't 100% positive someone is lying to keep the fear of being called out real. Like @PhilipKendall said, if you are only going to call "cheat" when you can prove it or when you are at the last opportunity to keep someone from winning, there is never any fear of being called as long as you make relatively conservative ...


6

Some cards are very dependent on the actions your opponents, and some are not. e.g. buy Tribute if you see your opponent to the left buy lots of different cards, don't buy it if they are not. However, in most cases, if your strategy can be influenced by opponents actions, then it is best to proactively consider those potential influences even before they ...


3

I don't know if you'd consider these "rules issues" or not; they're certainly not as bad as an instant on the field, but the rules as currently worded don't allow for subtypes to be associated with supertypes. If you make Tribal a supertype and start messing around with an object's types,things don't work out the same way; see the following examples. Maybe ...


2

From a game theory perspective, you'd have to analyze this in more concrete scenarios. Yes, if someone says "one ace" on the first turn where everyone else has the same card holding and nobody happens to have three or four aces, it's a pretty silly risk to call them on it - which is why nobody does call them on it in that scenario. (Although, if you have ...


2

The answer to this question will be very heavily dependent on your group, and their groupthink. In my experience, often bidding 3 on the blade would not result in getting it (I would probably be 2nd or 3rd, with someoen else going all in on the sword), while a bid of 2 on the Raven would probably be enough to get me at least one star (with someone else ...


1

You are missing a couple of important factors in your question that make it impossible to answer as it stands. Mainly that a game with perfect information available to both players doesn't mean that it is not balanced in one players favor. While it may be true that there are games out there where it is balanced between both players it is also true that ...


1

In a game where there is a scoring function, one can always rank players beyond the winner into 2nd, 3rd, etc. The real question is whether positions beyond first have any value. That question depends on many things, including player psychology, game design, and external incentives. Here are some examples of ways that this varies between games: Example 1:...


1

This isn't a good idea for several reasons. I'll focus on the main one: Burn decks don't want to play a grindy game where card advantage is paramount. Burn decks want to end the game as soon as possible with some haste creatures followed by burn spells. Playing a long game where drawing multiple cards actually becomes significant is not the plan. Sure it ...


1

This is actually a variation on the Game Theory problem The Volunteer's Dilemma. Essentially, there is a cost to you calling cheat (The chance of being wrong and taking cards), and a benefit to all for you doing it (Stopping an opponent). There are a lot of different possible equilibria, but if every player acts the same, then the only equilibrium (state ...


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