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MHill
Topic Author
Posts: 488
Joined: February 26th, 2010, 11:32 pm

### Chaos Tig

The kids were playing Chaos Tig. Everyone starts off as 'it'. If you get tigged, you sit down. If you get tigged at the same time as you are tigging the person tigging you, you do rock-paper-scissors to determine who sits down.If the person who tigged you sits down, you stand up and start playing again.The winner is the last one standing.How do you win?

Traden4Alpha
Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Chaos Tig

In the N=2 case: tig the opponent immediately and be ready to "win" rock-paper-scissors. That results in 0 ≤ P(Win) ≤ 1 depending on one's relative skill at rock-paper-scissors.In the N=3 case..... trickyEach player has three possible states defined by whether that player is "it" or has been tigged by a specific other player: {A_it, A_tigB, A_tigC}, {B_it, B_tigA, B_tigC}, {C_it, C_tigB, C_tigA}. Of the 27 possible states in the power set, many are impossible states (e.g., A_tigB & B_tigA can never occur) or transient states (e.g., if we start with A_tigB and then C tigs B to induce B_tigC, then A will revert to A_it).More later........

Traden4Alpha
Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Chaos Tig

QuoteOriginally posted by: outrunThere is no initial asymmetry like you have with "white starts" in chess. Anyone can thus execute the winning strategy if there was one, which can't thus be.Excellent point. For some types of games, there is no way to guarantee a win if the other players are also playing the best possible strategy.Yet if one is playing against imperfect players, then there's room for better or worse strategies or to define necessary elements of game play that are a prerequisite to winning.For example, in order to win, the last tig one does MUST be of a player that does not currently have someone that they tigged (otherwise one would merely awaken at least one other player). Moreover, we might hypothesize that one should tig whichever player has the least number of currently sleeping tigs (to reduce the number of resurrected opponents). P.S. There is a crucial asymmetry in this game for N>2. The players' choices of targets can break the initial symmetry of the game. Everyone gets to act on turn #1, but that turn determines who is left for turn #2 and how turn #2 affect subsequent turns.
Last edited by Traden4Alpha on June 17th, 2015, 10:00 pm, edited 1 time in total.

Traden4Alpha
Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Chaos Tig

BTW, the rules are not clear on a potential event in N>2 games. What if two or more players tig the same player at the same time? Do the tiggers play some side game to determine which one gets the credit or does the tigged player awaken if ANY of the tiggers get tigged in a subsequent round?

Traden4Alpha
Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Chaos Tig

QuoteOriginally posted by: outrunyou win by doing nothing!Almost!If player A tigs you but no one else tigs player A, you lose to player A.

Traden4Alpha
Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Chaos Tig

There's another interesting flaw in the rules. What if at the first instant of play, A tigs B, B tigs C, and C tigs A? Does the game enter a dead state, do all the players resurrect, or .....?

Traden4Alpha
Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Chaos Tig

QuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaThere's another interesting flaw in the rules. What if at the first instant of play, A tigs B, B tigs C, and C tigs A? Does the game enter a dead state, do all the players resurrect, or .....?those get eaten by the one eyed hamsterI hate when that happens!OK, so cycles are out for N=3 because no one (but the hamster) wins. For N>3, cycles might play an interesting role because they could knock-out M of N players.

Traden4Alpha
Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Chaos Tig

QuoteOriginally posted by: outrunOf all the people sitting down, is there anyone who is not sat down by someone still standing?It can happen if simultaneous tigs can occur. If A tigs B and B tigs C at the same time, then C is sitting down as so is B.
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