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Subject: Indonesian Finger Game Analysis rss

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Daniel Shultz
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Just after last years SPIEL convention I was introduced to an interesting perfect information finger game called "the indonesian finger game (TIFG)". Which is great because you only need two people with fingers to play. Later I was taught different rules by various Irish people one of which knew it as "finger bang (FB)". We of course argued about which was better... and had the more appropriate name.

goal:
(FB & TIFG) to force your opponent to retract all fingers and thus both hands.

setup:
(FB & TIFG) 2 people extend their index fingers.

mechanic #1 the touch
(FB & TIFG) When you touch a hand then the amount of fingers you have extended on your hand is added to the hand touched. The touching hand's number of extended fingers remains the same.
(TIFG) You may touch any of the 3 possible hands.
(FB) You may only touch your opponents hands.

mechanic #2 retraction
(TIFG) When a hand has been touched and the total fingers that must be extended is 5 or more then that hand closes and goes out of play.
(FB) When a hand has been touched then it takes the modular number (example: if you have 4 fingers extended and your opponent touches that hand with a 3 fingered hand then you end up with 2 fingers extended) A hand goes out of play only when the fingers add up to exactly 5.

mechanic #3 the split
(FB & TIFG) if you have one hand out of play you may choose to split your fingers with your other hand as long as there are 2 or more fingers on the hand in play.
(TIFG) If it's a 3 then you just split into 2 and 1.
(FB) 3s can't be split.

My questions are:
1. Which mixture of rules is best?
2. What makes certain rules better than others?
3. Is there some solid way to analyze this?

I'm really curious how one would examine a game such as this and come to a conclusion about which rule set is best.
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David Bush
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If both players are down to one hand each, do they get to split each hand into two game hands?

In FB, does the modulus value change for a split hand, or is it always 5?

In FB you say "3s can't be split." can 2 fingers be split 1-1? Then what happens if one of those fingers is touched and incremented by 1 to 2? Does the resulting 3 have to merge back into a single hand again?
 
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John Pierce
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Both of the games sound interesting. I don't know how one would go about answering which rule set is best, that seems like an impossible question to me.
 
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Daniel Shultz
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twixter wrote:
If both players are down to one hand each, do they get to split each hand into two game hands?


In both versions if it's my turn in either game I may split only if I have just 1 hand in play and that hand has 2 or more fingers on it. In FB the only split-able numbers are even (2 or 4)[/q]

twixter wrote:
In FB, does the modulus value change for a split hand, or is it always 5?


It's always 5.

twixter wrote:
In FB you say "3s can't be split." can 2 fingers be split 1-1? Then what happens if one of those fingers is touched and incremented by 1 to 2? Does the resulting 3 have to merge back into a single hand again?


2 fingers can be split into 1-1.
If one of those ones increases by '2' for example after being touched then the result is 3-1.

***This would be an easy game to play in a forum. BGG was looking for some way to make the abstract forum better. If there were a sandbox subcategory for abstracts where people could play ASCII games by forum post I think it might do well.

For example if we started a game I would just write:

twixter: 1 - 1
Daniel : 1 - 1

And if I were to go first it would be.

twixter: 2 - 1
Daniel : 1 - 1

I suppose we'd have to agree on the rules first. Shall we try it? FB or IFG? whistle

jfpierce wrote:
I don't know how one would go about answering which rule set is best, that seems like an impossible question to me.


We'd have to define 'best' first. Being able to force a win a move in advance is better than not being able to force at all. So maybe the rules which give possibilities for a single move force are better. Solvability also fits into there somewhere.
 
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Markus Hagenauer jr.
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I´d like to play a IFG.

So i would response:

Markus: 3 - 1
Daniel: 1 - 1
 
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Russ Williams
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Interesting question! The thing that comes to my mind is "Is the game draw-ish?" I can imagine it cycling (but perhaps my intuition is misleading me). So if one version makes it less likely to drag on forever, that version would seem better.
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Markus Hagenauer jr.
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russ wrote:
Interesting question! The thing that comes to my mind is "Is the game draw-ish?" I can imagine it cycling (but perhaps my intuition is misleading me). So if one version makes it less likely to drag on forever, that version would seem better.


I agree, ecpect one thing. If there is a not to difficult, clear win strategy for one player in one version, this can´t be the best version.
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ronaldinho @boardspace.net
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I assume you cannot pass?

Does split count as a turn. Do you split or touch, or can you split and then touch?
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Markus Hagenauer jr.
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drunkenKOALA wrote:
I assume you cannot pass?

Does split count as a turn. Do you split or touch, or can you split and then touch?


Split is a turn. You split or touch, not both in one turn.
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Russ Williams
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It seems every possible game state can be represented in the form:
x a1 a2 b2 b2

where:
x = a or b (indicating who's the current player, a or b)
a1 a2 = # fingers on a's 2 hands (from 0 to 5)
b1 b2 = # fingers on b's 2 hands (from 0 to 5)
For convenience and to reduce the number of game states, if the # fingers for a player are not equal, put the smaller number first (there is no difference between 3 on left and 4 on right, and 4 on left and 3 on right).

e.g. from state a1111 possible next states are b1211 and b1112.

Any state of the form x00mn or xmn00 is a final state with no successor states.

There are roughly only a couple thousand states; one could write a computer program to exhaustively analyze the game state transition graph. I leave this as an exercise for the motivated reader.
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Stephen Tavener
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If we prune out trivial wins, I reckon there are only around 200 states. I'll have a play later.
 
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Daniel Shultz
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IFG
(can touch own hand,
can split on 3,
5 or more retracts hand)
Markus: 4 - 1
Daniel: 1 - 1

@russ - I'm also awaiting the motivated reader
I played the FB rules today and got caught in a cycle. We both knew at some point that if either of us made a different move the other would win so we entered into a repeating cycle until I got bored and chose another option and lost.

Does anyone think there might be a way to shape this game so that cyclical movements can be broken without an inevitable loss?

Since Mark Steere has such a rigorous pass/fail test for his games I'd be a bit more than curious to see if he could come up with an interesting finger game which passes it!
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Markus Hagenauer jr.
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Markus: 4 - 1
Daniel: 5 - 1


Let´s see if we get caught in a cycle too.
Was the cycle in you FB game because of the modula, or could exactly the same circle come up at IFG?


Edit:
As there is no choice (or at least non that makes sense):

Markus: 5 - 1
Daniel: x - 1

Markus: x - 1
Daniel: x - 2

Markus: x - 1
Daniel: 1 - 1

Markus: x - 1
Daniel: 1 - 2


Tell me if you do not agree with the turns i made for you devil
 
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Daniel Shultz
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Markus: x - 1
Daniel: 1 - 3

Markus: x - 1
Daniel: 2 - 3

Markus: x - 1
Daniel: 5 - 3

Markus: x - 1
Daniel: x - 3

Markus: x - 1
Daniel: x - 4

Markus: x - 5
Daniel: x - 4

Markus: zombie
Daniel: x - 4

I took the same liberties. Let me know as well sauron

You're absolutely correct. The cycle from my other game was from the modular aspect.
Maybe without the self hitting rule it gets more interesting?
 
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Elstree
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mrraow wrote:
If we prune out trivial wins, I reckon there are only around 200 states. I'll have a play later.

I count 14 states for any individual player's hands, ignoring hand order and disregarding the lose state (0,0):
(0,1) (0,2) (0,3) (0,4)
(1,1) (1,2) (1,3) (1,4)
(2,2) (2,3) (2,4)
(3,3) (3,4)
(4,4)

When the two players have the same configuration of fingers showing then player turn is irrelevant and these states should only be counted once, that is A A(x,y) B(x,y) is equivalent to B A(x,y) B(x,y). Player turn is relevant only when the players' hands differ. This gives 14 * 13 = 178 possible game states (excluding end states).

Ignoring options to split, in IFG FB there are at most 4 possible moves each turn; in FB IFG there are 6. Splitting gives an additional option from certain states. States where the number of fingers showing on a hand duplicates those showing on another hand can result in fewer possible moves.

Including the lose state, the game could be represented as a 210 * 210 matrix, where a cell value of 1 represents a legal move from the row state that results in the column state, and a zero indicates no move from the row state will result in the column state.

By convention, let the first ordered pair listed indicate the finger state of the player whose turn it is in that state. Then, for example, the initial (row) state in IFG is (1,1) (1,1), and a 1 would appear in the column (1,2) (1,1), indicating that is the only possible state that can be reached on the first move. From (1,2) (1,1) the states (1,2) (1,2) and (1,3) (1,2) can be reached, represented by 1's in those columns of the (1,2) (1,1) row of the matrix. And so on.

Using this notation, the entire game may be represented relatively efficiently. You can also do some nifty matrix algebra tricks with it: by squaring the matrix, you get a matrix showing which column states can be reached from which row states in two moves; raising the matrix to the power n will show you which states can be reached in n moves.

[Edit: Corrected misplaced apostrophe.]
[Edit 2: Had FB/IFG swapped in second paragraph.]
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Markus Hagenauer jr.
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Elstree wrote:

Ignoring options to split, in IFG there are at most 4 possible moves each turn; in FB there are 6. Splitting gives an additional option from certain states.


IFG has 6 possible moves, FB 4

At the state you can split, you only have 3 optioins (or 2 if your opponent has only one active hand too).

So 6 respectivly 4 is the maximum number of options.


@ Daniel:Congratulation!

 
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David Bush
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guitarsolointhewind wrote:

twixter wrote:
In FB you say "3s can't be split." can 2 fingers be split 1-1? Then what happens if one of those fingers is touched and incremented by 1 to 2? Does the resulting 3 have to merge back into a single hand again?

2 fingers can be split into 1-1.
If one of those ones increases by '2' for example after being touched then the result is 3-1.

This does not answer my question. I gave the specific example where one of the 1-1 split is incremented by 1 not 2, resulting in 1-2, which is a split 3, which is the subject of my question. Is such a split three allowed, or must it merge back into one hand again?
 
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Daniel Shultz
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twixter wrote:
guitarsolointhewind wrote:

twixter wrote:
In FB you say "3s can't be split." can 2 fingers be split 1-1? Then what happens if one of those fingers is touched and incremented by 1 to 2? Does the resulting 3 have to merge back into a single hand again?

2 fingers can be split into 1-1.
If one of those ones increases by '2' for example after being touched then the result is 3-1.

This does not answer my question. I gave the specific example where one of the 1-1 split is incremented by 1 not 2, resulting in 1-2, which is a split 3, which is the subject of my question. Is such a split three allowed, or must it merge back into one hand again?


oops! sorry I didn't quite understand the question, but I think maybe I know what you mean now. In FB you may not merge your 1 and 2 together, and in neither version is it an automatic merging.
I hope that answers your question. If not maybe someone else can give it a shot?
 
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Elstree
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Markus Hagenauer wrote:
IFG has 6 possible moves, FB 4

At the state you can split, you only have 3 options (or 2 if your opponent has only one active hand too).

So 6 respectivly 4 is the maximum number of options.
Yes, sorry, got the rules swapped in my head. As you say, max 6 for IFG and 4 for FB.
 
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Andrew Schoonmaker
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twixter wrote:
guitarsolointhewind wrote:

twixter wrote:
In FB you say "3s can't be split." can 2 fingers be split 1-1? Then what happens if one of those fingers is touched and incremented by 1 to 2? Does the resulting 3 have to merge back into a single hand again?

2 fingers can be split into 1-1.
If one of those ones increases by '2' for example after being touched then the result is 3-1.

This does not answer my question. I gave the specific example where one of the 1-1 split is incremented by 1 not 2, resulting in 1-2, which is a split 3, which is the subject of my question. Is such a split three allowed, or must it merge back into one hand again?

I take the meaning of the rules to be: a split is simply a move that one makes on a turn, and it is the way to recover from having only one hand in play to having both in play once more. Once you make such a move, the game state does not "remember" that you split in the past, and under no circumstances would your hands unsplit.

So while it is illegal to make the move from X-3 to 1-2 in FB, nothing weird happens should the state of your hands go from X-2 -> 1-1 -> 1-2.
 
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Stephen Tavener
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I think it's impossible to win FB {
(FB) You may only touch your opponents hands.
(FB) When a hand has been touched then it takes the modular number.
(FB) 3s can't be split.
}
So, let's say a has just won, and work back. Two winning positions (a to move):
2? 03
4? 01
... 3? 02 and 1? 04 are not wins, because b can split.

Now, look at the precursors...

In the 2? 03 case, b was somehow forced to give a a 2. The only cases are:
44 03 and 22 03

in the 4? 01 case, b was somehow forced to give a a 4. The only cases are:
44 01 and 33 01

... so, in order to win, a needs a double. However, b can never be forced to give a double to a.

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Stephen Tavener
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IFG could be changed so that 5 was a legal holding (can be split into 2 and 3), and you retract a hand when you hit 6 or more. This feels more intuitive, since you have overflowed, i.e. can't store those extra digits, and adds a few extra game states.
 
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Daniel Shultz
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mrraow wrote:
IFG could be changed so that 5 was a legal holding (can be split into 2 and 3), and you retract a hand when you hit 6 or more. This feels more intuitive, since you have overflowed, i.e. can't store those extra digits, and adds a few extra game states.


That sounds like it could have potential. I'll have to give that one a try.

The use of Finger binary might also make it interesting

For example in finger binary one could split only on 2,4,8,16 since those numbers are represented by a single extended finger and split very nicely into different extended fingers.

Also if we were to find nice rules I rather like the name FiBi (FeeBee from fi.nger bi.nary)
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Daniel Shultz
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There are not many multiplayer abstracts that I like. That being said, I really like Triad which I attribute partly to being able to select who goes next with a type of move.

I was thinking that maybe for a 3 person version...
1. you can't touch your own hand
2. the person who was not touched goes next (or visa versa)
 
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Markus Hagenauer jr.
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guitarsolointhewind wrote:

2. the person who was not touched goes next


So two players can eliminate one opponent before he gets even one turn.
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