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Mancala» Forums » Strategy

Subject: Always Win if Go Second rss

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Jason Singleton
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My son came up with a creative way of always winning if he goes second. Basically, he just mirrors every one of my moves (until the last move or two). I'm hoping this is not an always win approach as that would make the game less enjoyable.

Can someone please tell me how one could defeat such a strategy? I have not come up with any combination of moves that stops him from always winning in this manner.

Thanks!
~Jason
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Moshe Callen
Israel
Jerusalem
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ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ/ πλάγχθη, ἐπεὶ Τροίης ἱερὸν πτολίεθρον ἔπερσεν./...
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Which mancala game are you playing? In the one I prefer this would only be a sure way to lose.
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lotus dweller
Australia
Melbourne
Victoria
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Are you playing with this rule,
"If you sow the last pebble onto your side of the board in an empty pit, you capture all of the pebbles on the opponent’s side of the board in the pit opposite of the one you sowed your last pebble into"?

If, "Yes" then proceed.

If you have 6 shared pits and start with 4 stones in each pit then empty your 1st (from your right) pit on your 1st move. This will move stones such that his 6th, 5th and 4th pits will have 5 stones in them.

He copies. Your 6th, 5th and 4th pits now have five stones in them.

Sow your 6th pit. The last stone will land in your 1st pit. Take all the stones from his pit opposite and put them in your home pit.

He cannot mirror this move as his 6th pit is now empty. And none of his other last stones will land in his empty 1st pit.

___________________
Starting position
_
xxxx|xxxx
xxxx|xxxx
xxxx|xxxx
xxxx|xxxx
xxxx|xxxx
xxxx|xxxx
_

___________________
After your 1st move
_
xxxx|xxxx
xxxx|xxxx
xxxx|xxxx
xxxx|xxxxx
xxxx|xxxxx
____|xxxxx
x
___________________
After his 1st move
x
xxxxx|____
xxxxx|xxxx
xxxxx|xxxx
xxxx|xxxxx
xxxx|xxxxx
____|xxxxx
x

___________________
During your 2nd move - your last stone (marked below with an X) is going into an empty pit opposite a pit containing 5 of his stones. You capture them.
x
_____|____
xxxxxx|xxxx
xxxxxx|xxxx
xxxxx|xxxxx
xxxxx|xxxxx
___X|xxxxx
x
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Jason Singleton
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Awesome and extra thanks for the diagrams! You rock!

I was playing with rules I found online which match yours, but have us only putting 3 stones in each hole. Are 4-stones more standard?

~Jason
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lotus dweller
Australia
Melbourne
Victoria
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The "more info" description on the page for this game says, "The commercial sets start the game with 4 pebbles in each pit (but you can also start with 3, 5, or 6 pebbles in each pit as variants)."

I was playing this a lot a few years ago with 6 stones and a board very much like this one with 7 shared pits on each side.

If you want to keep expanding with Mancala there are other games in the family with Oware being globally big.
 
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James W
Canada
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BGG: Helping parents beat their kids for 12 and a half years.

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lotus dweller
Australia
Melbourne
Victoria
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Assistants in the continuing mental development of those children who discover the mirror-move technique.

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Jason Singleton
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Thanks all. :-) I think 3-stone is flawed in a 6-hole board since 3 evenly divides into 6 it leads to problems like what we encountered with the mirror play. I think 4-stone will be much, much better.
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Evil Brother
Netherlands
Enschede
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Could you give an example of how a game would go with this 'mirror play'? I ask because I would think that the symmetry is broken quite quickly making mirror play impossible.
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Jason Singleton
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I've tried lots of different first moves. Start by having just 3 stones in the 6 hole board. No matter what you move, have the 2nd player copy that player. At some point late in the game (e.g. with maybe 2-3 piles remaining), the mirror player abandons the strategy and captures some stones. This leads to a 2-4 stone victory each time.

However, with 4 stones I don't think this will ever be a problem. I believe it comes from a function of the symmetry of 3-6.
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Evil Brother
Netherlands
Enschede
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I believe that your conclusion is somewhat premature. Take a look at the following:
0 - 3 - 3 - 3 - 3 - 3 - 3 - x
x - 3 - 3 - 3 -(3)- 3 - 3 - 0

0 - 3 - 3 - 3 - 3 - 3 - 3 - x
x - 3 - 3 - 3 - 0 - 4 -(4)- 1

0 - 3 - 3 -(3)- 4 - 4 - 4 - x
x - 3 - 3 - 3 - 0 - 4 - 0 - 2

1 -(4)- 4 - 0 - 4 - 4 - 4 - x
x - 3 - 3 - 3 - 0 - 4 - 0 - 2

2 - 0 - 4 - 0 - 4 - 4 - 4 - x
x - 4 - 4 -(4)- 0 - 4 - 0 - 2

2 - 0 - 4 - 0 - 4 - 4 - 4 - x
x - 4 - 4 - 0 - 1 - 5 -(1)- 3

2 - 0 - 4 - 0 - 4 - 4 - 4 - x
x - 4 - 4 - 0 - 1 -(5)- 0 - 4

2 - 0 - 4 - 0 - 5 - 5 - 5 - x
x - 4 - 4 - 0 - 1 - 0 - 1 - 5

You will have broken symmetry by your second turn. Or take a look at this:
0 - 3 - 3 - 3 - 3 - 3 - 3 - x
x - 3 - 3 - 3 -(3)- 3 - 3 - 0

0 - 3 - 3 - 3 - 3 - 3 - 3 - x
x - 3 - 3 - 3 - 0 -(4)- 4 - 1

0 - 3 - 3 -(3)- 3 - 4 - 4 - x
x - 3 - 3 - 3 - 0 - 0 - 5 - 2

1 - 4 -(4)- 0 - 3 - 4 - 4 - x
x - 3 - 3 - 3 - 0 - 0 - 5 - 2

2 - 5 - 0 - 0 - 3 - 4 - 4 - x
x - 4 - 4 - 3 - 0 - 0 -(5)- 2

2 -(5)- 0 - 1 - 4 - 5 - 5 - x
x - 4 - 4 - 3 - 0 - 0 - 0 - 3

3 - 0 - 0 - 1 - 4 - 5 - 5 - x
x - 5 - 5 -(4)- 1 - 0 - 0 - 3

3 - 0 - 0 - 1 - 4 - 5 - 5 - x
x - 5 - 5 - 0 - 2 - 1 -(1)- 4

3 - 0 - 0 - 1 - 4 - 5 - 5 - x
x - 5 -(5)- 0 - 2 - 1 - 0 - 5

3 - 0 - 0 - 1 - 4 - 5 - 5 - x
x - 5 - 0 - 1 - 3 - 2 -(1)- 6

3 - 0 - 0 - 1 - 4 - 5 - 5 - x
x - 5 - 0 - 1 - 3 -(2)- 0 - 7

3 - 0 - 0 - 1 - 4 - 5 - 5 - x
x - 5 - 0 - 1 - 3 - 0 -(1)- 8

3 - 0 - 0 - 1 - 4 - 5 - 5 - x
x - 5 - 0 - 1 -(3)- 0 - 0 - 9

3 - 0 - 0 - 1 - 4 - 5 - 5 - x
x - 5 - 0 - 1 - 0 - 1 -(1)- 10

3 - 0 - 0 - 1 - 4 - 5 - 5 - x
x -(5)- 0 - 1 - 0 - 1 - 0 - 11

3 - 0 - 0 - 1 - 4 - 5 - 0 - x
x - 0 - 1 - 2 - 1 - 2 - 0 - 17

By copying your second turn (by which I mean your third move), the second player will have lost the game. I have a feeling that you missed possibilities like this and that 'even' 3 stones still has strategies you have not yet discovered. Now it may well be that eventually 3 stones per hole is not interesting enough (I don't know, I'm not an expert), but it is my belief that you haven't exhausted it yet. I'm interested to hear what the result was of the above scenario's if you try them.
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