Another addicting game (1 Viewer)

[Ray Suarez]

I think I've figured out just about every possible way to beat this guy.

Chris Tsutsui's post got me thinking that the computer must have built in strategies that it won't deviate from but that you can use to beat it on a consistent basis.

Maybe using nim sum/mathematical model would be easier but I couldn't figure out the game doing this...so I wasted an hour of my life coming up with the following strategies. I hope it's not too confusing and that the time spent will be worth it to avoid hearing that guy's annoying laugh:wink:

The key, as stated above, is getting him into a 3-2-1 kill. If, on his turn, he is left with three rows of 3-2-1 you won't lose if you play smartly.

First some general rules

1. Let him go first.

2. As you can see there are four rows of three, four, five and six pearls. In the strategies below I will use 2/6, for example, to denote two pearls removed from the row of six or 1/3 to denote one pearl removed from the row of three and so on.

Now on to the fun.

3. He opens with four basic moves.

#1 1/3 (He takes one pearl from the row of three)
#2 3/4 (He takes three pearls from the row of four)
#3 3/5 (He takes three pearls from the row of five)
#4 5/6 (this strategy was described by Chris Tsutsui)

Strategy #1

He takes 1/3
You take 3/6 (You take three pearls from the row of six)
He takes 4/5 (He takes four pearls from the row of five)
You take 2/4 > 3-2-1 he's dead!

occasionally he will take 1/3 again on his second move (instead of 4/5), if so...
you take 3/6
he takes 3/5
you take 1/4 > 3-2-1

Strategy #2

Him 3/4
You 1/3
Him 1/4
You 1/5
Him 3/6
You 3/5 > 3-2-1

Occasionally he goes 2/3 on his second turn, if so...
you 2/6
him 2/6
you 2/5 > 3-2-1

Strategy #3

Him 3/5
You 3/3
Him 1/5
You 1/6
Him 2/6
You 2/4 > 3-2-1

I haven't noticed any variation by him in this strategy

Stategy #4 (Courtesy of Chris Tsutsui)

Him 5/6
You 3/3
Him 1/4
You 3/5 > 3-2-1

I haven't noticed any variation by him in this strategy




If you play enough you may notice that there are other strategies not covered here...but I haven't ran into any yet. I am not mathematically inclined, maybe this can be explained a lot easier by someone else. If so please let me know.

Ray

 

[BertFalasco]

Hope this also helps.
It felt good to beat that "schmuckdoosh's" colon.
http://world.std.com/~reinhold/math/nim.html
-Bert