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Topic: Wild wild west (Read 3872 times) |
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Moti
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Wild wild west
« on: Nov 25th, 2002, 7:36am » |
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Three cowboys are fighting for their lives, however, they don't all have equal shooting skills.
The grey cowboy has never missed a shot and has a 100%
chance of hitting the target.
The black cowboy hits every 2/3 and the red cowboy
(that's you) only get 1/3.
since the skills are not equal the judge decides to let you go first, then the black and finally the grey.
who would you shoot? (and why) 
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towr
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Re: Wild wild west
« Reply #1 on: Nov 25th, 2002, 7:52am » |
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the judge..
(there's a similar riddle about cyborgs around here somewhere)
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Speaker
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Re: Wild wild west
« Reply #3 on: Nov 28th, 2002, 12:20am » |
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You need to shoot at grey first. He's the most dangerous so should be eliminated as soon as possible. (This also provides the most beneficial reduction in the likelyhood of being hit when you are shot at).
Next, black will either shoot at you are grey. If you managed to hit grey, then black will shoot at you. Allowing you a 1 in 3 chance of surviving, better than a none in none chance against grey.
But, if you didn't manage to hit grey, then black should use the same logic and shoot for the most dangerous adversary. (Also, by not shooting at black, black may assume some sort of alliance exists between you and him, which he may be foolish enough to honor).
If both black and you miss grey, then grey is going to eliminate one of you from the game. In this case he should go for black the most dangerous adversary.
This leaves you with a final chance to hit grey.
Which, should you miss, leaves nothing save dukincover.
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towr
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Re: Wild wild west
« Reply #4 on: Nov 28th, 2002, 4:05am » |
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Assuming that when there are only two players left they will shoot at each other, and that when there are three they can shoot the judge (a deliberate miss) if they deem it necessary,
there are 27 possibilities to play (one of which won't ever end).
Here's the complete list with chances (generated with model):
0) [000] red:0.00 black:0.00 grey:0.00
1) [001] red:0.00 black:66.67 grey:33.33
2) [002] red:33.33 black:0.00 grey:66.67
3) [010] red:0.00 black:0.00 grey:100.00
4) [011] red:0.00 black:22.22 grey:77.78
5) [012] red:11.11 black:0.00 grey:88.89
6) [020] red:42.86 black:57.14 grey:0.00
7) [021] red:28.57 black:60.32 grey:11.11
8) [022] red:39.68 black:38.10 grey:22.22
9) [100] red:0.00 black:0.00 grey:100.00
10) [101] red:0.00 black:44.44 grey:55.56
11) [102] red:22.22 black:0.00 grey:77.78
12) [110] red:0.00 black:0.00 grey:100.00
13) [111] red:0.00 black:14.81 grey:85.19
14) [112] red:7.41 black:0.00 grey:92.59
15) [120] red:24.49 black:32.65 grey:42.86
16) [121] red:19.05 black:40.21 grey:40.74
17) [122] red:26.46 black:25.40 grey:48.15
18) [200] red:14.29 black:85.71 grey:0.00
19) [201] red:4.76 black:73.02 grey:22.22
20) [202] red:26.98 black:28.57 grey:44.44
21) [210] red:6.12 black:36.73 grey:57.14
22) [211] red:4.76 black:43.39 grey:51.85
23) [212] red:12.17 black:28.57 grey:59.26
24) [220] red:30.61 black:69.39 grey:0.00
25) [221] red:23.81 black:68.78 grey:7.41
26) [222] red:31.22 black:53.97 grey:14.81
[012] means red will miss (0) in this problem that could be shooting the judge (considering it's a "_who_ will you shoot first?" question), black will shoot his worst opponent (1) in this case that's red, grey will shoot his best opponent (2) in this case that's black.
You can reduce the list by first letting grey optimize his choice, giving:
2) [002] red:33.33 black:0.00 grey:66.67
3) [010] red:0.00 black:0.00 grey:100.00
8) [022] red:39.68 black:38.10 grey:22.22
9) [100] red:0.00 black:0.00 grey:100.00
12) [110] red:0.00 black:0.00 grey:100.00
17) [122] red:26.46 black:25.40 grey:48.15
20) [202] red:26.98 black:28.57 grey:44.44
23) [212] red:12.17 black:28.57 grey:59.26
26) [222] red:31.22 black:53.97 grey:14.81
then black optimizes his choices:
8) [022] red:39.68 black:38.10 grey:22.22
17) [122] red:26.46 black:25.40 grey:48.15
26) [222] red:31.22 black:53.97 grey:14.81
from which red chooses his best choice:
8) [022] red:39.68 black:38.10 grey:22.22
having the best chance to survive out of the three
If you can't make a deliberate miss then the best red can do is:
26) [222] red:31.22 black:53.97 grey:14.81
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| « Last Edit: Nov 28th, 2002, 4:06am by towr » |
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