60
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Rock, Paper, Scissors and Trump
Looks like
One strategy would be to
The opponent will naturally soon realise what's happening. But it won't help. Here are the possible results from Alicia's point of view:
So whatever the ...
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40
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Will a greedy algorithm solve Tatham's Flood?
It's definitely not optimal! Here's a counterexample:
Start from the white area.
Greedy algorithm would make you do all the colours on the top right (5 moves: yellow, green, dark green, blue, dark ...
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39
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Will a greedy algorithm solve Tatham's Flood?
That problem is NP-hard, so an efficient strategy to calculate the optimal moves would be a major breakthrough in computer science. Of course, there might be a greedy strategy, but not an efficient ...
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Shortest game of Monopoly
If you are trying to lose the game as quickly as possible then you can do it in 1 turn and 2 rolls of the dice. This is using the UK version as I'm not sure about the US one.
Roll 1:
Roll 2 (Because ...
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16
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15
votes
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13
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Winning strategy in a calendar game
I think that your proposed method is correct. Here's a quick visual representation of the same method (by no means a formal proof):
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Angels & Demons (Open question)
I just came back home and was about to draw a diagram illustrating this, but I can't do any better than @noedne already did.
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13
votes
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2019 gold coins to share
I can ensure that I receive at least
To get this amount of coins, I could apply the following strategy:
My friend can also ensure that I do not get more coins than this in the following way:
So it ...
- 5,127
12
votes
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What is the optimal strategy for the Dictionary Game?
Let's assume every player knows the exact same list of words. Player 1 can ensure a loss for player 3 on the first turn by selecting the second word from the list. This allows player 2 to pick the ...
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12
votes
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12
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The median game
Consider that
Given that, I see play proceeding as follows
N.B. I'm assuming here that strategies which are equally optimal for a given player are equally likely to be executed. This seems to be ...
- 133k
11
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Shortest game of Monopoly
No, the game given in the OP is not the shortest possible Monopoly game (using the American edition). As with the UK edition solution given by William Pennanti, a two-player game can be lost in a ...
- 251
11
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Buzzword Bingo Boss Battle!
So, we are playing misère Tic-tac-toe with the option of taking more than one turn in a row. Seems quite interesting, so let's take a stab at it.
The flow of the narrative here is a bit messy, because ...
- 75.8k
11
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Can you stop copy Alice?
Edit
2012rcampion observed that we also need to multiply by 2 the distances on the plane
Not an answer with a strict proof of the final behavior, but instead a simulation with code that show a ...
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11
votes
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11
votes
11
votes
Which parent should you start playing against?
Mary should play her first game against
To prove this, notice that if $n$ were even,
For the case presented in the puzzle, with $n$ odd:
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10
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Playing blindfolded 2048
Source: I played this game a lot while distracted and this seems to work pretty well.
[Sort of unrelated, but 2048 is one of the first C++ programs I wrote. Code is here: link to code.]
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10
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Lap Theory Optimal Betting Game
Their best strategy is
Their chances with this strategy are
Optimality
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9
votes
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Pirate Puzzle Double Twist
The 4th and 5th pirates...
Also...
Why this might work...
Why does the third even consider going along...
So it all depends on...
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9
votes
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9
votes
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9
votes
9
votes
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How long can you survive at the devil's playground?
You're screwed in constant time, no matter your speed, since the devil has a good strategy.
I cannot claim to having found the devil's optimal strategy, but I do claim that there is an upper bound to ...
- 451
9
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Beyond earth and countries fighting for land
I'm presuming here that each player's primary goal is to win (i.e. claim, or otherwise be rewarded with) as much land as possible, and that a secondary, tie-breaking goal is to minimize the amount of ...
- 2,925
8
votes
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Who Wins At Horsie-Push?
Here's the situation:
Working backwards...
Keep going...
Therefore...
So finally...
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Only top scored, non community-wiki answers of a minimum length are eligible