58 votes
Accepted

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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  • 68.2k
40 votes

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 votes

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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  • 1,065
29 votes

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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25 votes
Accepted

Who shall come to the tea party?

All but Mr. Bun will attend the tea party, with Duke Froggington II as the guest of honor. The total number of animals who will be attending the party is $(6*12+2)-1=73$. Looking at some specific ...
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  • 3,066
24 votes
Accepted

Tic-tac-toe 1000 in a row

Yes, X can win. To simplify things I'm going to take advantage of your rules that O cannot win, so that X doesn't need to worry about O getting 1000 in a row. Just consider a 1 dimensional game, ...
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  • 1,048
23 votes

Who shall come to the tea party?

I am not myself a perfect logician, but here the behaviour I observed at my own tea parties, and the explanation my own favourite nounours gave as years passed. Party of one This issue was quickly ...
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  • 487
16 votes
Accepted

Angels & Demons (Open question)

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  • 14.5k
15 votes
Accepted

Reverse dots and boxes

I would suggest an alternate (simpler) strategy:
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  • 940
13 votes
Accepted

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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  • 7,070
13 votes

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
Accepted

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 ...
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  • 5,057
12 votes
Accepted

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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  • 67.4k
11 votes

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 ...
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11 votes
Accepted

A knight chased by three knights

Observation: Implication: Conclusion:
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11 votes
Accepted

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 ...
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  • 68.2k
11 votes
Accepted

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 ...
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  • 123k
10 votes
Accepted

Reverse dots and... cubes? - Snowflake edition

The player who can win is by this strategy:
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  • 136k
10 votes

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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  • 10.1k
10 votes
Accepted

Lap Theory Optimal Betting Game

Their best strategy is Their chances with this strategy are Optimality
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  • 2,816
9 votes
Accepted

Devious auction game

Case I: Let us suppose that each player can bid any integer equal to or above the current minimum bid. Then: Barry O'Neill develops a simple formula for this strategy in a 1986 article in the ...
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  • 465
9 votes
Accepted

Games and Puzzles

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  • 13.4k
9 votes
Accepted

Reverse dots and boxes, swastika edition

First player wins Example:
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  • 18.4k
9 votes

Time to call the bluff

How about
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  • 2,872
8 votes
Accepted

Who Wins At Horsie-Push?

Here's the situation: Working backwards... Keep going... Therefore... So finally...
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  • 4,975
8 votes
Accepted

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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  • 9,301
8 votes

Dollar Auction with Perfect Logicians

I believe Why: Additionally, As such,
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  • 4,597
8 votes
Accepted

Dollar Auction with Perfect Logicians

What happens: Why:
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  • 31.3k

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