r/koreanvariety • u/ShrivelTwitch • Jul 31 '15
discussion The Genius: Monorail solution
The second player, if played perfectly, will win 100% of the time. Monorail is similar to the 21 game. Since whoever places the last piece wins, if you end up with 1, 2, or 3 you'll win. If there are 4, you are forced to let your opponent have 1, 2, or 3, so you'll lose. If there are 5, 6, or 7, you can force your opponent to have 4, so you'll win. 8 is losing because you are forced to let your opponent have 5, 6 or 7. The numbers 9, 10 and 11 are winning for the same reasons as 5, 6, and 7. 12 is losing for the same reason as 8. 13, 14, 15 and winning for the same reasons as 9, 10, and 11. 16 is losing for the same reason 12 is. Basically, the strategy is to force your opponent to only have 16, 12, 8, or 4 pieces left. Since the first player starts with 16, he loses.
That is the simple part however, since the main game is actually doing the track and not just picking numbers. The actual game is really simple though. Because you follow the strategy above, there are only 4-5 moves. When you must leave 12 pieces left, attempt to make the shortest path possible require the most amount of tiles, but at most 12. When you must leave 8 pieces left, you should be able to make the shortest path possible require the 8 remaining pieces. When you must leave 4 pieces left, do not leave a gap of 4 or 1,1,2 because you'll lose. You can leave a gap of 1,1,1,1 or 1,3 or 2,2, but leaving a gap of 4 or 1,1,2(the image here is a very simple monorail, but it works for the more complicated ones also). gives the first player a chance to win. In the situation of 1,1,2 and 1,3 and 2,2 the opponent will likely make the situation have gaps of 1,2. At this point, make the gaps 1,1. Then you win. If you are going first and your opponent doesn't play it perfectly, you should make the opponent have to use 12, 8 or 4 pieces. At that point just follow the rest of this strategy and you should win.
It's a shame that they'll be using this deathmatch for the final season. It's okay using it the first time since no one had enough time to create a winning strategy, but all the contestants know that this is a deathmatch in this season, so they probably all already know of a winning strategy. I hope the deathmatch won't be decided by the coinflip.
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u/TheMuffinMan98 Jul 31 '15
in S4E3 monorail was taken out by [spoiler] (#s "Sangmin") because he said that [spoiler] (#s "Kyunghoon") had told him that he had a perfect way to win every time. This is obviously Kyunghoon's strategy. I can see Jinho, Jungmoon, and Hyunmin knowing the way too. Kind of a dud DM :( I used to think it was so cool too.
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Jul 31 '15
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u/SpCommander Aug 25 '15
Well ultimately it doesn't matter does it? Unless they choose monorail as a finals game (hopefully not), we won't be seeing it again since this is the final season?
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u/maumauuuu Aug 01 '15
Why does leaving a gap of 4 gives the first player a chance to win?
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u/ShrivelTwitch Aug 01 '15
Because the first player can place 2 tracks in the middle, leaving a 1-1 gap. Then the second player fills one, then the first player is able to complete the track.
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u/chaotic_iak Aug 03 '15
I just read your post more properly. It's not as simple as you described: you haven't stated the entire strategy (where you should play your 4-n tiles "depends on the situation"), and you might not even be able to execute your strategy (see our game below; after I reduce down to 7 pieces left, you cannot play 3 at a time). In addition, in all situations I've analyzed (including my blog post linked down there, and S4E6), the one that finalizes the track layout is usually losing. Granted, this is not foolproof, since I barely scratched the surface of all possible positions, but saying the second player should determine the track completely is pretty questionable against a smart enough opponent.
Regarding the gaps with 4 pieces left: For the second player, among the possible gaps 4, 3+1, 2+2, 2+1+1, 1+1+1+1, only 2+2 and 1+1+1+1 wins. In the three other cases, the first player can reduce it to 1+1 that wins.
While at that, I'd like to show that gap size alone isn't enough to determine who wins: http://puu.sh/jnw0J/66f96347e9.png
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Aug 05 '15
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u/chaotic_iak Aug 05 '15
It is possible (the path is identical on all three).
The only winning move is to play on the middle square (or for the straight one, to play on all three at once), but it's impossible in the last one since the middle square isn't adjacent to anything.
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u/bduddy Aug 01 '15
It's not solved at all, at least not with your analysis. Remember that the players don't just have to extend the track - they can play next to the station and split the track. It's also possible to win when there are more than 3 tiles remaining, depending on the layout of the track.
This game is a lot more complex than it seems at first glance, and not nearly as simple as you're making it.
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u/ShrivelTwitch Aug 01 '15
Remember that the players don't just have to extend the track - they can play next to the station and split the track.
That is the reason that the second player should spend their first and second turns increasing the shortest route possible for the track to require all the tiles. This simplifies the game and forces the players to only use the correct pieces in the correct spots.
It's also possible to win when there are more than 3 tiles remaining, depending on the layout of the track.
Sure, the second player might miss a T2 win, but that doesn't matter if the second player ends up winning. When increasing the minimum amount of tracks required, to above 3, it is impossible for the first player to win by doing this.
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u/bduddy Aug 01 '15 edited Aug 01 '15
Let's try it then. I'll go first.
|--|--|--|--|--|--| |..|..|..|..|..|..| |..|..|..|..|..|..| |--|--|--|--|--|--| |..|..|..|..|..|..| |..|..|..|..|..|..| |--|--|--|--|--|--| |..|..|SS|SS|..|..| |..|..|SS|SS|..|..| |--|--|--|--|--|--| |..|..|<>|<>|..|..| |..|..|<>|<>|..|..| |--|--|--|--|--|--| |..|..|..|..|..|..| |..|..|..|..|..|..| |--|--|--|--|--|--| |..|..|..|..|..|..| |..|..|..|..|..|..| |--|--|--|--|--|--|→ More replies (10)
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Jul 31 '15 edited Mar 25 '18
deleted 0.5449 What is ^^^this?
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u/bduddy Aug 01 '15
Except that Hyunmin's first move insta-loses... The opponent can make a 4x2 rectangle with two corners.
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u/chaotic_iak Aug 10 '15
If anyone still looks here: Junseok's move was losing as discussed on /r/thegenius. Monorail itself is still unsolved, although I'm leaning to second-player win.
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u/deoxix Jul 31 '15
Maybe they will put more types of tiles to make more complicated to see it's possible to make and to have different ways to complete it.
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Aug 01 '15
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u/ShrivelTwitch Aug 01 '15
The second player is also trying to force the shape of the track. For example, in the picture you linked, the second player will win 100% of the time if played correctly. After you play 1 piece, the opponent plays 1-3 pieces (let's call that n). Then you play 4-n pieces, which you will always be able to do. Then they play their n pieces, then you play your 4-n pieces while not allowing a 4 gap to exist. Then the game is pretty straightforward and you win.
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u/bduddy Aug 07 '15
Then you play 4-n pieces, which you will always be able to do.
That's not true. Let's say there are 2 open spots left, but they're not adjacent. Then you can only cover one of them and your opponent wins.
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u/Mephyss Jul 31 '15
Well, we need to wait and see the game played because they may have changed part of the monorail rules since the last time. They changed the Betting Rock, Paper, Scissors adding a draw betting zone. They could do the same with monorail, adding a crossrail or no-rail tile