6 nimmt theoretical puzzle

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clemens49
Posts: 18
Joined: 20 August 2023, 11:26

6 nimmt theoretical puzzle

Post by clemens49 »

I wondered about this a longer time ago and it caught my attention again some days ago. I had promising approaches, but won't show them here yet.

can you safely get 0 penalty points (oxes) in a round with the following conditions?
  • 5 players
  • tactics + professional
  • you can freely choose the 4 cards on the starting board and in your hand
  • the cards in the opponents hands and their play is to your maximum disadvantage


so, for tactics only, getting guaranteed 0 points with a manipulated deck is rather easy/simple/straighforward
- 54 53 52 51 on the board, you have 41-50, play from highest to lowest
but also:
- 54 53 52 51 board, anything from 38-50 in your hand
- anything from 50-54 / 49-54 / 48-54 on the board, anything from 38-49 / 38-48 / 38-47 in your hand
however it doesnt seem to work when you have a card 50 or higher or if not all your cards are lower than the starting board.

the question now is, is there also at least one board + hand card distribution with guaranteed 0 points for tactics + professional?
if yes, what is it and how to play it?
if no, what's the lowest possible guaranteed score and the accompanying distribution?

what would be different with less than 5 players?
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Wreckage
Posts: 300
Joined: 18 January 2017, 02:10

Re: 6 nimmt theoretical puzzle

Post by Wreckage »

My first thought is to start with lowest cards, but I see there are issues..

I think this works:
On the table 50, 52, 53, 54
My hand 41, 42, 43, 44, 45, 46, 47, 48, 49, 51
Play 51 first, then from biggest to smallest..

Oh, I see this doesn't work...hmmm, it's tricky...I'll think about it later and get back to you.
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Wreckage
Posts: 300
Joined: 18 January 2017, 02:10

Re: 6 nimmt theoretical puzzle

Post by Wreckage »

So the riddle is: Is there a hand in 5p pro that is absolutely safe no matter what opponents play?

It seems like there should be a solution. But I messed around with this for about 20 minutes without solving it. Pro is so dynamic, it's tough to figure out. It's an interesting puzzle.
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clemens49
Posts: 18
Joined: 20 August 2023, 11:26

Re: 6 nimmt theoretical puzzle

Post by clemens49 »

ok, thanks for your reply :D

yes, the main task is to find a hand + starting board for 5 players tactic professional that safely gets 0 points independent of opponents play.

the next or implied question - if 0 is impossible or as long as it's unsolved - is about the lowest score. so what would be yours so far?
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Wreckage
Posts: 300
Joined: 18 January 2017, 02:10

Re: 6 nimmt theoretical puzzle

Post by Wreckage »

I spent some more time on this, and thought I was close to a solution a couple times, but it is indeed impossible. I haven't spent any time trying to solve the absolute minimum points I could be forced to take, but I imagine it would be at least two rows of cards.

You must have figured out a good answer to this? It seems like it would be complex to determine.
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katjes22
Posts: 7
Joined: 18 January 2024, 05:26

Re: 6 nimmt theoretical puzzle

Post by katjes22 »

how about this:

board 1 2 3 4

hand 5 6 7 8 9 10 11 12 13 14

ok i see, it certainy does nor work for 0 points, but maybe for one trick maximum
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yovine
Posts: 3
Joined: 31 May 2024, 10:36

Re: 6 nimmt theoretical puzzle

Post by yovine »

starting board
1 5 9 13

hand
2 3 4 6 7 8 10 11 12 14

1. move - play 11 left from 13, row gets taken
2. move - play 7, put it next to 5 or 9 depending on which gets taken or which is better for your next move
3. move - play 6 or 8, put it next to 5/7 or 7/9 ... (see above)
4. move - play 3, put it next to 1 or 5 ... (see above)
5. move - play 2 or 4, put it next to 1/3 or 3/5 ... (see above)

here it's 5 safe moves already with more to follow. the only threat should be taking the highest row with a low number from left. this aside, it should get 0 points often, and 1 trick at most.
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