6 nimmt theoretical puzzle

[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?

[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.

[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.

[clemens49]

ok, thanks for your reply

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?

[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.

[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