The probabilistic portion of the question has been answered and there’s no debate over that.
It’s the psychological part that’s being addressed now. If your answer is “if it is permissible, it is not rude”, that’s a valid opinion but one not shared by a majority of posters and likely a majority of humanity.
There are plenty of things one could do that are not against rules or laws that, nonetheless, would result in being treated like a jerk.
The solution is to give each player the illusion of choice.
The entire concept of this game is illusion of choice. It is utterly fair to just deal the players their cards off the top of the deck, but the decision is made collectively to play “cut for your card” instead. As the group opted to let each player “choose”, that should be what the players do when the time comes to play, and each player should also allow for the other players to “choose” their card.
While I agree there seems to be no difference from a randomness viewpoint, there also seems to be a phycological difference in this mode of gameplay. One player’s ability to restrict the options and convenience of the others does give an edge in motivation to that player. If this was a one off, like how we may use rock paper scissors of who takes out the trash, that’s one thing but if this goes into a game playing session I would suggest having each cut be a complete cut, restoring the deck to full minus their one card for the next cut.
OP here. Thanks for your responses. It was supposed to be a simple solution to a simple problem. I am glad to see that I was technically right that everything was fair. As mentioned by others I thought that the 1st guy was a jerk by cutting so deep.
Next time (if there is a next time) I will have the 1st person cut the deck however deep or shallow they want, look/show their bottom card, and place their pile back on the deck. Repeat for 2nd, 3rd, etc. If a tie (2 people cutting at the same exact spot) they will do a separate cut for a tie breaker.
Sometimes, like this instance, I don’t think it is worth the extra pay I receive to supervise/manage people.
If the players cannot agree that the procedure is fair, why not do something else? For example, flip coins (everybody flips a fair coin; heads go before tails; for every group of cardinality two flip the coin once)
e.g. say (A, B, C, D, E) ↦ (T, H, T, H, H)
to resolve between A and C, flip ↦ H, so A goes before C
But any choice the first player makes restricts the choices made by the other players. There is no cutting that gives everyone the same illusion of choice. There’s no point in saying that players should do something that’s impossible, nor in complaining about jerkishness when they fail to do the impossible.
Assuming all the participants here trust the OP / manager, probably the most efficient and still fair approach is to:
Manager thoroughly shuffles the deck.
Worker A cuts the deck in two, putting the sub-pile that was on the top onto the bottom.
Manager deals one card from the top of the resulting deck face down to each worker, going in order around the circle.
All workers turn over their card simultaneously and the winner is immediately seen by all and designated as such by the manager.
Why yes, this does represent exactly how ordinary card games are dealt. After how many gazillion trials have we arrived at this system as both statistically fair and psychologically seen-as-fair?
I see no reason to reinvent this particular wheel. And many ways, ref the OP, for the re-invention to give a bumpier ride than the tried-and-true standard solution.
Why not reshuffle the entire deck, minus the cards already selected, after each cut? There’s no reason to keep everything above each cut out of play for the next person.
Agreed, it doesn’t change the odds for each subsequent person, but it sounds like it would make them feel better. Give the nth person a 53-n card deck to draw from.
While the methodology of drawing cards is statistically sound, the judging is flawed. Everybody should know that the Ace of Spades is the highest card in the deck, and the Deuce of Clubs is the lowest.
Depending on ranking system your using, but here in the US we seem to use bridge suit order, so I guess that works. I play a lot of Central European games, with a different value of suits.
At any rate, why aren’t we just fanning out the cards (whether in hand or on a table) and just have people choose single cards that way?
Correct. I play a game called ‘Thirteen’ which originated in Vietnam. Suit rankings are hearts, followed by diamonds, clubs, spades, which could be the ranking used by the OP.
Yeah, doesn’t matter as long as everyone agrees – but not everyone seems to remember or know suit rankings in bridge, and in most games, there are none, so a tie is just a tie. (I play skat a lot, where it’s DHSC low to high, and a Polish game called Tysiąc where it’s SCDH low to high.)