I have 5 people, needing a way to decide who goes first, who goes last. All want to go first.

Decided to have them cut cards. High card (ace of hearts is high, 2 of spades is low) goes first, then in order of the cards. Took a standard deck of cards, jokers removed, shuffled multiple times, and each person picks up a random amount of cards (cutting) from that deck. Went in alphabetical order for who cuts when.

1st person makes a deep cut, taking about 1/2 the deck leaving the other 4 to take smaller stacks to leave some for the final person.

The 4 people after the person taking the first cut cry foul and say that he has better odds of getting the high card because he took the most cards. I disagreed and said he could have left 4 cards and the odds would still be the same due to the randomness after shuffling. I don’t know if I was right or wrong, but I am the boss so that was the way it was done.

So was I right? Or wrong? Does the amount of cards left in a shuffled deck of cards after a cut(s) change the odds of getting a high card?

If he gets to look through all the cards he took and keep the highest one, they’re right.

But if all that matters is which single card he cut to, then you’re right that it shouldn’t matter. But it would probably look fairer if you had each person just pick a single card, rather than have them cut the deck and keep a whole stack.

Could you please clarify the exact procedure? The first person cuts the deck, then what? Which card counts for him? The top card of the remaining stack?

You’re correct. It’s just a way of picking a random card. It changes the level of participation in the creation of randomness for the others, but since it, as you say, is really the shuffling that makes it all random that’s not relevant.

Did they know what card he has ? If so, they may have wanted to try to redo his draw . Or maybe they thought there was a possibility they would have to look through the cards they have and find the highest card in there. well they do follow the leader and repeat what the first person said… sheep… group think.

The person picks (grabs) his stack/cut of cards, the bottom card of his stack is his card. You don’t look through your cards, bottom card is your card. You show the card as you pick your stack/cut so everybody knows your card as soon as you cut the deck.

It sounds to me like each person gets a random card.

However, if the first person has, let’s say, the highest possible card [aren’t spades higher than hearts?!?], then everyone else can tell that their chances of going first are now zero, no matter what card they draw.

You are correct. Odds are same for all. If what they is true then if you took a randomly shuffled deck and dealt 5 cards off the bottom of it, they are saying the 5th card dealt has the best odds of being the highest. There’s absolutely no reason it would be.

I could see people feeling they didn’t have much of, or any, choice if the first person cuts very deeply, especially if they cut down to all but the last 4 cards.

And it’s true that in the latter situation, the 2nd through 5th players will have no choice as to how deep they can cut. But that doesn’t change the fact that all five players will each choose a totally random card.

It depends. When the first person draws or cuts a particular card, it changes the odds for the rest. OTOH, that’s only bad if someone before you pick a high card. If someone draws an ace, odds you’ll draw an ace are reduced. If someone picks a 2, odds you’ll pick an ace have gone up. Admittedly, not much. Simplest is to not show your card chosen until everyone has picked, to prevent people being discouraged. (Schrodinger’s draw, I guess…)

Sure, but the change in odds for the rest depends only on what card the first person drew, it doesn’t make any difference where in the pack that card was drawn from.

Correct me if I’m wrong on this but let me take this to the extreme.

If the people complaining about the deep cut actually have a valid point then being left the very bottom card (which is the most extreme of deep cuts) should show a statistically lower value than that second from last card exposed by the first person performing that deep cut.

Seems like that would be easy to test in real life and I can’t see any reason why it would end up being true.

I was not talking about the math of a fair and randomly shuffled deck. I was saying that if the cutter is doing something annoying that is pointless in a fair deck, that could be a red flag that they are cheating somehow. That an Ace is slightly bent, for example, allowing you to cut to it.

If 4 people are all supposed to be cutting to choose a card, and you pointlessly take away most of the pack on the first cut so there’s not much left for three people to cut from, it seems to me that you’re being a jerk.

Of course they’re being a jerk. If I cut down to the 4th from last card, the other 3 people have to take the top card. I have effectively chosen their cards for them, without their consent. It’s still fair, but I’m being a jerk by restricting the other people’s choices.

And if I choose any card other than the top card, I’m still restricting other players’ choices more than I need to. So the solution is to instead force the first player to take the top card?