[JM]

lol, answered my question as I was posting it! Thanks!

[daveyboy]

Here is a simple, easy, and quick way we choose seats and figure who gets the dealer button. If we have 8 players, we take out the Ace to 8 from the deck and spread them on the table. Each player picks a card (doesn't matter who picks first) from the pile. The person who holds the Ace will choose his seat. The 2 will sit to the left of the Ace and the 3 will sit to the left of the 2 and so on...in a clockwise fashion till all is seated. The person holding the Ace will also have the dealer button.

Simple and quick.

[JM]

Originally Posted by R Deckard

Your probability analysis is faulty. No one has any better chance of getting any seat. It's like saying that being the small blind (i.e. getting dealt the first card), you have a better chance of being dealt an A than the rest of the players. Being first doesn't mean anything.

Just for some hypothetical fun, wouldn't the first guy getting dealt a card have the best chance at getting a particular card, say the ace of spades? He's got the 1 in 52 chance of it, which initially is the worst odds assuming the card he gets is not returned to the deck and is not the ace of spades. But if he does get it, then any subsequent recipients have a 0.000000000000000% chance of getting it. So I'm saying he has the best initial chance at the unique card, but if he doesn't get it then each subsequent person has better odds than the preceeding person did until it gets picked. (I know over a billion or so iterations it all evens out anyway)

[JM]

Originally Posted by daveyboy

Here is a simple, easy, and quick way we choose seats and figure who gets the dealer button. If we have 8 players, we take out the Ace to 8 from the deck and spread them on the table. Each player picks a card (doesn't matter who picks first) from the pile. The person who holds the Ace will choose his seat. The 2 will sit to the left of the Ace and the 3 will sit to the left of the 2 and so on...in a clockwise fashion till all is seated. The person holding the Ace will also have the dealer button.

Simple and quick.

Thanks, I kinda like that way, except it definitely gives seat #1 the advantage of having the button on the first hand. I think I'll probably do it this way and then do the high card for the button as deckard suggested.

[SpaceMonkey]

Originally Posted by daveyboy

Simple and quick.

And also basically what scott does and I described.

I'm a big stickler for having a separate draw for the button though. For those of you who do both seats and button at the same time, why do you do this? To save time? Not worth the hassle of a second draw? Just curious.

[JM]

Originally Posted by SpaceMonkey

And also basically what scott does and I described.

There was a subtle difference. The ace chose where he wanted to sit and that seat becomes #1 and they then go clockwise from there.

[R Deckard]

Here is the math that shows why being first to pick a number out of a hat doesn't matter:

For simplicity's sake, let's say there are five cards, A through 5, in a hat. You are trying to draw the Ace.

1st Draw

• Probability of drawing the Ace: 0.2
  Probability of missing: 0.8

2nd Draw

• Probability of drawing the Ace: 0.25 x (the probability the 1st draw missed) = 0.25 x 0.8 = 0.2
  Probability of missing: (the probability of the 1st draw hitting) + (the probability of the 1st draw missing x the probability of the 2nd draw missing) = 0.2 + (0.8 x 0.75) = 0.8

I could continue this, but I'm sure you get the point--I'll leave it as an exercise for the industrious lurkers out there.

Of course if you get the Ace on the first draw, you then have zero probability of getting it on any subsequent draws. But probability analysis is based on a starting set of conditions based upon incomplete information. Once you start adding information or changing it, you change the initial conditions, and your original question becomes moot.

If you really think the first person who is dealt a card is more likely to get any particular card than anyone else, then you will have a hard time learning the other probabilistic factors of poker.

[JM]

Originally Posted by R Deckard

If you really think the first person who is dealt a card is more likely to get any particular card than anyone else, then you will have a hard time learning the other probabilistic factors of poker.

No, not more likely, but the best chance at getting it at that point in time since there's 100% chance that it is available to him and he gets the first draw/deal. Everyone elses chances are yet to be determined. Of course, after that everything changes depending upon whether he got it or not. But I never thought anyone would be more likely to get a particular card than anyone else.

[daveyboy]

Originally Posted by SpaceMonkey

And also basically what scott does and I described.

I'm a big stickler for having a separate draw for the button though. For those of you who do both seats and button at the same time, why do you do this? To save time? Not worth the hassle of a second draw? Just curious.

It was a random draw that the person got the Ace, so why not make that person get the button too, do we really neeed to go through the same process again?? It's all about playing some Texas Hold-em. To change it up, you can designate before hand another card that will get the button. Remember, "Simple and quick".

[R Deckard]

Originally Posted by JM

No, not more likely, but the best chance at getting it at that point in time since there's 100% chance that it is available to him and he gets the first draw/deal. Everyone elses chances are yet to be determined. Of course, after that everything changes depending upon whether he got it or not. But I never thought anyone would be more likely to get a particular card than anyone else.

Your definition of "best chance" has changed the original question, then, and you've actually added additional ones as well:

The question originally was: "If five people draw out of the hat, who has the best chance of drawing the Ace?" Answer: "Nobody, they all have a 1 in 5 chance of getting it."

Your new Question #1 is: "Who has the best chance of getting the Ace on the first draw?" Answer: "The person who makes the first draw (of course)."

Question #2: If the first person to draw doesn't get the Ace, what are the chances of the others getting it? Answer: "Each of the others have a 1 in 4 chance of getting it."

It is a rather subtle point I'm making, and so is yours. But we are talking about two completely different problems.

Here's a mindblowing little puzzle that helps to illustrate the subtlety of probability thinking:

You're playing "Let's Make a Deal" with Monty Hall. You have a choice of picking Door Number 1, 2, or 3. Behind one of the doors is a fabulous prize, behind the other two doors are gag gifts. The game will proceed as follows:

1. Monty will first ask you to pick a door.
2. After you make your pick, Monty will open one of the other doors. Monty knows what is behind each door, so he will always open a door to one of the gag gifts.
3. Monty will then ask you if you want to stay with your initial door selection, or if you want to change it and pick the other remaining closed door.

The Question: What should you do?

1. Stay with your initial selection
2. Switch to the other door
3. It doesn't matter, the chances of winning are the same

I'll give the answer and reasoning tomorrow, unless someone else comes up with it before then!