The poker dealer
Quote: KloppFour people are going to play poker. To determine the dealer, they are dealt in turn a card until an ace appears. The player receiving the first ace becomes the dealer. Is the procedure fair, that is, does every player have the same chance of becoming the dealer?
Obviously not.
Most (all?) casinos will deal each player, then use high card, then break ties by suit. Suits are ranked alphabetically. If you're not sure if that means C,D,H,S or S,H,D,C, remember that there's a reason the Ace of Spaces is fancy. Dealers will usually stop dealing if the Ace of Spaces shows up.
As a poker league dealer, I'll say that if the Ace of Spaces shows up before the last person is dealt a card, I usually will deal one more card, only because my automatic motions are faster than my reflexes. Some dealers will continue to deal a card to every player regardless.
Note that for a home game, if you don't want to use suits, you can also brea ties by dealing a second card only to the players that have a matching high card - but you have to decide that before the first deal.
Om a side note, if the winning card is the King of Hearts, I'll often announce the card, but slur it a little and follow it up, as such, "King of Farts. He farts a lot that's why he's King. Or maybe that's why he's trying to kill himself." (He's the suicide king.)
YES. It was used by the ex-fbi profiler turned professional poker player o my favorite tv program so don't say nothin' against it.Quote: KloppIs the procedure fair,
Quote: FleaStiffYES. It was used by the ex-fbi profiler turned professional poker player o my favorite tv program so don't say nothin' against it.
Not fair at all as the first person to get a card is more likely than the others to be the dealer. High card or low card it fair.
First guy has a 7.7% chance of getting an ace
Second guy has a 7.3% chance of first guy not getting one and himself getting one.
Quote: michael99000If it were just 2 people ..
First guy has a 7.7% chance of getting an ace
Second guy has a 7.3% chance of first guy not getting one and himself getting one.
Yes, but if you keep going the first person is most likely to get it.
The first player to receive a card will receive the first ace approximately 28.0 % of the time.Quote: KloppIf not, how much differ the chances of the four players?
The second player to receive a card will receive the first ace approximately 25.9 % of the time.
The third player to receive a card will receive the first ace approximately 24.0 % of the time.
The fourth player to receive a card will receive the first ace approximately 22.1 % of the time.
Quote: EdCollinsThe first player to receive a card will receive the first ace approximately 28.0 % of the time.
The second player to receive a card will receive the first ace approximately 25.9 % of the time.
The third player to receive a card will receive the first ace approximately 24.0 % of the time.
The fourth player to receive a card will receive the first ace approximately 22.1 % of the time.
An "infinite-deck model" of this procedure gives results similar to yours:
| Player | Prob. |
|---|---|
| 1 | 0.28077 |
| 2 | 0.25917 |
| 3 | 0.23923 |
| 4 | 0.22083 |
| Sum | 1.00000 |
In the infinite-deck model with the constant probability of an ace = 1/13 = a, the players' probabilities of winning are:
P(1) = a / [1 - (1-a)4]
P(2) = a(1-a) / [1 - (1-a)4]
P(3) = a(1-a)2 / [1 - (1-a)4]
P(4) = a(1-a)3 / [1 - (1-a)4]
In holdem games, the dealer is last to act for each betting round (except pre-flop because of the blinds). This gives the dealer the advantage since he can see what his opponents do before he has to make a decision. That's why the extra chip in a split pot goes to the player furthest from the button.Quote: onenickelmiracleWhat advantage is there in being the dealer? They are proving being the dealer is not fair, but if there is no advantage in being the dealer, isn't it?
There is no advantage for stud games as the betting order for each round is determined by the cards dealt.
Quote: KloppFour people are going to play poker. To determine the dealer, they are dealt in turn a card until an ace appears. The player receiving the first ace becomes the dealer. Is the procedure fair, that is, does every player have the same chance of becoming the dealer? If not, how much differ the chances of the four players?
I get the following, which agree with Ed Collins's results.
| Player | Prob. |
|---|---|
| 1 | 0.280288115246 |
| 2 | 0.259303721489 |
| 3 | 0.239519807923 |
| 4 | 0.220888355342 |
| Sum | 1 |
