What the odds for dealer to get 26 on 3 cards

[abukase7]

Here at Hawaiian garden casino if dealer get 26 in 3 cards all players that bust push

what will be the odds for it

any information will be greatly appreciated

yossi

[Dog Hand]

Here at Hawaiian garden casino if dealer get 26 in 3 cards all players that bust push

what will be the odds for it

any information will be greatly appreciated

yossi

abukase7,

To get a 3-card 26, the dealer must have a 2-card 16 and then hit with an X. The dealer therefore must have one of these five hands:

1. X, 6, X
2. 6, X, X
3. 9, 7, X
4. 7, 9, X
5. 8, 8, X

The answer depends on the number of decks, which you did not specify, so I'll assume it is a 6D game. I'll also neglect rounds where all the players have BJ, so the dealer needn't complete her hand.

Probability of 1: (96/312)*(24/311)*(95/310) = 218,880/30,079,920 = 0.00727662

Probability of 2: (24/312)*(96/311)*(95/310) = 218,880/30,079,920 = 0.00727662 (same as 1, obviously)

Probability of 3: (24/312)*(24/311)*(96/310) = 55,296/30,079,920 = 0.00183830

Probability of 4: (24/312)*(24/311)*(96/310) = 55,296/30,079,920 = 0.00183830 (same as 3, obviously)

Probability of 5: (24/312)*(23/311)*(96/310) = 52,992/30,079,920 = 0.00176171

Summing, we get the probability of a dealer 3-card 26 as 0.0199915, or 1 in 50.02 rounds.

Hope this helps!

Dog Hand

[Phoebe]

What about 2-card 15 and an ace?

[Midwest Player]

What about 2-card 15 and an ace?

That is only a 16 and dealer will take another hit. If the dealer gets a 10 then that will be a four card 26.

[Phoebe]

Oups. I only wake up

[abukase7]

Thank you that helpfull .
ok it is a 2 deck game 55 cut

[abukase7]

Abd 6 to 5 if it make any different ones

[Dog Hand]

abukase7,

UPDATE: it's a 2D game. Here are the updated calculations.

To get a 3-card 26, the dealer must have a 2-card 16 and then hit with an X. The dealer therefore must have one of these five hands:

1. X, 6, X
2. 6, X, X
3. 9, 7, X
4. 7, 9, X
5. 8, 8, X

I'll neglect the rounds where all the players have BJ, so the dealer needn't complete her hand.

Probability of 1: (32/104)*(8/103)*(31/102) = 7,936/1,092,624 = 0.00726325

Probability of 2: (8/104)*(32/103)*(31/102) = 7,936/1,092,624 = 0.00726325 (same as 1, obviously)

Probability of 3: (8/104)*(8/103)*(32/102) = 2,048/1,092,624 = 0.0018744

Probability of 4: (8/104)*(8/103)*(32/102) = 2,048/1,092,624 = 0.0018744 (same as 3, obviously)

Probability of 5: (8/104)*(7/103)*(32/102) = 1,792/1,092,624 = 0.0016401

Summing, we get the probability of a dealer 3-card 26 in a DD game as 0.019915, or 1 in 50.2 rounds, or slightly more often than in a 6D game.

Hope this helps!

Dog Hand

[abukase7]

That perfect answer . Thank you .

[21forme]

So how much does it alter house edge?

[DSchles]

Summing, we get the probability of a dealer 3-card 26 in a DD game as 0.019915, or 1 in 50.2 rounds, or slightly more often than in a 6D game.

Nope. Slightly less often!

Don

[DSchles]

So how much does it alter house edge?

First, the player has to bust. The global bust rate for the BS player is about 16%, but that's against all upcards. Since the dealer's upcard can be only 6, 7, 9, or X, you have to figure that the player will bust a little more frequently, standing short only on 6 and hitting to 17 on all the other upcards. Let's just say the player will bust about 20% of the time, or once every five such hands.

The dealer will bust with 26 once every 50 hands. Together, the bust becomes a push once every 250 hands, which is adding 0.4% to the player's edge.

Don

[Sharky]

First, the player has to bust. The global bust rate for the BS player is about 16%, but that's against all upcards. Since the dealer's upcard can be only 6, 7, 9, or X, you have to figure that the player will bust a little more frequently, standing short only on 6 and hitting to 17 on all the other upcards. Let's just say the player will bust about 20% of the time, or once every five such hands.

The dealer will bust with 26 once every 50 hands. Together, the bust becomes a push once every 250 hands, which is adding 0.4% to the player's edge.

Don

...and then subtract when the player would've won anyways by beating the dealer's made hand?

haha...nevermind...dealer doesn't bust in those situations....hit happy hr already....happy Halloween!!!hahaha