gospeedgo11
Joined: Mar 1, 2018
• Posts: 12
December 10th, 2020 at 11:45:13 AM permalink
Chumba Casino recently introduced a new version of blackjack with a interesting side bet based on player and dealer blackjacks. They provide a RTP of the base game of 99.43% and 97.14% but I am having trouble calculating the return on the side bet.

Blackjack Rules:
6 Decks reshuffled after every hand
3-2 BJ
No insurance
No surrender
Double on any 2
Double after split
Split hand once
No drawing to split Aces
Stand on soft 17
Hole card is dealt before player action but is played like European Blackjack (doubles and splits lose if dealer BJ)

Based on the Wizard's calculator, this is a house edge of 0.56918% which is in line with their RTP.

Special side bet:

If the dealer or player has a blackjack, the game will roll 3 dice randomly and is paid based on the outcome:
1/1/1 - 11 to 1
2/2/2 - 22 to 1
3/3/3 - 33 to 1
4/4/4 - 44 to 1
5/5/5 - 55 to 1
6/6/6 - 66 to 1
Any other combination: 8 to 1
If both the dealer and player have a blackjack, the side bet win is quadrupled.

The game rules do not make it clear whether or not it is multiplied only if the roll is one of the six matches or if it is on any roll. On their rules it has the following statements: "If the dealer and the player both have Blackjacks, the side play wins are quadrupled" and "If all three dice have the same result, and both Dealer and Player het a Blackjack, the wins are quadrupled.", then the table layout says "Dice bonus boosts winnings when dealer or player have blackjack and all matching dice".

I tried the calculations on paper but it is not adding up, any help calculating the 97.14% return would be appreciated.
ChesterDog
Joined: Jul 26, 2010
• Posts: 986
December 10th, 2020 at 2:33:45 PM permalink
Quote: gospeedgo11

Chumba Casino recently introduced a new version of blackjack with a interesting side bet based on player and dealer blackjacks. They provide a RTP of the base game of 99.43% and 97.14% but I am having trouble calculating the return on the side bet.

Blackjack Rules:
6 Decks reshuffled after every hand
3-2 BJ
No insurance
No surrender
Double on any 2
Double after split
Split hand once
No drawing to split Aces
Stand on soft 17
Hole card is dealt before player action but is played like European Blackjack (doubles and splits lose if dealer BJ)

Based on the Wizard's calculator, this is a house edge of 0.56918% which is in line with their RTP.

Special side bet:

If the dealer or player has a blackjack, the game will roll 3 dice randomly and is paid based on the outcome:
1/1/1 - 11 to 1
2/2/2 - 22 to 1
3/3/3 - 33 to 1
4/4/4 - 44 to 1
5/5/5 - 55 to 1
6/6/6 - 66 to 1
Any other combination: 8 to 1
If both the dealer and player have a blackjack, the side bet win is quadrupled.

The game rules do not make it clear whether or not it is multiplied only if the roll is one of the six matches or if it is on any roll. On their rules it has the following statements: "If the dealer and the player both have Blackjacks, the side play wins are quadrupled" and "If all three dice have the same result, and both Dealer and Player het a Blackjack, the wins are quadrupled.", then the table layout says "Dice bonus boosts winnings when dealer or player have blackjack and all matching dice".

I tried the calculations on paper but it is not adding up, any help calculating the 97.14% return would be appreciated.

I get an off-the-top return of 97.14476% for the side bet. It's nice that my answer agrees with the number 97.14% you give.

For the side bet, I assumed that ALL pays are quadrupled when both the player and dealer have blackjacks.

For both the player and dealer getting blackjacks, I get a probability of 0.002166500.

And for only the player or dealer getting blackjack, I get 0.090645975. And for neither, I get 0.907187524.
teliot
Joined: Oct 19, 2009
• Posts: 2269
December 11th, 2020 at 5:49:16 AM permalink
intuitively, this is massively countable, with the blackjack count. A = -4, TJQK =-1, all others +1.

Could one of you brilliant programmers run this? I got rid of my workstation when I retired.
Poetry website: www.totallydisconnected.com
kuma
Joined: Feb 10, 2018