Hi all, I'd like to ask experts if this side bet could be mathematically profitable.
Basically it consists of betting to get a blackjack of the same colour, for example Ace of Hearts+King of Diamonds and is paid 35 to 1.
You play with 6 decks and you can bet 5 or 10€ at tables with minimum bet of 10€, and 10 or 20€ at tables with minimum bet of 20€.
I tried to do some calculations and knowing that the odds of getting a blackjack are about 4.74% (1/21 hands) and that the odds of getting a blackjack of the same colour are 2.37% (1/42 hands), I assumed a scenario like this:
- 2 decks played (so 4 decks left)
- 4 aces out (so still 20 aces to play, therefore 5 aces per deck)
- 28 figure cards out (so still 68 figure cards to play)
Essentially we are at a TC=2 with hi-lo system.
Applying the formula to find the probability of getting a blackjack we yields this:
F=(10s_left/cards_to_play)*[Aces_left/(cards_to_play-1)]+
(Aces_left/cards_to_play)*[10s_left/(cards_to_play-1)]= 6.31%
So, in this condition we would get a blackjack every 16 hands and a coloured blackjack every 32 hands, so would be advantageous since it pays 35 to 1.
Assuming then the same proportion of aces at a TC=7 we would be at 8.17% (one coloured blackjack every 25 hands).
Looking at this it seems a mathematically advantageous bet in certain situations, or maybe I have not considered some variable? What do you think?
Thanks to discuss
Basically it consists of betting to get a blackjack of the same colour, for example Ace of Hearts+King of Diamonds and is paid 35 to 1.
You play with 6 decks and you can bet 5 or 10€ at tables with minimum bet of 10€, and 10 or 20€ at tables with minimum bet of 20€.
I tried to do some calculations and knowing that the odds of getting a blackjack are about 4.74% (1/21 hands) and that the odds of getting a blackjack of the same colour are 2.37% (1/42 hands), I assumed a scenario like this:
- 2 decks played (so 4 decks left)
- 4 aces out (so still 20 aces to play, therefore 5 aces per deck)
- 28 figure cards out (so still 68 figure cards to play)
Essentially we are at a TC=2 with hi-lo system.
Applying the formula to find the probability of getting a blackjack we yields this:
F=(10s_left/cards_to_play)*[Aces_left/(cards_to_play-1)]+
(Aces_left/cards_to_play)*[10s_left/(cards_to_play-1)]= 6.31%
So, in this condition we would get a blackjack every 16 hands and a coloured blackjack every 32 hands, so would be advantageous since it pays 35 to 1.
Assuming then the same proportion of aces at a TC=7 we would be at 8.17% (one coloured blackjack every 25 hands).
Looking at this it seems a mathematically advantageous bet in certain situations, or maybe I have not considered some variable? What do you think?
Thanks to discuss