Counting system for Blackjack sidebet
The Blackjack game is fairly standard UK rules: Dealt from a shu, 4 decks, dealer stands soft 17, double any 2 cards, double after split allowed, no surrender, dealer doesn't peek, unlimited resplits, only 1 card to split aces. Typical penetration of 75%.
The sidebet allows bets of between £1-£5. If the player gets Blackjack the payouts on this sidebet are:
Blackjack (different colour): 10 to 1
Blackjack (same colour, different suit): 15 to 1
Blackjack (suited): 40 to 1
My questions are:
1) Can anybody calculate the house edge of this sidebet? (Or point me to a resource so I can calculate it myself).
2) Can anybody think of a counting system or method of developing one which could beat this sidebet? My initial thoughts are that keeping a count of the aces in relation to the number of cards left in the pack one would know once the point was reached that playing became EV+. I'm just not sure how to calculate the point at which the density of aces makes it worth playing.
Quote: blackjackladA casino near me has recently added an interesting sidebet which I think can be beaten with a counting system. I can't find any evidence anywhere of this particular sidebet being discussed, apologies if I've missed it.
The Blackjack game is fairly standard UK rules: Dealt from a shu, 4 decks, dealer stands soft 17, double any 2 cards, double after split allowed, no surrender, dealer doesn't peek, unlimited resplits, only 1 card to split aces. Typical penetration of 75%.
The sidebet allows bets of between £1-£5. If the player gets Blackjack the payouts on this sidebet are:
Blackjack (different colour): 10 to 1
Blackjack (same colour, different suit): 15 to 1
Blackjack (suited): 40 to 1
My questions are:
1) Can anybody calculate the house edge of this sidebet? (Or point me to a resource so I can calculate it myself).
2) Can anybody think of a counting system or method of developing one which could beat this sidebet? My initial thoughts are that keeping a count of the aces in relation to the number of cards left in the pack one would know once the point was reached that playing became EV+. I'm just not sure how to calculate the point at which the density of aces makes it worth playing.
I have a spreadsheet at http://miplet.net/blackjack/ . Just download the bj bounty one. You can edit the pays and deck composition. Here is your pay table with 4 decks:
| Event | Pays | Commbinations | Probability | Return |
|---|---|---|---|---|
| Suited | 40 | 256 | 0.01189149015 | 0.4756596061 |
| Colored | 15 | 256 | 0.01189149015 | 0.1783723523 |
| Mixed | 10 | 512 | 0.0237829803 | 0.237829803 |
| Loser | -1 | 20504 | 0.9524340394 | -0.9524340394 |
| Total | 21528 | 1 | -0.06057227796 |
The 6% HE is very small for a side bet and can easily be overcome if the probability of BJ is increased by about 13%. I don't have simulation software to give you exact values, but based on miplet's reply and this https://www.blackjackincolor.com/truecount6.htm
my educated guess would be that it becomes +EV at TC+2, I would play it at TC>+3.
