Casino offers 2:1 on blackjack suited hearts

tedsuxs

Well-Known Member
#1
So a-10, a-j , a-q , a-k of hearts get paid 2:1 on blackjack

How much does this improve odds? 6 deck

Is it worth having a side count of the ace of hearts?
 

Renzey

Well-Known Member
#3
tedsuxs said:
So a-10, a-j , a-q , a-k of hearts get paid 2:1 on blackjack

How much does this improve odds? 6 deck

Is it worth having a side count of the ace of hearts?
It's 0.14%. Side count? Dunno. Probably not.
 

BJgenius007

Well-Known Member
#7
Iron Man said:
Could you show how you arrived at 0.14% and why a side count would not be advantageous ? Thanks !
When Blackjack pays 3 to 2, the player get 4.8% advantage.

The mathematics behind this is

8/169 x 50% = 2.37%

Basically, you get 2.37% advantage from Blackjack that pay 3 to 2.

Now to calculate Heart suite bonus. You have 1/4 of chance to get ten of heart, 1/4 of chance to get ace of heart, so

2.37%/ 16 = 0.147%
 

NightStalker

Well-Known Member
#9
not sure how you concluded

BJgenius007 said:
When Blackjack pays 3 to 2, the player get 4.8% advantage.

The mathematics behind this is

8/169 x 50% = 2.37%

Basically, you get 2.37% advantage from Blackjack that pay 3 to 2.

Now to calculate Heart suite bonus. You have 1/4 of chance to get ten of heart, 1/4 of chance to get ace of heart, so

2.37%/ 16 = 0.147%
but your answer is correct :)
 

MangoJ

Well-Known Member
#10
Here is the exact calculation with explanaitions.

On 6 decks (312 cards) we have the probability of a 3:2-payed blackjack:
(2 * 24/312 * 96/311) * (1 - 2 * 23/310 * 95/309) = 4.5323%.

The first factor is getting dealt a Blackjack (roughly 8/169). The second factor is the probability the doesn't get a blackjack (roughly 1 - 8/169) conditioned that you have a blackjack (1 ace and 1 ten missing).

As all suits are equal regarging a normal blackjack, there are 4*4 = 16 different suit combinations, 12 are unsuited, and 4 are suited, obviously 1 of them is the hearts BJ. We only get the bonus on hearts, so we divide the probability by 16, to get the probability of a hearts-suited BJ (while dealer has no blackjack):

4.5323% / 16 = 0.2833%

The bonus pays 2:1 instead of 3:2, which is half (50%) the initial wager.

Hence the player advantage (per initial wager) is
0.2833% * 50% = 0.1416%.

If the bonus is also paid when the BJ pushes (dealer also has blackjack), then we need to add things up:
Probability of a BJ push: (2 * 24/312 * 96/311) * (2 * 23/310 * 95/309) = 0.2166%

A BJ push while player has a hearts-suited:
0.2166% / 16 = 0.0135%

Normal pay is 1:1, if bonus pays 2:1, this is a full wager (100%), hence
0.0135% * 100% = 0.0135%

We add both up (since they are mutual excluded):
0.1416% + 0.0135% = 0.1552%

Of course a side count would help. If you can only keep 1 side count, I guess the Aces of Hearts are best indicators. More accurate would be two side counts with Aces and Tens of Hearts of course. One should do simulations regarding indexes and probabilities.
 

Nynefingers

Well-Known Member
#12
MangoJ said:
If the bonus is also paid when the BJ pushes (dealer also has blackjack), then we need to add things up:
Probability of a BJ push: (2 * 24/312 * 96/311) * (2 * 23/310 * 95/309) = 0.2166%

A BJ push while player has a hearts-suited:
0.2166% / 16 = 0.0135%

Normal pay is 1:1, if bonus pays 2:1, this is a full wager (100%), hence
0.0135% * 100% = 0.0135%

We add both up (since they are mutual excluded):
0.1416% + 0.0135% = 0.1552%
Normal pay on a BJ push is 0 (no win, no loss), so if you get paid 2:1 on a heart BJ when the dealer also had a BJ, that's a 2 unit bonus on those hands. In my experience, these bonuses only pay on winning suited blackjacks, although hopefully they'll throw you a bone since it's only 1 suit.

Regarding an Ah side count, a quick look at the math suggests that if the Ah density is doubled, you will roughly double your chances at getting a heart BJ, which would double your edge from the promo. The takeaway here is you'd have to see 3 decks dealt with no Ah seen just to add another 0.14% to your edge. It's going to happen infrequently enough and be worth little enough to you that it won't be worth side counting aces of hearts. Ten valued hearts would be even less useful.
 

MangoJ

Well-Known Member
#13
Yes you're right, both with push (it's embarassing, did that mistake now twice) and performance. Even at better penetration, say 3 Ah to come at 85% penetration, gives just 0.5% advantage.

Not worth for keeping a side count. But if you play this game for other reasons it's okay.
 
#16
tedsuxs said:
So a-10, a-j , a-q , a-k of hearts get paid 2:1 on blackjack

How much does this improve odds? 6 deck

Is it worth having a side count of the ace of hearts?
Now for the one question that wasn't answered. Where is this promotion?

I know of a place that paid 2:1 on blackjack in suited diamonds with a few extra's thrown in.
 

Midwestern

Well-Known Member
#17
Nynefingers said:
Normal pay on a BJ push is 0 (no win, no loss), so if you get paid 2:1 on a heart BJ when the dealer also had a BJ, that's a 2 unit bonus on those hands..
I have played at casinos where they pay 3:2 on suited heart
Blackjacks before the dealer peeks.
 

Nynefingers

Well-Known Member
#18
Midwestern said:
I have played at casinos where they pay 3:2 on suited heart
Blackjacks before the dealer peeks.
I'll take whatever bonus I can get, but that only adds about 0.02% for a basic strategy player (6 deck game). It will be slightly more helpful for counters since you'll be more likely to have your bigger bets out when you and the dealer both have blackjack.
 
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