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21forme
21forme
Joined: Feb 27, 2011
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May 28th, 2011 at 8:19:45 AM permalink
Galaxy Gaming has introduced new side bets for BJ.

The first is called 21 Magic with payoffs as follows:
BJ 6:1
2 card 21 (after splitting) 6:1
3 card 21 8:1
4 card 21 9:1
5 & 6 card 21 10:1
7+ card 21 25:1


Second one is called Bust Bonus. After you play your hand, you may place a Bust bet. Payoff is based on dealer's up-card. You win if dealer busts. If you bust, you cannot make a Bust bet. For the suited payoffs, ALL cards in dealer's hand must be suited. Unlike the Bust-it side bet of Double Attack BJ, this bet applies to any number of dealer cards.

///
Up card non-suited bust suited bust
Ace 3 50
2 1 25
3 1 15
4 1 10
5 1 5
6 1 3
7 2 15
8 2 10
9 2 20
10 2 20
888 25 75


Wonder if anyone (Mr. Wiz?) can provide house edge's on these side bets? I couldn't find them on WOO

Thanks.
Zcore13
Zcore13
Joined: Nov 30, 2009
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May 30th, 2011 at 2:18:12 PM permalink
Quote: 21forme

Galaxy Gaming has introduced new side bets for BJ.

The first is called 21 Magic with payoffs as follows:
BJ 6:1
2 card 21 (after splitting) 6:1
3 card 21 8:1
4 card 21 9:1
5 & 6 card 21 10:1
7+ card 21 25:1


Second one is called Bust Bonus. After you play your hand, you may place a Bust bet. Payoff is based on dealer's up-card. You win if dealer busts. If you bust, you cannot make a Bust bet. For the suited payoffs, ALL cards in dealer's hand must be suited. Unlike the Bust-it side bet of Double Attack BJ, this bet applies to any number of dealer cards.

///
Up card non-suited bust suited bust
Ace 3 50
2 1 25
3 1 15
4 1 10
5 1 5
6 1 3
7 2 15
8 2 10
9 2 20
10 2 20
888 25 75


Wonder if anyone (Mr. Wiz?) can provide house edge's on these side bets? I couldn't find them on WOO

Thanks.



Add this to the right side of your chart...

House Edge
24.41%
8.32%
9.05%
7.71%
9.17%
11.30%
6.19%
6.46%
10.36%
8.88%
Not sure about the 888
I am an employee of a Casino. Former Table Games Director,, current Pit Supervisor. All the personal opinions I post are my own and do not represent the opinions of the Casino or Tribe that I work for.
21forme
21forme
Joined: Feb 27, 2011
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June 3rd, 2011 at 7:54:42 PM permalink
Quote: Zcore13


Add this to the right side of your chart...

House Edge
24.41%
8.32%
9.05%
7.71%
9.17%
11.30%
6.19%
6.46%
10.36%
8.88%
Not sure about the 888


How did you calculate this?

Doesn't seem intuitively correct. You're syaing the HE for busting with a 5 or 6 up is greater than a 2 or 3?
johnnyg
johnnyg
Joined: Feb 10, 2012
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February 10th, 2012 at 4:46:51 PM permalink
I was curious about this side bet after it showed up at a local casino. No offense to the earlier post but I was curious so I coded it up myself (straight probability, not monte carlo), and came up with these answers based on 8 decks and dealer hits on soft 17.

I ran it for before and after the blackjack check since the dealers here were inconsistent about that and it annoyed me -- obviously it's pretty dumb to bet on a bust when dealer blackjack is still a possibility.

As for the intuition, the house edge depends on more than just the chance of busting -- as the up card is lower, the paytable for suited busting ramps up more quickly than the hitrate decreases, which balances it out. The 888 bonuses make a pretty big contribution.

Total return Card No bust pays return U/S Bust pay return S. Bust pay return U/S 888 pay return S. 888 pay return
-7.46%264.33%-1-64.33%34.78%134.78%0.88%2522.09%
-8.37%362.31%-1-62.31%36.53%136.53%1.16%1517.41%
-7.19%460.19%-1-60.19%38.35%138.35%1.46%1014.65%
-9.00%558.09%-1-58.09%40.12%140.12%1.79%58.97%
-7.93%656.07%-1-56.07%41.83%141.83%2.10%36.31%
-5.98%773.80%-1-73.80%25.02%250.03%1.19%1517.79%
-4.13%875.60%-1-75.60%22.73%245.45%1.13%1011.27%0.52%2512.92%0.02%751.83%
-10.30%977.10%-1-77.10%21.74%243.48%1.17%2023.32%
-15.79%10 early78.76%-1-78.76%20.10%240.20%1.14%2022.78%
-37.09%A early86.09%-1-86.09%13.75%341.26%0.15%507.74%
-8.75%10 late76.99%-1-76.99%21.78%243.56%1.23%2024.68%
-9.03%A late79.89%-1-79.89%19.89%359.67%0.22%5011.20%
Zcore13
Zcore13
Joined: Nov 30, 2009
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February 14th, 2012 at 9:22:38 AM permalink
The chart I listed above for the house advantage on each card is for somewhere where the Dealer stands on S17. If the Dealer hits on S17 the HE is this:

A- 9.0451%
2- 7.6716%
3- 8.4546%
4- 7.1714%
5- 8.9163%
6- 7.9676%
7- 6.2131%
8- 4.9112%
9- 10.3338%
10 - 8.8372%

Both charts are with 6 deck shoes...
I am an employee of a Casino. Former Table Games Director,, current Pit Supervisor. All the personal opinions I post are my own and do not represent the opinions of the Casino or Tribe that I work for.
kmcd
kmcd
Joined: Jul 10, 2011
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May 6th, 2012 at 3:57:57 PM permalink
Does anyone know the indexes for this?
nobody
nobody
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Thanks for this post from:
FishDawg
May 10th, 2015 at 2:03:21 PM permalink
I just wrote a computer program that calculated this for me, because I can't trust this thing this other person has calculated and if you want something done right, I have to do it myself, and all that, and after seeing the results, I see I was correct. Here is the REAL answer. By the way, the first person who thought that the house edge on the bust bonus if an A is showing is huge was obviously failing to account for the fact that you don't lose the bet if the dealer has blackjack, but no, here in 'Murika, it's just like doubling down or splitting, you only lose the original bet.

%Return per dollar bet:

%A: -0.0897
%2: -0.0686
%3: -0.0807
%4: -0.0721
%5: -0.0922
%6: -0.0779
%7: -0.0535
%8: -0.0178
%9: -0.1019
%10: -0.1548 ouch, that's almost as bad as keno, don't ever take this bet if the upcard is 10.

This was calculated on an infinite deck, with the dealer hitting on soft 17.

It looks like 8 is the best, right? Well, no. The bust bonus on the 8 is largely unaffected by the count and becomes only slightly advantageous for strongly negative counts of below -5.3, with a player advantage of 0.5% even with a count of -8.3 (and if the count is that negative, you should be finding some excuse to leave the table anyway, because you'll face a house edge of 5% in the main bet on your hand at that level), while the bust bonus on ace and 2-6 become advantageous when the count becomes strongly positive. The bust bonus on 7, 9 and especially 10 are sucker bets no matter what the count is. The first one to become advantageous is a dealer's upcard of 4, which reaches breakeven when the count reaches 3.8, and then rapidly gains advantage at a differential rate of 2.0% per truecount, meaning that when the count is up to 4.8, the player advantage of taking the bust bonus when the dealer's upcard is 4 is already 2%, meaning every dollar bet returns 1.02 on average. The next best is a dealer's upcard of 2 or 3, which have breakeven thresholds of 4.3 each and gain at a differential rate of 1.6% for the 2 and 2.0% for the 3, meaning when the count is 5.3, the bust bonus on the 3 has a player advantage of 2.0% and on the 2 has a player advantage of 1.7%. Breakeven for the ace and 5 is a count of 5.5 each, but the 5 gains faster than the ace, the 5 gains at 1.8% per count and the ace gains at 1.6% per count. Kelly optimal bet amounts for a bankroll of 5000 dollars are about 100 dollars per count in excess of 3.8 if you're up against a dealer 4, which means it really takes off in a hurry once it gets past that threshold, if the count is 4.8, you should already be betting 100 dollars on the bust bonus against a dealer's 4. Remember that the ace return is competitive with respect to the others, but because it involves a higher payout at a smaller fraction of a time, the kelly optimal fraction of bankroll to wager is about 1/3 as much per differential change in advantage, so wager more like 25 dollars for each one the count is past 5.5, so if the count is 7.5, you'd still be only wagering 50 dollars against a dealer's ace, but against a 4, you'd be betting nearly 400 dollars.

At least it beats the lucky ladies bet. I figured out before that in the 2 deck game, you shouldn't take the lucky ladies bet until the count gets past 8.3. I only took that bet once, and I was betting 200 on the main hand at the time. I'm not too broken up about losing the lucky ladies 5 dollar bet since I won the main hand.

However, unlike the insurance sidebet, both the lucky ladies bet and the bust bonus bet have strong POSITIVE correlation to the outcome of the main hand (if you lose the main bet, you're likely to lose the bust bonus bet, because the dealer not busting is likely the cause of your loss), so when it comes to kelly optimality (maximizing your expected return on a logarythmic scale), take it with a grain of salt when I tell you the right amount to bet, if the count is already highly positive, you already are going to have a lot riding on the outcome of the main hand and if the dealer ends on 21, you're going to lose them both, whereas the nice thing about insurance is its negative correlation, i.e. if you lose the main hand when the dealer shows an ace, it's likely because the dealer had blackjack.
Zcore13
Zcore13
Joined: Nov 30, 2009
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May 10th, 2015 at 8:08:02 PM permalink
Quote: nobody

I just wrote a computer program that calculated this for me, because I can't trust this thing this other person has calculated and if you want something done right, I have to do it myself, and all that, and after seeing the results, I see I was correct. Here is the REAL answer. By the way, the first person who thought that the house edge on the bust bonus if an A is showing is huge was obviously failing to account for the fact that you don't lose the bet if the dealer has blackjack, but no, here in 'Murika, it's just like doubling down or splitting, you only lose the original bet.

%Return per dollar bet:

%A: -0.0897
%2: -0.0686
%3: -0.0807
%4: -0.0721
%5: -0.0922
%6: -0.0779
%7: -0.0535
%8: -0.0178
%9: -0.1019
%10: -0.1548 ouch, that's almost as bad as keno, don't ever take this bet if the upcard is 10.

This was calculated on an infinite deck, with the dealer hitting on soft 17.

It looks like 8 is the best, right? Well, no. The bust bonus on the 8 is largely unaffected by the count and becomes only slightly advantageous for strongly negative counts of below -5.3, with a player advantage of 0.5% even with a count of -8.3 (and if the count is that negative, you should be finding some excuse to leave the table anyway, because you'll face a house edge of 5% in the main bet on your hand at that level), while the bust bonus on ace and 2-6 become advantageous when the count becomes strongly positive. The bust bonus on 7, 9 and especially 10 are sucker bets no matter what the count is. The first one to become advantageous is a dealer's upcard of 4, which reaches breakeven when the count reaches 3.8, and then rapidly gains advantage at a differential rate of 2.0% per truecount, meaning that when the count is up to 4.8, the player advantage of taking the bust bonus when the dealer's upcard is 4 is already 2%, meaning every dollar bet returns 1.02 on average. The next best is a dealer's upcard of 2 or 3, which have breakeven thresholds of 4.3 each and gain at a differential rate of 1.6% for the 2 and 2.0% for the 3, meaning when the count is 5.3, the bust bonus on the 3 has a player advantage of 2.0% and on the 2 has a player advantage of 1.7%. Breakeven for the ace and 5 is a count of 5.5 each, but the 5 gains faster than the ace, the 5 gains at 1.8% per count and the ace gains at 1.6% per count. Kelly optimal bet amounts for a bankroll of 5000 dollars are about 100 dollars per count in excess of 3.8 if you're up against a dealer 4, which means it really takes off in a hurry once it gets past that threshold, if the count is 4.8, you should already be betting 100 dollars on the bust bonus against a dealer's 4. Remember that the ace return is competitive with respect to the others, but because it involves a higher payout at a smaller fraction of a time, the kelly optimal fraction of bankroll to wager is about 1/3 as much per differential change in advantage, so wager more like 25 dollars for each one the count is past 5.5, so if the count is 7.5, you'd still be only wagering 50 dollars against a dealer's ace, but against a 4, you'd be betting nearly 400 dollars.

At least it beats the lucky ladies bet. I figured out before that in the 2 deck game, you shouldn't take the lucky ladies bet until the count gets past 8.3. I only took that bet once, and I was betting 200 on the main hand at the time. I'm not too broken up about losing the lucky ladies 5 dollar bet since I won the main hand.

However, unlike the insurance sidebet, both the lucky ladies bet and the bust bonus bet have strong POSITIVE correlation to the outcome of the main hand (if you lose the main bet, you're likely to lose the bust bonus bet, because the dealer not busting is likely the cause of your loss), so when it comes to kelly optimality (maximizing your expected return on a logarythmic scale), take it with a grain of salt when I tell you the right amount to bet, if the count is already highly positive, you already are going to have a lot riding on the outcome of the main hand and if the dealer ends on 21, you're going to lose them both, whereas the nice thing about insurance is its negative correlation, i.e. if you lose the main hand when the dealer shows an ace, it's likely because the dealer had blackjack.



Edit- You came up with the same HE on all the cards I posted above.


ZCore13
I am an employee of a Casino. Former Table Games Director,, current Pit Supervisor. All the personal opinions I post are my own and do not represent the opinions of the Casino or Tribe that I work for.
blackhawkphil
blackhawkphil
Joined: May 1, 2017
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May 5th, 2017 at 10:35:13 AM permalink
Can someone come up with the House Edge for the Magic 21 side bet?
If a player has equal bets on the blackjack wager and the Magic 21 side bet, then hits every time until they bust or get 21, what is the house advantage?
I ask because there is player using this strategy and winning an unbelievable amount...
Wizard
Administrator
Wizard
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July 3rd, 2017 at 11:13:23 AM permalink
I published an analysis of Bust Bonus. Stay tuned for an analysis of 21 Magic.

Do those wins for a 21, other than the one for two cards, apply after splitting?
Last edited by: Wizard on Jul 4, 2017
It's not whether you win or lose; it's whether or not you had a good bet.

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