• Posts: 4
Joined: Oct 27, 2017
October 29th, 2017 at 1:49:39 AM permalink
So theres a Blackjack game that just came out at a Casino near me. They brought in Double Up Blackjack. Well theres a Side Bet that i cant find anywhere on the internet. So i need help with the Math for thise sidebet.

Named: Bonus 16.
If the Dealer gets a 16 Push, you win the Side Bet.
Minimum \$1; Maximum \$25.
2 Card 16 = 3 to 1
3 Card 16 = 5 to 1
4 Card 16 = 10 to 1
5 Card 16 = 50 to 1
6+ Card 16 = 100 to 1.

Can anyone do the math on the odds on each payout and and if its a Player Favored or House Advantage bet on expected values? It really feels like a Player Favored side bet, and i wanna know by how much.
Thank you everyone! And please explain the math if possible as well!
BleedingChipsSlowly
• Posts: 1033
Joined: Jul 9, 2010
October 29th, 2017 at 4:05:13 AM permalink
The name is “16 Bonus” according to Score Gaming’s rack card. I can’t help with the maths, but I doubt the bet is to the player’s advantage. Sure, it looks like a good bet at first glance. If it didn’t people wouldn’t put up a bet. If it actually is a good bet casinos won’t offer it. It looks like the rack card publication date is over a year ago. I would think the bet has been proven a money maker for casinos if it has survived that long.
“You don’t bring a bone saw to a negotiation.” - Robert Jordan, former U.S. ambassador to Saudi Arabia
DJTeddyBear
• Posts: 11032
Joined: Nov 2, 2009
October 29th, 2017 at 7:55:12 AM permalink

If the Dealer gets a 16 Push...

What is a '16 push'?

For the record, I read the rack card, and I don't understand the concept of this game.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ————————————————————————————————————— Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
SM777
• Posts: 762
Joined: Apr 8, 2016
October 29th, 2017 at 7:59:42 AM permalink
Math = Don't play it.

Next.
BleedingChipsSlowly
• Posts: 1033
Joined: Jul 9, 2010
October 29th, 2017 at 8:34:47 AM permalink
Quote: DJTeddyBear

What is a '16 push'?

For the record, I read the rack card, and I don't understand the concept of this game.

The Wizard of Odds site has a write up about how Double Up Blackjack is played including strategy, but it doesn't delve into the 16 Bonus side bet.
“You don’t bring a bone saw to a negotiation.” - Robert Jordan, former U.S. ambassador to Saudi Arabia
ThatDonGuy
• Posts: 6549
Joined: Jun 22, 2011
October 29th, 2017 at 10:10:05 AM permalink
I did a Monte Carlo simulation with infinite decks, and get about a 21.5% house advantage.
OOPS - here's an idea: how about not subtracting 1 from each of the payouts? That makes it match what the Wizard gets...

About 1 out of every 7 dealer hands is a 16.

Of these, half are 2-card 16s, about 3/8 are 3-card, 10% are 4-card, 2% are 5-card, and the rest (1/440 or so) are 6 or more.
Last edited by: ThatDonGuy on Oct 29, 2017
Wizard
• Posts: 26842
Joined: Oct 14, 2009
October 29th, 2017 at 3:06:44 PM permalink
I get a house edge of 16.97%. This assumes six decks and the dealer hits a soft 17. Remember, the dealer does NOT hit soft 16 in this game.

Event Pays Probability Return
16 with 6+ cards 100 0.000156 0.015632
16 with 5 cards 50 0.001731 0.086548
16 with 4 cards 10 0.012009 0.120089
16 with 3 cards 5 0.047738 0.238692
16 with 2 cards 3 0.076923 0.230769
All other -1 0.861442 -0.861442
Total 1.000000 -0.169711

Here is some more detail, if anyone cares.

Event Probability
Dealer blackjack 0.047489488
Total of 17 0.133763556
Total of 18 0.127769103
Total of 19 0.122183591
Total of 20 0.168019932
Total of 21 0.061376129
Bust 0.200840473
16 with 2 cards 0.076923077
16 with 3 cards 0.047738425
16 with 4 cards 0.01200894
16 with 5 cards 0.001730969
16 with 6 cards 0.000148316
16 with 7 cards 7.75531E-06
16 with 8 cards 2.42174E-07
16 with 9 cards 3.96286E-09
16 with 10 cards 2.54373E-11
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
BleedingChipsSlowly
• Posts: 1033
Joined: Jul 9, 2010
October 29th, 2017 at 4:40:14 PM permalink
Nice work, thanks. Since you've already done the work, why not add it to your Wizard of Odds article about Double Up Blackjack? The side bet is on the rack card, so it looks like it's sold as part of the standard installation. The main game's hold is pretty low: perhaps the side bet is a major selling point.
“You don’t bring a bone saw to a negotiation.” - Robert Jordan, former U.S. ambassador to Saudi Arabia
DogHand
• Posts: 1722
Joined: Sep 24, 2011
October 29th, 2017 at 8:28:51 PM permalink
Quote: Wizard

I get a house edge of 16.97%. This assumes six decks and the dealer hits a soft 17. Remember, the dealer does NOT hit soft 16 in this game.

Event Pays Probability Return
16 with 6+ cards 100 0.000156 0.015632
16 with 5 cards 50 0.001731 0.086548
16 with 4 cards 10 0.012009 0.120089
16 with 3 cards 5 0.047738 0.238692
16 with 2 cards 3 0.076923 0.230769
All other -1 0.861442 -0.861442
Total 1.000000 -0.169711
<snip>

Wizard,

I ran an 800-million-round CVData sim and obtained the following results:

16 Pays Probability Return
>5-card 100 0.00018129 0.018129
5-card 50 0.00190624 0.095312
4-card 10 0.01268905 0.126890
3-card 5 0.04873760 0.243688
2-card 3 0.07688938 0.230668
No 16 -1 0.85959644 -0.859596
EV 1.00000000 -0.144909

Our results differ quite a bit. Any idea how they can be this far apart?

Meanwhile, I'll re-run the sim to see how reproducible my results are.

Dog Hand
Wizard
• Posts: 26842
Joined: Oct 14, 2009
October 29th, 2017 at 9:51:58 PM permalink
Quote: DogHand

Our results differ quite a bit. Any idea how they can be this far apart?

Meanwhile, I'll re-run the sim to see how reproducible my results are.

The problem is they are not far apart enough. These small differences are hard to track down who is in error and why. I speculate that the rule about standing on a soft 16, while hitting a soft 17, has something to do with it.

For what its worth, my results are recursive in nature so should be exactly right, save programmer error, which is a distinct possibility.

It might help if you also output the other events, like dealer ending up with 17-21, blackjack, or busting, just so we have more to compare against.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
beachbumbabs
• Posts: 14268
Joined: May 21, 2013
October 29th, 2017 at 11:54:19 PM permalink
Total guess out of ignorance, but those results are so close, I would guess you're not using the same amount of decks to calculate it. Each individual result is within 1/1000 or less, but cumulatively they add up to a somewhat significant HE difference.

JMVHO.
If the House lost every hand, they wouldn't deal the game.
Wizard
• Posts: 26842
Joined: Oct 14, 2009
October 30th, 2017 at 7:38:13 AM permalink
Quote: DogHand

Our results differ quite a bit. Any idea how they can be this far apart?

How are you shuffling? If using a cut card, I would expect to see more small cards, and thus higher expected value.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
DogHand
• Posts: 1722
Joined: Sep 24, 2011
October 30th, 2017 at 7:39:02 AM permalink
Wizard,

Ok... I ran another sim to check for "other" outcomes.

Here is a table with the Wizard's results, Dog Hand's results, and the Difference (Wizard - Dog Hand):

Event Wizard Dog Hand W-DH
Dealer blackjack 0.047489488 0.0474169 0.0000726
Total of 17 0.133763556 0.1226878 0.0110758
Total of 18 0.127769103 0.1294826 -0.0017135
Total of 19 0.122183591 0.1239091 -0.0017255
Total of 20 0.168019932 0.1696117 -0.0015917
Total of 21 0.061376129 0.0631546 -0.0017784
Bust 0.200840473 0.2033319 -0.0024914
Any 16 0.138557728 0.1404054 -0.0018477
16 with 2 cards 0.076923077 0.0768894 0.0000337
16 with 3 cards 0.047738425 0.0487376 -0.0009992
16 with 4 cards 0.01200894 0.0126890 -0.0006801
16 with 5 cards 0.001730969 0.0019062 -0.0001753
16 with >5 cards 0.000156317 0.0001813 -0.0000250

Still puzzled. Wiz has slightly more dealer BJ's and 2-card 16's (probably because the sim is a sim) but significantly more dealer 17's.

Wizard, are you sure your dealer is hitting on soft 17?

Dog Hand

P.S. Oh, beachbumbabs: both the Wizard and I used 6-deck shoes.
Romes
• Posts: 5607
Joined: Jul 22, 2014
October 30th, 2017 at 11:45:52 AM permalink
Curious if anyone tries an "even/odd count" and only bets this when the even or odd count is off far in either direction. If only even cards remain, the dealer will draw to even totals. If only odd remain, the dealer will draw to even totals every 2 cards. Otherwise I suppose you could do a count where 10's and 6's are important against all others. I don't mind sharing these random thoughts because I've never heard of or even seen this bet AND more importantly I don't think these two off the top of the head suggestions are the right way to go about anything anyways. Just think they would make for some fun maths and discussion.
Playing it correctly means you've already won.
• Posts: 4
Joined: Oct 27, 2017
October 30th, 2017 at 1:37:59 PM permalink
I would love to know these kind of things! Just like Bust it Blackjack bring so vulnerable, possible this one is. Its a 6 Deck shoe game here too.
miplet
• Posts: 2128
Joined: Dec 1, 2009
October 30th, 2017 at 2:45:23 PM permalink
Wizard, where is your 11 card 16 of 5 aces followed by a 2 ,5,then 4 more aces?
HandProbability
bj0.047489488
170.122636962
180.12945526
190.12391232
200.169754564
210.063106966
bust0.203347259
16 2 card0.076923077
16 3 card0.048657576
16 4 card0.012639555
16 5 card0.001896262
16 6 card0.000170876
16 7 card9.50695E-06
16 8 card3.21501E-07
16 9 card5.99712E-09
16 10 card5.13691E-11
16 11 card1.19773E-13
“Man Babes” #AxelFabulous
Donuts
• Posts: 171
Joined: Oct 17, 2014
October 30th, 2017 at 2:51:09 PM permalink
Deleted - Double post
Donuts
• Posts: 171
Joined: Oct 17, 2014
October 30th, 2017 at 2:51:34 PM permalink
Quote: Wizard

The problem is they are not far apart enough. These small differences are hard to track down who is in error and why. I speculate that the rule about standing on a soft 16, while hitting a soft 17, has something to do with it.

For what its worth, my results are recursive in nature so should be exactly right, save programmer error, which is a distinct possibility.

It might help if you also output the other events, like dealer ending up with 17-21, blackjack, or busting, just so we have more to compare against.

Curious if you ever share your code?

I've done a few simulations on various games but they results are always off by a bit due to random error - similar to the guy you quoted.
Wizard
• Posts: 26842
Joined: Oct 14, 2009
Thanked by
October 30th, 2017 at 3:01:30 PM permalink
Quote: miplet

Wizard, where is your 11 card 16 of 5 aces followed by a 2 ,5,then 4 more aces?

Miplet, did I ever mention that you're worth your weigh in palladium?

In checking my code, I was indeed standing on a soft 17, despite my intention. Here are my updated tables.

Event Pays Probability Return
16 with 6+ cards 100 0.000181 0.018071
16 with 5 cards 50 0.001896 0.094813
16 with 4 cards 10 0.012640 0.126396
16 with 3 cards 5 0.048658 0.243288
16 with 2 cards 3 0.076923 0.230769
All other -1 0.859703 -0.859703
Total 1.000000 -0.146366

Event Probability
Dealer blackjack 0.047489488
Total of 17 0.122636962
Total of 18 0.12945526
Total of 19 0.12391232
Total of 20 0.169754564
Total of 21 0.063106966
Bust 0.203347259
16 with 2 cards 0.076923077
16 with 3 cards 0.048657576
16 with 4 cards 0.012639555
16 with 5 cards 0.001896262
16 with 6 cards 0.000170876
16 with 7 cards 9.50695E-06
16 with 8 cards 3.21501E-07
16 with 9 cards 5.99712E-09
16 with 10 cards 5.13691E-11
16 with 11 cards 1.19773E-13
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
miplet
• Posts: 2128
Joined: Dec 1, 2009
Thanked by
October 30th, 2017 at 3:34:02 PM permalink
Quote: Donuts

Curious if you ever share your code?

I've done a few simulations on various games but they results are always off by a bit due to random error - similar to the guy you quoted.

I sometimes share my code. Because I’m evil, I used php to build a spreadsheet. It’s Recycled code from when I did some busting side bet. You can see it at http://miplet.net/buster/16.phps . Sorry for lack of comments.

I’ll post my final spreadsheet later. You’ll be able to edit the deck composition and pay table.
“Man Babes” #AxelFabulous
DogHand
• Posts: 1722
Joined: Sep 24, 2011
October 31st, 2017 at 7:03:28 AM permalink
Quote: Wizard

How are you shuffling? If using a cut card, I would expect to see more small cards, and thus higher expected value.

Wizard,

You are correct: I was using a fixed 75% penetration.

I re-ran the sim, this time using a fixed 50-round shoe. Here are the results:

No Cut Card Effect:
Oucome Pays Probability Return
>5-card 100 0.00018019 0.018019
5-card 50 0.00189434 0.094717
4-card 10 0.01263906 0.126391
3-card 5 0.04865155 0.243258
2-card 3 0.07692357 0.230771
No 16 -1 0.85971130 -0.859711
EV 1.00000000 -0.146557

This new EV alue agrees with the -0.146366 value you posted after fixing the S17 bug.

Dog Hand
DogHand
• Posts: 1722
Joined: Sep 24, 2011
November 5th, 2017 at 2:33:57 PM permalink
Folks,

Just for kicks, using eleven 400-million-round CVData sims I calculated the EoR for this Bonus 16 sidebet: the EoR's are shown in the table below, along with the level 2 tags that can be used to count the SB. The IBA column gives the IBA for the Full 6D shoe (with the cut card effect, to simulate a real shoe) in the "Full" row: the succeeding rows are for a shoe depleted by six of the indicated rank. The EoR is simply one-sixth of the difference between the depleted shoe's IBA and the Full IBA.

Shoe IBA EoR Tags 2
Full -14.49%
-6 A's -18.13% -0.61% -1
-6 2's -19.57% -0.85% -2
-6 3's -17.57% -0.51% -1
-6 4's -16.18% -0.28% -1
-6 5's -14.84% -0.06% 0
-6 6's -17.53% -0.51% -1
-6 7's -12.93% 0.26% 0
-6 8's -12.27% 0.37% 1
-6 9's -12.27% 0.37% 1
-6 X's -11.54% 0.49% 1

I was frankly surprised at the magnitude of the EoR for the deuce: off-hand, I would have guessed those for the six and ten would have been the highest. In retrospect, I suppose the relatively large bonuses for multicard 16's helped sway the value of the lowly deuce.

I then ran two CVData sims for the SB: in the first, I found the trigger count to be +5. Below is the SB IBA as a function of the TC (calculated with the tags given above, of course). I chopped off the extremely high TC's: these accounted for fewer than 10,000 rounds in all.

Units Bet # Won EV WR
TOT
33,742,185
5,214,655
5.64%
\$23.79
17
11,236
2,008
52.65%
\$0.07
16
25,285
4,391
43.84%
\$0.14
15
46,993
8,075
39.20%
\$0.23
14
94,280
15,794
37.75%
\$0.44
13
174,363
29,145
30.21%
\$0.66
12
337,654
56,107
27.31%
\$1.15
11
586,313
96,116
21.96%
\$1.61
10
1,039,063
168,156
18.31%
\$2.38
9
1,757,215
281,010
14.06%
\$3.09
8
3,062,732
482,476
10.50%
\$4.02
7
4,967,528
772,225
7.18%
\$4.46
6
8,210,828
1,263,004
4.06%
\$4.16
5
13,419,099
2,034,492
0.78%
\$1.31

The sim ran 800-million rounds at 75% penetration, so as you can see the SB is +EV about 4.2% of the time. The Win Rates shown are for flat-betting \$100 on any +EV round.

Naturally, deeper penetration would provide additional +EV betting opportunities, and so would lead to higher WR's.

Now, go crush 'em! ;-)

Dog Hand
• Posts: 4
Joined: Oct 27, 2017
November 6th, 2017 at 1:44:05 AM permalink
Heres a question when it comes to the game itself Double Up. We know by Wizard, the odds of Double Up is .32% house advantage which is extremely small. What would the indexes be for the Basic Strategy depending on the count?
For instance, 18 vs 5, Double Up. But 18 vs 4 is a stay. What does the count have to be for us to Double Up, and how much of an edge do i gain? Anyway you stat and calc wizards can do that?
Im only asking for the really close ones.
9 vs 3, DD?
18 vs 4 DU?
Soft 18 vs 3 DD?
20 vs 10 when do you stay instead of DU?
Is there anytime you DU with a 17?
odiousgambit
• Posts: 9691
Joined: Nov 9, 2009
November 6th, 2017 at 3:33:01 AM permalink
Quote: Wizard

Miplet, did I ever mention that you're worth your weigh in palladium?

Quite a compliment, Miplet ... I am in a silly mood at the moment, so ...

it is \$998 per oz at the moment; if M. is average US weight of 195.7 pounds and it is troy ounces on the chart like I suspect, then such an average guy would be worth \$2,847,599.388

195.7 * 14.58 * 998

PS: come to think of it, is he not worth his weight in gold? \$3,627,122.587
PPS: looking into it, some of the metal superstars have come down lately while gold is holding. Recent article in WSJ indicates the speculators are going for bitcoin these days, hurting speculation in metals

the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
odiousgambit
• Posts: 9691
Joined: Nov 9, 2009
November 6th, 2017 at 3:50:48 AM permalink
Perhaps the bigger compliment today would puzzle folks,

Miplet, I think you are as valuable as an asteroid!

https://www.space.com/19758-asteroid-worth-billions-2012-da14-flyby.html
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
DogHand
• Posts: 1722
Joined: Sep 24, 2011
November 21st, 2017 at 7:39:48 AM permalink
Quote: miplet

I sometimes share my code. Because I’m evil, I used php to build a spreadsheet. It’s Recycled code from when I did some busting side bet. You can see it at http://miplet.net/buster/16.phps . Sorry for lack of comments.

I’ll post my final spreadsheet later. You’ll be able to edit the deck composition and pay table.

miplet,

Dog Hand
miplet
• Posts: 2128
Joined: Dec 1, 2009
November 21st, 2017 at 9:02:30 AM permalink
Quote: DogHand

miplet,

Dog Hand

I’m having problems getting it to upload to my website. Try this link https://1drv.ms/x/s!An-wpe6448nOgw7N0DUiy_F9Ei_J , but I don’t know if it will work.
“Man Babes” #AxelFabulous
Wizard
• Posts: 26842
Joined: Oct 14, 2009
February 23rd, 2022 at 5:22:48 PM permalink
I just saw this game at the Four Queens yesterday. They follow the more liberal 4-5-10-50-100 pay table.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
DogHand
• Posts: 1722
Joined: Sep 24, 2011
March 20th, 2022 at 2:05:33 PM permalink
Quote: miplet

Quote: DogHand

miplet,

Dog Hand

I’m having problems getting it to upload to my website. Try this link https://1drv.ms/x/s!An-wpe6448nOgw7N0DUiy_F9Ei_J , but I don’t know if it will work.