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!

What is a '16 push'?Quote:AdikarIf the Dealer gets a 16 Push...

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

Next.

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.Quote:DJTeddyBearWhat is a '16 push'?

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

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.

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 |

Quote:WizardI 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.

<snip>

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

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

Quote:DogHandOur 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.

JMVHO.

Quote:DogHandOur 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.

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.

Hand | Probability |
---|---|

bj | 0.047489488 |

17 | 0.122636962 |

18 | 0.12945526 |

19 | 0.12391232 |

20 | 0.169754564 |

21 | 0.063106966 |

bust | 0.203347259 |

16 2 card | 0.076923077 |

16 3 card | 0.048657576 |

16 4 card | 0.012639555 |

16 5 card | 0.001896262 |

16 6 card | 0.000170876 |

16 7 card | 9.50695E-06 |

16 8 card | 3.21501E-07 |

16 9 card | 5.99712E-09 |

16 10 card | 5.13691E-11 |

16 11 card | 1.19773E-13 |

Quote:WizardThe 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.

Quote:mipletWizard, 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 |

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

Quote:WizardHow 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

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

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?

Quote:WizardMiplet, 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

https://www.google.com/search?source=hp&ei=ykUAWuuuN8-CjwPqkqv4Cg&q=average+male+us+weight&oq=average+male+us&gs_l=psy-ab.1.2.0l5j0i22i30k1l5.321.4200.0.9642.16.11.0.0.0.0.2080.2827.6-1j9-1.2.0....0...1.1.64.psy-ab..14.2.2826.0..0i131k1j0i20i264k1.0.7A_w3Bwva30

http://www.kitco.com/charts/livepalladium.html

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

https://www.space.com/19758-asteroid-worth-billions-2012-da14-flyby.html

Quote:mipletI 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,

Have you posted your final spreadsheet on this yet?

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.Quote:DogHandmiplet,

Have you posted your final spreadsheet on this yet?

Dog Hand

Quote:mipletI’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.Quote:DogHandmiplet,

Have you posted your final spreadsheet on this yet?

Dog Hand

link to original post

miplet,

I finally saw your post, thanks to the Wiz reviving this thread. The link worked fine for me... Thanks!

Dog Hand