SuperNatural
SuperNatural
Joined: Dec 22, 2020
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October 23rd, 2021 at 7:17:52 PM permalink
I am trying to find the house edge for this side bet .. 21st Century Baccarat v10.0

LUCKY MATCH PAY TABLE
WINNING HANDS PAYS
5 OR 6 OF A KIND 250 - 1
DOUBLE TRIPLETS 100 - 1
4 OF A KIND 30 - 1
FULL HOUSE 15 - 1
3 OF A KIND 6 - 1
2 OR 3 PAIRS 4 - 1

"The Lucky Match wager takes into account the cards in the bankerís hand and the cards in the playerís hand. If a player wagers on the Lucky Match Bonus Bet and the cards in bankerís hand in combination with the cards in the playerís hand make a qualifying hand as described below, the Lucky Match Bonus Bet wager shall win. For example, if the bankerís hand is composed of 2-K-4 and the playerís hand is composed of 4-K-4, then the Lucky Match Bonus Bet wager wins and is paid 15 to 1. A pair must be formed by two cards of the same rank, a Jack and a King canít form a pair even though they have the same value of 0. Note that a 4-of-a-kind and a pair will be paid as a 4-of-a-kind."

I ran a 1 billion round sim and have a 8.87% HE.

Combinatorial analysis resulted in a 9.71% HE.

I can't post links/images due to my post count.

Any idea where I erred? Hoping someone out there has a solid number. Thanks in advance.
gordonm888
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gordonm888
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October 24th, 2021 at 7:49:38 AM permalink
The analysis of this sidebet seems to me to be a bit tricky, because sometimes the banker and/or the player will stand on their first two cards. So you will never have "6 of a kind" of 4's, for example, and never have a full-house when both banker and player stand. Did you correctly take that into account?
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
Marcusclark66
Marcusclark66
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October 24th, 2021 at 8:15:59 AM permalink
Quote: gordonm888

The analysis of this sidebet seems to me to be a bit tricky, because sometimes the banker and/or the player will stand on their first two cards. So you will never have "6 of a kind" of 4's, for example, and never have a full-house when both banker and player stand. Did you correctly take that into account?
link to original post



Looking back at my scorecards I have 24 hands identified for four different shoes Iím looking at.

First one is seven hands of six cards pulled, nine hands of five cards pulled, and eight hands of four cards pulled for 24 consecutive hands.

The second one is six hands of six cards pulled, nine hands of five cards pulled and nine hands for four cards pulled for 24 consecutive hands.

The third shoe was eight hands of six cards pulled, twelve hands of five cards pulled and four hands of four cards pulled for 24 consecutive hands.

The fourth shoe was six hands of six cards pulled, five hands of five cards pulled and thirteen hands of four cards pulled for 24 consecutive hands.
Marcus Clark. Real Person; AKA MarcusClark66. *Professional Casino Security Expert. *Certified EMT *Certified Company Firearms Instructor. *Certified Gaming Regulations Interpreter for Corporate Applications. *Domestic UrbanTactical Combat Casualty Expert. *Tic-Tac-Toe Expert (Real Competitive Versions) & Mastering Chess. *Honorary & Official #1 Fan of the MDawg Adventures Club. *Mastering Cracking it. Bit-by-Bit, Piece-by-Piece Crediting Forum Members. *Certified Casino Property Entry & Exit Point Analyzer *Baccarat Winning Session Record: 12 out of 12 & 1 out of 1 Mini Session. Baccarat Losing Session Record: 2 Losing Sessions.
Marcusclark66
Marcusclark66
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October 24th, 2021 at 8:16:03 AM permalink
Delete. Double posting.
Marcus Clark. Real Person; AKA MarcusClark66. *Professional Casino Security Expert. *Certified EMT *Certified Company Firearms Instructor. *Certified Gaming Regulations Interpreter for Corporate Applications. *Domestic UrbanTactical Combat Casualty Expert. *Tic-Tac-Toe Expert (Real Competitive Versions) & Mastering Chess. *Honorary & Official #1 Fan of the MDawg Adventures Club. *Mastering Cracking it. Bit-by-Bit, Piece-by-Piece Crediting Forum Members. *Certified Casino Property Entry & Exit Point Analyzer *Baccarat Winning Session Record: 12 out of 12 & 1 out of 1 Mini Session. Baccarat Losing Session Record: 2 Losing Sessions.
SuperNatural
SuperNatural
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October 24th, 2021 at 8:34:04 AM permalink
Yes, I had to use the entire bacc universe of 302,500 possible 6 card hands to accomplish this. I first check each row for 4, 5 or 6 cards used and only evaluate those.

Here are my numbers for the sim and CA ..(I included a single pair just for checking)

5 or 6 of a Kind 71,873
Double Trips 123,004
4 of a Kind 2,454,014
Full House 8,010,490
3 of a Kind 41,583,707
2 or 3 Pairs 77,099,663
Pair 423,214,861
Other 447,442,388
1,000,000,000

5 or 6 of a Kind 330,651,336,960
Double Trips 580,991,385,600
4 of a Kind 11,880,028,677,120
Full House 38,888,044,339,200
3 of a Kind 208,563,763,445,760
2 or 3 Pairs 384,191,087,149,056
Pair 2,118,892,793,102,336
Other 2,235,070,916,067,328
4,998,398,275,503,360
gordonm888
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gordonm888
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Thanks for this post from:
SuperNatural
October 24th, 2021 at 1:23:47 PM permalink
Quote: SuperNatural

Yes, I had to use the entire bacc universe of 302,500 possible 6 card hands to accomplish this. I first check each row for 4, 5 or 6 cards used and only evaluate those.

Here are my numbers for the sim and CA ..(I included a single pair just for checking)

5 or 6 of a Kind 71,873
Double Trips 123,004
4 of a Kind 2,454,014
Full House 8,010,490
3 of a Kind 41,583,707
2 or 3 Pairs 77,099,663
Pair 423,214,861
Other 447,442,388
1,000,000,000

5 or 6 of a Kind 330,651,336,960
Double Trips 580,991,385,600
4 of a Kind 11,880,028,677,120
Full House 38,888,044,339,200
3 of a Kind 208,563,763,445,760
2 or 3 Pairs 384,191,087,149,056
Pair 2,118,892,793,102,336
Other 2,235,070,916,067,328
4,998,398,275,503,360
link to original post



Okay, I've taken a shot at calculating the number of combinations that are 4oak.

There are 4,998,398,275,503,360 total combinations.

4oak, TTTT-KKKK: 4,696,705,105,920 combinations

4oak, 2222- 9999: 7,577,256,453,120 combinations

Total 4oak: 12,273,961,559,040 combinations, 0.002455579


So, that's a slightly higher number than your combination analysis but is in good agreement with your simulation.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
DogHand
DogHand
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Thanks for this post from:
SuperNatural
October 24th, 2021 at 2:07:07 PM permalink
Quote: SuperNatural

Yes, I had to use the entire bacc universe of 302,500 possible 6 card hands to accomplish this. I first check each row for 4, 5 or 6 cards used and only evaluate those.
<snip> link to original post



SuperNatural,

The (10*9/2)^2*(10)^2 = 302,500 value applies only when all the 0-cards are lumped together, so we have only 10 ranks. If you have to treat all 13 ranks separately, then the number of combinations is (13*12/2)^2*(13)^2 = 1,028,196.

Hope this helps!

Dog Hand
charliepatrick
charliepatrick
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SuperNaturalMrCasinoGames
October 24th, 2021 at 2:22:52 PM permalink
I get slightly different numbers (though I haven't checked the logic just that they add up to the correct total), the T6 number does correspond to 9*32*31*30*39*28*27 (2 5 6 7 T J Q K A) and it does get your House Edge of 8,89%.
Overall Result:
T6:5872124160
T5:351070863360
T42:892093378560
T4:11381868180480
T33:616417689600
T32:40022630768640
T3:207858985697280
T222:8980961689600
T22:376313536741376
T2:2115449740328960
T1:2236525098041344
T0:0
Tot:4998398275503360

Return for sidebet:
T6:1473903164160
T5:88118786703360
T42:27654894735360
T4:352837913594880
T33:62258186649600
T32:640362092298240
T3:1455012899880960
T222:44904808448000
T22:1881567683706880
Tot:4554191169181440
PayBack:0.9111301097195609
gordonm888
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gordonm888
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charliepatrick
October 24th, 2021 at 3:18:38 PM permalink
I'm so glad that help has arrived!

Charlie, the sum of your T42 and T4 numbers matches my combination math calculation for 4oak (posted earlier) to all 14 places! Which is a pretty good confirmatory spot-check, since 4oak straddles 4-card, 5-card and 6-card bacarrat hands.

So, I think we should assume CharliePatrick's results are most likely correct.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
charliepatrick
charliepatrick
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October 24th, 2021 at 3:47:10 PM permalink
As it took a while to knock up a quick program I hadn't seen the "afternoon"'s updates when posting my results, but thanks if your figures agree with mine for 4oak; it gives me a warmer feeling.

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