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 banker’s hand and the cards in the player’s hand. If a player wagers on the Lucky Match Bonus Bet and the cards in banker’s hand in combination with the cards in the player’s hand make a qualifying hand as described below, the Lucky Match Bonus Bet wager shall win. For example, if the banker’s hand is composed of 2-K-4 and the player’s 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 can’t 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.

Quote:gordonm888The 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 I’m 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.

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

Quote:SuperNaturalYes, 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.

Quote:SuperNaturalYes, 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

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

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.

All my numbers now agree with charliepatricks.

Thanks all!

Lucky Match Sidebet documentation is also here: Lucky Match Sidebet Rules and Description

Quote:gordonm888The Bicycle Casino in LA offers this sidebet, and their website even has the paytable Bicycle Casino

Lucky Match Sidebet documentation is also here: Lucky Match Sidebet Rules and Description

link to original post

Thank you. I'm on it. I see they have another side bet called the Super Tie. Please follow the link to see my analysis of that. I welcome a second opinion on it.

Double triplets 100 616,417,689,600 0.000123

Four of a kind 30 12,273,961,559,040 0.002456

The main reason is that Doublet triplets has restrictive requirements on teh ranks of all six cards, while 4oak only has restrictive requirements on 4 of 6 cards.

Another reason, though, is that double triplets requires a six card hand (both player and banker draw a card) and there are some combinations of ranks, such as (4,3) and (0,9) that are forbidden to be double triplets by the gameplay rules of Baccarat. Other combinations of ranks are limited in how they can be formed, which lower their probability. For example, a double triplet of (6,0) can be formed by:

P(0,0); D(6,6); 6, 0

but not by

P(0,6); D(0,0). X, X

IMO, its an interesting mathematical system.