Table Blackjack Side bet

I was wondering if there’s a way to figure out the return for the Trilux Super 3 side bet for table blackjack.

It is like many other bj side bets where you use both your cards and the dealer up card, here are the payouts.

3 of a kind (suited) 270-1
Straight flush 180-1
3 of a kind 90-1

I would like to see the math behind the house edge on this side bet for a 6 deck shoe, and if it’s not too hard an 8 deck shoe aswell.

Thanks!

Wizard has a similar game but the payouts are much lower. Hopefully someone can help explain the game.

Welcome to the forum.

If I'm reading this correctly, Trilux Super 3 is a subsidiary side bet which can only be placed if the main Trilux sidebet is placed.

edit: I believe the official name is Trilux Bonus.

See Top-3. http://www.ukcasinotablegames.info/blackjacktop3.html

Top 3 is an additional wager that the first two cards dealt to a player, combined with the first card dealt to the dealer, will make a three card poker hand against the following list of winning hands:-

Three of a Kind 90 to 1
Straight Flush 180 to 1
Three of a Kind Suited 270 to 1

Quote: MrCasinoGames

...See Top-3. http://www.ukcasinotablegames.info/blackjacktop3.html...

I agree that's where I'd have pointed you. The sidebet was, it might still be, available for small wagers in some Grosvenor casinos. It provides a nice payout to accompany the 21+3 bet (see https://wizardofodds.com/games/blackjack/side-bets/21plus3/ ) Where I saw it you could place either "21+3" or "Top 3" or both in addition to your main BJ bet and I think there was another sidebet option.

Sounds like a major sucker bet to me. Stick to house money or pair square if you are
playing BJ in my opinion. Getting pairs and straight flushes are hard enough with two cards.

Pair square suited pairs happen 1/60 hands and pay 15-1: pairs happen 1/16 hands and pay 10-1.

House money from my experience. pairs only pay 3-1 and straight flushes only 4-1 unless you hit
A-K suited for the 9-1 (which odds are 1/60). With house money you can add your side bet winnings
into your main bet also up to the table max of course. Which I do if I hit a 20 or 21 or sometimes as
low as 18 depending on what the dealer is showing...

Still hitting 90-1 on a $5 bet would still be 450 but odds are around 1/16*1/13 probably once out of
every 208 hands and most houses will cap the side bets at table max anyways...

Good luck !!!

Quote: Brandon32

I was wondering if there’s a way to figure out the return for the Trilux Super 3 side bet for table blackjack.

It is like many other bj side bets where you use both your cards and the dealer up card, here are the payouts.

3 of a kind (suited) 270-1
Straight flush 180-1
3 of a kind 90-1

I would like to see the math behind the house edge on this side bet for a 6 deck shoe, and if it’s not too hard an 8 deck shoe aswell.

Thanks!
link to original post

The first thing that we would want to do is determine the probability of getting a three-of-a-kind, which is going to be pretty easy. We have:

52 * 6 = 312 Cards

Cards per Rank: 24

Suited Cards per Rank: 6

The first card that comes out is completely irrelevant, so that leaves us with needing:

(23/311) * (22/310) = 0.00524841821

From that, we will want to subtract out the suited Trips as they pay differently. The same principle applies, so the first card doesn't matter and we are left with:

(5/311) * (4/310) = 0.00020744736

Probability Suited Trips: 0.00020744736

Probability Unsuited Trips: 0.00524841821 - 0.00020744736 = 0.00504097085

After that, we just multiply the pays to get the return. I'm assuming the pays are on a "To One," basis:

Suited Trips Return: 0.00020744736 * 270 = 0.0560107872

Unsuited Trips Return: 0.00504097085 * 90 = 0.4536873765

It's sometimes easier to use work that has already been done, so the SF for this bet will have the same probability as six-decks 21+3 bet, which can be found on Wizard of Odds here:

https://wizardofodds.com/games/blackjack/side-bets/21plus3/

The probability is 0.002068 and we multiply by 180 pays to get return of 0.37224

In order to arrive at the House Edge, we simply subtract the sum of returns from 1:

1 - (.0560107872 + .4536873765 + .37224) = 0.1180618363

Thereby reflecting a House Edge of 11.80618%, which is terrible, though I have seen much worse on a side bet.

I know you didn't ask, but the hit rate is:

1/(0.00504097085+0.00020744736+0.002068) = 1 in about 136.6789

Thank you this is exactly what I was trying to figure out, very helpful!!