Suited Trips on 21+3

What are the odds of the players first 2 cards and dealer up card are suited trips? Thanks for your help.

Quote: Rovert22

What are the odds of the players first 2 cards and dealer up card are suited trips? Thanks for your help.

How many decks?

Quote: Mission146

How many decks?

Standard I've seen is 6 deck. Probably also available in 8 deck.

Quote: beachbumbabs

Standard I've seen is 6 deck. Probably also available in 8 deck.

Thanks, I probably could have just done it for both. The first card can be anything.

Six-Decks: (1 * 5/311 * 4/310) = 0.00020744736 or 1/0.00020744736 = 1 in 4,820.50

Eight Decks: (1 * 7/415 * 6/414) = 0.00024445608 or 1/0.00024445608 = 1 in 4,090.7143729

The reason it is more likely with eight decks is because the effect-of-removal isn't as great. Let's say the card is an Ace of Spades, the percentage of Aces of Spades to start the show is always 0.01923076923, or 1.923076923%, but with six decks:

5/311 = 0.01607717041, so 1.607717041% of the remaining cards are Aces of Spades after one has been taken away.

4/310 = 0.0129032258, so 1.29032258% are after two have been taken away.

With eight decks:

7/415 = 0.01686746987, so 1.686746987% are after one is taken away.

6/414 = 0.01449275362 so 1.449275362% are after two have been taken away.

Even small differences become pretty meaningful when the Ace of Spades becomes the specific card you want.

I just found this?? Which one is correct? Thanks for your help.

For blackjack, which is the probability to obtain three suited seven in a 6 deck shoe.

I attempt to work this out in my blackjack appendix 8 but I’ll work through it more slowly here. We’ll ignore dealer blackjacks to keep things simple and assume the player always hits after two cards. The number of ways to arrange 3 cards in a 6-deck shoe is combin(312,3)=5,013,320. There are 24 sevens in the shoe. The number of ways to arrange 3 sevens out of 24 is combin(24,3)=2024. The probability is the number of winning combinations divided by total combinations, or 2024/5013320=0.0004, or about 1 in 2477.

You didn’t specify sevens in the OP.

Anyway, why are you using combinatorics for this? A much blunter tool will get the job done.

There are 312 cards in the shoe, 24 are sevens, but once a seven comes out, only five other sevens match it.

(24/312 * 5/311 * 4/310) = .00001595748

1/.00001595748 = 1 in 62,666.5363203

You’ll notice that’s roughly the six-deck result in my previous post for any trips multiplied by thirteen, and that’s because there are thirteen ranks.

You had the right general idea with your combinatorics to figure out three sevens, but your equation did nothing to specify they be suited.

Mission thanks again for your help.
Basically I just wanted to know the odds of hitting the top bet award on TriLux super bet +3. The casinos pay 270 to 1. Its the players first 2 cards and the dealers up card. 6-Deck shoe..

Suited trips 270-1
Straight Flush 180-1
Trips90-1.

Thanks again.