KrazyKurt
KrazyKurt
  • Threads: 2
  • Posts: 11
Joined: Feb 20, 2024
February 27th, 2024 at 9:46:28 AM permalink
I am trying to figure out how many possible combinations there are for a 6-card 0 to 0 tie that consists of 6 zero value cards; 8 deck Baccarat.

There are 128 Zero Value cards in a 8 deck shoe; 10s, Jack's, Queens, Kings

Currently, I have the probability as follows:
P(x)=(128÷416)×(127÷415)×(126÷414)×(125÷413)×(124÷412)×(123÷411) = 0.0007812503

First question, is that calculation above correct?

The main question, can I take P(x) times the total possible outcomes in a 8-deck shoe to get the answer I'm looking for? Or, is this a much more complicated problem?

Thanks!
Mental
Mental
  • Threads: 13
  • Posts: 1292
Joined: Dec 10, 2018
February 27th, 2024 at 10:28:42 AM permalink
Quote: KrazyKurt

I am trying to figure out how many possible combinations there are for a 6-card 0 to 0 tie that consists of 6 zero value cards; 8 deck Baccarat.

There are 128 Zero Value cards in a 8 deck shoe; 10s, Jack's, Queens, Kings

Currently, I have the probability as follows:
P(x)=(128÷416)×(127÷415)×(126÷414)×(125÷413)×(124÷412)×(123÷411) = 0.0007812503

First question, is that calculation above correct?

The main question, can I take P(x) times the total possible outcomes in a 8-deck shoe to get the answer I'm looking for? Or, is this a much more complicated problem?

Thanks!
link to original post


I am not clear on what answer you are looking for. You already have the probability that the first 6 cards off the deck are among the ranks T,J,Q,K:
(128 choose 6)/(416 choose 6) = 0.00078125028
If just typed (128 choose 6)/(416 choose 6) into the google search bar to get this answer.
This forum is more enjoyable after I learned how to use the 'Block this user' button.
KrazyKurt
KrazyKurt
  • Threads: 2
  • Posts: 11
Joined: Feb 20, 2024
February 27th, 2024 at 10:45:46 AM permalink
I am trying to find the total number of possible combinations for a 6-card All Zero Value Tie.
unJon
unJon 
  • Threads: 14
  • Posts: 4597
Joined: Jul 1, 2018
February 27th, 2024 at 10:46:16 AM permalink
What is a combination? For example there are 8 king of diamond cards. Is each identical or distinct for counting combos? Does order matter for all three cards in a hand or just for the third card?

Or do you mean permutations?
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
unJon
unJon 
  • Threads: 14
  • Posts: 4597
Joined: Jul 1, 2018
February 27th, 2024 at 12:05:29 PM permalink
If you mean permutations where every card is distinct and the order of each card matters then you just need the numerator of your probability equation.

128x127x126x125x124x124

If some of those permutations should be treated as ďidenticalĒ (see my post above) then you need to find the right denominator as well.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
gordonm888
Administrator
gordonm888
  • Threads: 60
  • Posts: 5049
Joined: Feb 18, 2015
February 27th, 2024 at 12:10:53 PM permalink
You are missing multicard combos that add up to zero, such as:

64|73-K|K

or

12|12-7|7
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
KrazyKurt
KrazyKurt
  • Threads: 2
  • Posts: 11
Joined: Feb 20, 2024
February 27th, 2024 at 12:13:41 PM permalink
Quote: gordonm888

You are missing multicard combos that add up to zero, such as:

64|73-K|K

or

12|12-7|7
link to original post



I am not interested in those. I only care about All Zero Value Ties consisting of 6 cards.
So Player and Banker have 3 cards each, and those 3 cards are all Zero Value.
KrazyKurt
KrazyKurt
  • Threads: 2
  • Posts: 11
Joined: Feb 20, 2024
February 27th, 2024 at 12:19:31 PM permalink
Quote: unJon

What is a combination? For example there are 8 king of diamond cards. Is each identical or distinct for counting combos? Does order matter for all three cards in a hand or just for the third card?

Or do you mean permutations?
link to original post



Let me see if I can explain this in a different way since I'm not an expert with statistics. Hopefully this will clear up my question.

In a 8 deck shoe there are 475,627,426,473,216 possible Tie combinations. I want to know out of those possible combinations, how many are a 0 to 0 Tie with all 6 cards being a Zero Value card.

Total combinations in a 8 deck Baccarat shoe are 4,998,398,275,503,360. This info can be found at /games/baccarat/basics/#eight-deck-analysis
unJon
unJon 
  • Threads: 14
  • Posts: 4597
Joined: Jul 1, 2018
February 27th, 2024 at 12:23:20 PM permalink
Never mind.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
KrazyKurt
KrazyKurt
  • Threads: 2
  • Posts: 11
Joined: Feb 20, 2024
February 27th, 2024 at 12:33:12 PM permalink
Quote: unJon

Never mind.
link to original post



Did I not explain it well enough or is it too difficult lol?
unJon
unJon 
  • Threads: 14
  • Posts: 4597
Joined: Jul 1, 2018
February 27th, 2024 at 12:50:43 PM permalink
Quote: KrazyKurt

Quote: unJon

Never mind.
link to original post



Did I not explain it well enough or is it too difficult lol?
link to original post



No itís all good. Your numbers indicate you are looking for permutations not combinations. So the answer you want is 128! / 122! = 3,905,000,064,000
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
KrazyKurt
KrazyKurt
  • Threads: 2
  • Posts: 11
Joined: Feb 20, 2024
February 27th, 2024 at 12:56:27 PM permalink
Quote: unJon

Quote: KrazyKurt

Quote: unJon

Never mind.
link to original post



Did I not explain it well enough or is it too difficult lol?
link to original post



No itís all good. Your numbers indicate you are looking for permutations not combinations. So the answer you want is 128! / 122! = 3,905,000,064,000
link to original post



WOW!!! That's awesome! Thanks man!!

Are you able to explain how the denominator is 122!?
KrazyKurt
KrazyKurt
  • Threads: 2
  • Posts: 11
Joined: Feb 20, 2024
February 27th, 2024 at 12:58:22 PM permalink
Or at least a website that explains that. I've been trying to figure this out for a couple days lol
unJon
unJon 
  • Threads: 14
  • Posts: 4597
Joined: Jul 1, 2018
February 27th, 2024 at 1:00:25 PM permalink
Quote: KrazyKurt

Or at least a website that explains that. I've been trying to figure this out for a couple days lol
link to original post



Itís just:

128 x 127 x 126 x 125 x 124 x 123

ETA: you would get the same answer if you take the total permutations of all hands in an 8 deck shoe from your post above multiplied by the probability of getting a zero tie with all zeroes from your first post.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
  • Jump to: