Baccarat question

So a few of my friends developed this idea: 4 proposed patterns will be put to the test, and the winner will take the pot. I want to know what the chances are for each happening (and which is most likely) so that I can hopefully win this pot hahaha... The idea is simple: the first pattern to show will win (ties are ignored)

Pattern 1:
6 alternating Player/Banker wins: Either PBPBPB or BPBPBP

Pattern 2:
3 alternating pairs of wins: Either PPBBPP or BBPPBB

Pattern 3:
2 alternating triplet wins: Either PPPBBB or BBBPPP

Pattern 4:
6 wins in a row: Either PPPPPP or BBBBBB

The rules we agreed on also state that the first part of the pattern can be part of a previous streak. So:
PPPP
BB
PPP
this streak of 4 players, then 2 bankers, then 3 players would've counted as a win for Pattern 2

I tried using the "Baccarat Streaks" appendix on the Wizard's site, but I didn't really know how to use it since I'm not too proficient in math. The table we end up watching might be either a normal table or an EZ bacc table... not sure how the different table types will affect the chances

Thanks

Edit: Also, just wondering what the chances are that this will be settled in one shoe (or alternatively, approximately how many shoes will we need to observe before someone wins)? Originally we were going to go for 12 hand patterns instead of 6, but we thought it would likely take forever before anyone got a winning result

Quote: ljg7118

So a few of my friends developed this idea: 4 proposed patterns will be put to the test, and the winner will take the pot. I want to know what the chances are for each happening (and which is most likely) so that I can hopefully win this pot hahaha... The idea is simple: the first pattern to show will win (ties are ignored)

Pattern 1:
6 alternating Player/Banker wins: Either PBPBPB or BPBPBP

Pattern 2:
3 alternating pairs of wins: Either PPBBPP or BBPPBB

Pattern 3:
2 alternating triplet wins: Either PPPBBB or BBBPPP

Pattern 4:
6 wins in a row: Either PPPPPP or BBBBBB

The rules we agreed on also state that the first part of the pattern can be part of a previous streak. So:
PPPP
BB
PPP
this streak of 4 players, then 2 bankers, then 3 players would've counted as a win for Pattern 2

I tried using the "Baccarat Streaks" appendix on the Wizard's site, but I didn't really know how to use it since I'm not too proficient in math. The table we end up watching might be either a normal table or an EZ bacc table... not sure how the different table types will affect the chances

Thanks

Pattern 4 and here's why:

The cards have no memory of who won previously.
Each pattern specified above requires a specific outcome of a specifically numbered hand essentially making all of the patters six in a row.
And since Banker has the best chance of winning any single hand...

Pattern 4, six Bankers in a row.

Quote: s2dbaker

Pattern 4 and here's why:

The cards have no memory of who won previously.
Each pattern specified above requires a specific outcome of a specifically numbered hand essentially making all of the patters six in a row.
And since Banker has the best chance of winning any single hand...

Pattern 4, six Bankers in a row.

If I understand the bet correctly, someone picking pattern 4 would win on PPPPPP or BBBBBB. So he is picking both the most and least likely outcomes.

This symmetry makes me think that all 4 patterns have the same probability of winning, but I must admit that a proof does not immediately come to mind.

deleted

Assuming pushes don't matter.

#1, 0.0312325, 24.977%
#2, 0.0312441, 24.986%
#3, 0.0312325, 24.977%
#4, 0.0313373, 25.061%

So, #4 wins. It will occur first 25.061% of the time.

Quote: s2dbaker

Pattern 4 and here's why:

The cards have no memory of who won previously.
Each pattern specified above requires a specific outcome of a specifically numbered hand essentially making all of the patters six in a row.
And since Banker has the best chance of winning any single hand...

Pattern 4, six Bankers in a row.

While there is a finite number of cards, the dealt cards MAY influence the remaining cards. I think the revelant term is called "effect of removal" and the EOR isn't as great in Bacarrat as in Blackjack. And what gives EOR teeth is the concept of dependency, or stated differently, an 8-deck shoe plays differently than from CSM.

If s2dbaker stated that the game was using a CSM, then I would be more inclined to agree that the cards have no memory.

Quote: teliot

Assuming pushes don't matter.

#1, 0.0312325, 24.977%
#2, 0.0312441, 24.986%
#3, 0.0312325, 24.977%
#4, 0.0313373, 25.061%

So, #4 wins. It will occur first 25.061% of the time.

Very interesting, I assume that it is because the Banker wins more often than player that this is the case, as was previously noted. I bet a significant majority of the public would think that #4 is the least likely of the sets.

Quote: bigfoot66

Very interesting, I assume that it is because the Banker wins more often than player that this is the case, as was previously noted. I bet a significant majority of the public would think that #4 is the least likely of the sets.

Same, I definitely thought pattern 1 would've been the most likely. I'm assuming teliot's math is correct so I'll wager on the 6 consecutives instead. Although, it doesn't seem like any of the patterns has a substantial edge over the others since they're all quite close (less than a tenth of a percentage advantage)

Any ideas on how likely this wager will be settled within 1 shoe? Assuming 8 decks. Or, any idea how many shoes we'll need to sit through before declaring a winner?

Quote: ljg7118

Same, I definitely thought pattern 1 would've been the most likely.
I'm assuming teliot's math is correct so I'll wager on the 6 consecutives instead.

I disagree with teliot conclusion (So, #4 wins.), not his math.

I think teliot answered a different question than what I think you asked in your first post.

His math is for just play 6 non-tie hands in a row and see if there is a winner. If no winner...
Then play 6 more hands and check for a winner.


I read your Q as play a shoe(s) continuously of hands (non-tie)
and the winner is who's sequence first appears, not in just any 6 hands.

This is the classic (variation being no coin toss)
Walter Penney game named Penney Ante from a 1969 math article.

Here is a pdf by RS Nickerson about the concept.
Lots of math and some very non-intuitive stuff about races between sequences or patterns.

Download the free pdf. Google link:
PenneyAnte PDF

The math for this (a race between sequences) is quite complex.
It requires a very large absorbing transition matrix to start, and it does not interest me at all to do this,
maybe someone else wants the challenge.

A simulation is faster and the results are more impressive because most do not understand Markov Chains.

Quote: ljg7118

Although, it doesn't seem like any of the patterns has a substantial edge over the others since they're all quite close (less than a tenth of a percentage advantage)

If you play until a winner is found there IS a clear winner and order of finishings.
If one would just run a simulation, one sees who would win.
(Maybe teliot may do this for you. It is a new year)

I say it is the BBBPPP & PPPBBB sequences because they have no overlaps in them.
The pdf I linked to explains this.

FWIW...
I had run one sim a few years back just with these 6 patterns
(my program only does a max 6 sequences and I am way too lazy to re-do it to answer your exact Q)
#1
BBPPBB
PPBBPP
#2
BBBPPP
PPPBBB
#3
BBBBBB
PPPPPP
add them up...
The results were, as expected,
#1)37.8%
#2)39.4%
#3)22.8%

The sequences
BBBPPP
PPPBBB
each have no overlaps in them and that seems to be a good indicator of wins of a race between many patterns,
unlike just a race between 2 patterns or sequences.
BBPPBB
PPBBPP each have just 2 overlaps in them.


BTW,
for my sim of 6 sequences
the average number of hands (non-tie) until a winner was found is:
18.11 with a standard deviation of 13.15
Hey, Not a normal distribution, a geometric one.

Quote: ljg7118

Any ideas on how likely this wager will be settled within 1 shoe? Assuming 8 decks.
Or, any idea how many shoes we'll need to sit through before declaring a winner?

This is an easier question to answer.
Take the probability in an 8 deck shoe of each sequence NOT occurring and multiply them all together and subtract that answer from 1.

Not happening in one shoe:
0.0006415 or
1 in 1558.785647 non-tie hands

you can check my math if you want
My data from a few sims
Probability of each sequence NOT occurring in an 8 deck shoe (with a 14 card ribbon)
PBPBPB
41.67%
BPBPBP
41.69%
BBBBBB
54.51%
PPPPPP
58.54%
PPBBPP
35.70%
BBPPBB
34.05%
PPPBBB
30.98%
BBBPPP
30.73%

Nice question!
Good Luck

Quote: bigfoot66

Very interesting, I assume that it is because the Banker wins more often than player that this is the case, as was previously noted.
I bet a significant majority of the public would think that #4 is the least likely of the sets.

And #4 (by my simulations) is the least likely of the sequences to win
IF
we play hand after hand and declare the winner to be the first sequence to show, not in just any 6 hands played.

Wow, 7craps thanks for that info... that article looks quite interesting. I hope I'm able to understand it heh

You were also correct in your understanding of my situation. We will be observing a shoe being played at a table and the first pattern to show will be the winner. Unfortunately I've already placed my bet on the 6-in-a-row and can't change it =(

But still interesting... if we do it again I'll be sure not to wager on the same pattern haha

deleted

Quote: ljg7118

Unfortunately I've already placed my bet on the 6-in-a-row and can't change it =(

But still interesting... if we do it again I'll be sure not to wager on the same pattern haha

A one time play as the dog ain't all that bad.
Next time just know better.

Have some sim data in front of you or just play the 3-element Penney Ante game to start that
sodawater showed in his page one post
with a coin flip to get started.
You will always have an advantage if you choose your pattern last and
use the Wizard's method of selecting the winning sequence once your opponent chooses their sequence.

FYI:
Of the 2^6 = 64 possible 6-element B/P sequences
BBBBBP and PBBBBB both have the smallest wait times at 60.63 trials
That is because of no overlaps in the sequence (a sequence concept in wait times)

The longest wait times are
BBBBBB
117.605462 trials
and
PPPPPP
135.157697 trials
from
http://www.pulcinientertainment.com/info/Streak-Calculator-enter.html#ev-patterns

Now, In a race between BBBBBB and BBBBBP
BBBBBB wins (first occurs) about 50.8% of the time.

How much did you wager?
Good Luck!

Nothing crazy, just $50. We each chose one pattern and put $50 each, winner takes all cuz nobody picked the same pattern

I'm still having trouble believing some of the things you've put forward, such as the BBBBBB beating BBBBBP. Essentially that claim would mean I would find more columns of 6 bankers on the scoreboard than I would columns of 5 bankers wouldn't it? Hard to wrap one's head around

I guess that's why I'm not good with math heh... We'll probably be going sometime this weekend to settle the bet. I did a couple shoes from online sims and it looks like the other patterns are more prevalent... I'll be crossing my fingers

BBBBBB is more likely than BBBBBP because B is more likely than P and each round is nearly independent from the previous round.

but don't fall into wrong conclusions. While a *specific* 5 bankers sequence is less likely than a specific 6 bankers sequence, finding 5 bankers in a given number of rounds is more likely - because there are more possible 5 bankers patterns than 6 bankers in a given number of rounds.

Quote: ljg7118

Nothing crazy, just $50. We each chose one pattern and put $50 each, winner takes all cuz nobody picked the same pattern

Just have fun with it and Good Luck

Quote: ljg7118

I'm still having trouble believing some of the things you've put forward, such as the BBBBBB beating BBBBBP.
Essentially that claim would mean I would find more columns of 6 bankers on the scoreboard than I would columns of 5 bankers wouldn't it? Hard to wrap one's head around

Not that hard.
As I put forth the "wait time" or average number of trials for BBBBBB is about 118 Vs. 61 for BBBBBP or PBBBBB.

When it comes to a race for just the 2 sequences
a clinch state becomes more important for most sequences, the pdf talks about it.
It took me about a month to finally get it and I ran may sims to prove the math was correct.
Many math guys still do not grasp the Walter Penney Ante game concept of sequence races. (coin flipping races)

Here is one.
HH Vs. TH
In any 2 coin flips it is a coin toss...
But, Keep Flipping until one shows first. (avg length of the game is just 3 flips)
Wait times are 6 and 4 trials

But the TH kicks ass and wins 75% of the time
That is 3 to 1
You could make good money on that bet until your opponent figures it out.
There is even a 4-element sequence that beats a 3-element sequence.
Lots of cool surprises in the Penney Ante game.

Some one should turn that into a casino game. Maybe JB for some Bac sequences...

Quote: ljg7118

We'll probably be going sometime this weekend to settle the bet. I did a couple shoes from online sims and it looks like the other patterns are more prevalent... I'll be crossing my fingers

I played a shoe at the WoO and the winning sequence was PPBBPP
Twice it was almost BPBPBP, but almost does not win.

added: In a race between PPBBPP and BPBPBP it is PPBBPP winning about 53% of the time
avg wait time
PPBBPP: 71.9
BPBPBP: 84.0
It is not always the lower wait time sequence that will win a race between 2 sequences.
In this case it is.

Have fun!

Quote: 7craps

I played a shoe at the WoO and the winning sequence was PPBBPP
Twice it was almost BPBPBP, but almost does not win.

This is slightly off-topic, but may I ask what browser you were using when you played the game? I notice the icons in the big road are improperly sized and improperly positioned. They should fit perfectly, like this:



Alternatively, did you have the page zoomed to a level other than 100%?

Quote: JB

This is slightly off-topic, but may I ask what browser you were using when you played the game? I notice the icons in the big road are improperly sized and improperly positioned. They should fit perfectly, like this:



Alternatively, did you have the page zoomed to a level other than 100%?

Nice observation JB.
Nothing to worry about.
I use Google Chrome and my zoom level for WoO is 125% about 90% of the time.
Then after print screen to Photoshop I downsized the original.