Equilibrium Stats and Baccarat shoes.

Hi

I am after some rationale on the following observation regarding Baccarat shoes.

Often I notice a shoe running "dead even" regarding Banker vs Player outcomes after 20, 30, 50, 'the entire shoe (70 hands)'. I accept it is by no means a unique event.

However when you consider the maths, for a shoe to be equal in terms of Banker v's Player results say after 50 hands;

The number of possible combinations 50^2, to be in Equilibrium 126,410,606,437,752, to be Imbalanced 999,489,300,404,872.

In basic terms it has a 88.8% chance of it not being in Equilibrium and a 11.2% chance of it being equal, Yet it can be quite a common event (after 20/30 hands).

I want to lay this to rest and realise it is not remarkable, however I struggling to understand why I see a shoes within the same session defy the statistical expectation 89% v's 11% with a degree of regularity.

Help me understand why this isn't remarkable.

Quote: CyrusV

Often I notice a shoe running "dead even" regarding Banker vs Player outcomes after 20, 30, 50, 'the entire shoe (70 hands)'.

The Wizard has a large number of sample 8-deck baccarat hands. Over an average shoe of 82 hands, the Banker on average wins one more hand than does the Player. Because the probability of either Banker or Player winning is almost equal, one should expect the total number of hands won to remain pretty close to one another.

I'm not quite sure how you are mixing in "combinations" in your analysis. If a shoe begins with 3 Banker wins, it could still have 20 wins in 40 hands. Another shoe might begin with 3 Player wins and a total of 20 wins in 40 hands [ignoring Ties for simplicity], even though the "combination" of Ps and Bs at any intermediate point might differ from that of the first shoe. I'm unsure how this defies your "statistical expectation." Apologies if I sound confused, because I am.

Quote: CyrusV

Help me understand why this isn't remarkable.

It isn't remarkable because the game was designed that way. The Banker and the Player each have an almost identical probability of winning any random hand. That results in them sometimes [sometimes too frequently?] finishing with identical win totals for a shoe.

Thank you for your response, sure I understand that for all intense purpose a Baccarat outcome is akin to a 50/50 coin toss.

However if you choose a smaller sample of say 4 hands (ignoring ties), we can have any of the 16 possibilities.

B B B B
B B B P
B B P B
B B P P
B P B B
B P B P
B P P B
B P P P
P B B B
P B B P
P B P B
P B P P
P P B B
P P B P
P P P B
P P P P

Of which 6 are in equilibrium and 10 are imbalanced. The larger the sample the greater the ratio swing to imbalanced over equilibrium.

If you toss a coin 50 times, I would not expect 25 heads and 25 tails, indeed the maths points to a 11% probability of this occurring and a 88% of it not occurring. This doesn't fit with what I'm seeing at the tables or as you point out what the Wiz's shoes indicate. So what am I not grasping here??

The reason I pose the question, is sometimes I notice (as an example) a shoe sitting on 25 Banks and 23 Players. Two more outcomes needed to reach the 50 mark. The maths point to a 88% chance of not being in equilibrium, therefore bet Bank for 2 hands maximum, skipping the second bet if the you win the first. Only to see the shoe sit at 25 each side after 50 hands.

Quote: CyrusV

The reason I pose the question, is sometimes I notice (as an example) a shoe sitting on 25 Banks and 23 Players. Two more outcomes needed to reach the 50 mark. The maths point to a 88% chance of not being in equilibrium, therefore bet Bank for 2 hands maximum, skipping the second bet if the you win the first. Only to see the shoe sit at 25 each side after 50 hands.

The maths might have pointed to 88% chance of non-equilibrium before any rounds were dealt. If 48 rounds are in the past with only 2 rounds to play, then those 48 outcomes HAVE been decided. your 88% has moved on and you are looking at a new future sample size of about 2 rounds. You know how those two rounds could go.
What you propose is similar to tallying the hands up to the penultimate one and (wrongly) expecting to know with almost absolute certainty which way the last hand will go.

The question isn’t the probability that the shoe is even at exactly 20 or exactly 30 hands. It’s the probability that it is even at least once during hands 20-40. Or am I misunderstanding? That’s 11 shots at evenness.

Quote: unJon

The question isn’t the probability that the shoe is even at exactly 20 or exactly 30 hands. It’s the probability that it is even at least once during hands 20-40. Or am I misunderstanding? That’s 11 shots at evenness.

Nope, it was the shoe being even at a exact point within a shoe.

Quote: OnceDear

The maths might have pointed to 88% chance of non-equilibrium before any rounds were dealt. If 48 rounds are in the past with only 2 rounds to play, then those 48 outcomes HAVE been decided. your 88% has moved on and you are looking at a new future sample size of about 2 rounds. You know how those two rounds could go.
What you propose is similar to tallying the hands up to the penultimate one and (wrongly) expecting to know with almost absolute certainty which way the last hand will go.

Thanks for that, I do understand that odds\expectation only relate to the number of bets actually placed. I would avoid a situation such as 25 v's 24, as it only offers a single shot (or just bet the table minimum). Rather would look for 25 v's 21 or 22 scenarios. Now I understand spotting something like this and when it gets down to the final bet it is just another 50-50 outcome. Personally I prefer to treat bets as within a series and not individually.

I understand from your reply, that this 88% simply never enters the equation, implied probability perhaps (Barstow)? Does such a thing exist!!

Thanks for your response.

Now I’m confused. The chance of being even at exactly that point is low (call it 11%). The OP says even at 20, 30, 40 or even 70 hands. The chance of being even at any one of those points (which would trigger a memory that it’s ANOTHER even shoe) is much higher. Back of envelope (not correct but close for the lazy) would be 1-(1-0.11)^4. Or 37%. Add in 50 and 60 points to check and you get to 50/50.

Quote: OnceDear

The maths might have pointed to 88% chance of non-equilibrium before any rounds were dealt. If 48 rounds are in the past with only 2 rounds to play, then those 48 outcomes HAVE been decided. your 88% has moved on and you are looking at a new future sample size of about 2 rounds. You know how those two rounds could go.
What you propose is similar to tallying the hands up to the penultimate one and (wrongly) expecting to know with almost absolute certainty which way the last hand will go.

Sorry, I think you're confused on this one.

Problem: in 50 hands (or 50 coin tosses) what is the frequency distribution for how often the dealer wins m hands, m =0-50. When you do that analysis, you will find that the chance of winning exactly 25 of 50 hands is low. I think the OP is citing standard statistics.

Quote: gordonm888

Sorry, I think you're confused on this one.

Problem: in 50 hands (or 50 coin tosses) what is the frequency distribution for how often the dealer wins m hands, m =0-50. When you do that analysis, you will find that the chance of winning exactly 25 of 50 hands is low. I think the OP is citing standard statistics.

Thanks Gordon,
I was taking the OP's word for it that the chance of it not being a 25:25 split was of the order of 88%. I.e. 12% probability that it would be. I did think that was on the high side but couldn't be bothered to check. Actually that was why I used the words 'might have'.
I was just trying to allude to the fact that after 48 known outcomes (24 of each), that the 88% / 12% was ancient history with no predictive value for those last 2 outcomes. I.e. if we were facing just two coin tosses in the future, the probability of exactly 1 head and 1 tails would be 50% and certainly not 12%
I stand by that point, even if the originally quoted stats were in error.

Quote: CyrusV

Help me understand why this isn't remarkable.

In craps, there is an 11% chance of rolling a nine. Would you find that remarkable? In blackjack, there is less than an 11% chance of getting dealt 20. I don't find those all that remarkable. It isn't remarkable, because when something happens even with an 89% chance of it not happening, it generally isn't considered remarkable.

Now if you have records of it happening much more often than 11% of time, that would be different

If you're at hand 49, with 25B and 23P gone past, you have a 25% chance the next 2 hands will go P-P for a 25-25 split. (None of those counting ties.) So your 88% is in the rear view mirror some hands ago.

And a 75% chance of snaring a Banker win in the next two hands, on something whilst it has no bearing on the actual odds of the placed bets, it "did have" a 88% chance of not happening at the onset. Yes the 88% maybe be in the rear view mirror, but it was there at some point for your consideration and is now locked in your memory bank even thought not applicable to when you start betting.

whenever I see the word 'equilibrium' relating to gambling I tend
to go back to the roulette wheel analogy.
Neither the wheel nor the little white ball know that you have
approached the table and commenced an equilibrium test.

Baccarat shoes are arbitrary groupings of events that are very likely to
be even over any time period but if it happens that there is some
disequilibrium at an arbitrary point there is no natural force of the
universe that is going act upon that final few hands to restore
some sort of 'proper result'.

I am often called 'mister banker' at Baccarat, but that ever so
slight 'edge' for Banker is rarely going to prevail and I might
as well be 'mr. player' at the end of the day or the end of the shoe.

Quote: CyrusV

And a 75% chance of snaring a Banker win in the next two hands, on something whilst it has no bearing on the actual odds of the placed bets, it "did have" a 88% chance of not happening at the onset. Yes the 88% maybe be in the rear view mirror, but it was there at some point for your consideration and is now locked in your memory bank even thought not applicable to when you start betting.

Cyrus,
I honestly don't know whether you are trying to support the idea that you have an advantageous foresight or not, because I really cannot interpret your writing well enough. Call it a language barrier.

But let's try a dead simple thought experiment with just a coin flip to consider, because Baccarat is too obtuse for me.

You have a fair coin. You are about to flip that coin a few times. It is 3 minutes to noon. You will flip the coin 3 times: Once at 2 minutes to noon: Once again at 1 minute to noon and finally once more at noon.

Probability theory is quite clear: There is a 50% chance that the first flip will be Heads: There is a 25% chance that the both the first flip and second flip will both be Heads: There is a 12.5% chance that the first flip and second flip and third flips will be all be heads.

You flip the coin once: It's heads.
What is the probability that it's heads? Earlier we agreed it was 50%. Is it still 50%? (No. it's 100%. We can see it)

You flip the coin again, for the second time: It's heads.
What is the probability that it's heads? Earlier, we agreed that if the probability of both the first coin flips being heads was 25%. Is it still 25% (No. It's 100%. We just watched the first two flips )

You flip the coin a third time. What's the probability that it will be heads? We already agreed, just a few minutes ago, that the probability of all three flips being heads was 12.5%. Were we wrong? No. but time has moved on. Unknown future events are now known past events. Re-evaluate.

And so it is with your baccarat shoe. You had some calculated probability* that there would be an outcome for exactly 25 Player and 25 Banker after 50 hands. But after you've observed 48 hands, that evaluation is ancient history. You need to accept that whatever you just observed has happened with a probability of 100%, no matter how unlikely it was at the outset.

As you say, the 88%* is locked in your memory. You needed to re-evaluate and overwrite it as events unfolded.

* and I'm neither accepting nor rejecting your 88%.

Quote: CyrusV

Often I notice a shoe running "dead even" regarding Banker vs Player outcomes after 20, 30, 50, 'the entire shoe (70 hands)'. I accept it is by no means a unique event.

depends on your definition of 'unique'

One can simulate or calculate this over an 8 deck shoe
I used 72 non-Tie hands.

I see an average of about 5.825 such Banker = Player wins per 8 deck shoe.
(Fair coin flip = 5.84 times)
considering there are only 36 possible 'equals' in an average shoe
I would agree with those that say it is 'by no means a unique event'

Many Baccarat players would violently disagree with this saying the shoe was stacked for this, like when Player wins a few in a row and the whole table decides it is NOW time for Banker to win and Player still wins, the whole table says the game is rigged.
classic stuff

hope this can help out

Thanks for the responses, I understand. I'm not defending or trying to promote any potential advantage, rather was interested in expanding my understanding of why I'm noticing many shoes in equilibrium after 50, 60 hands when the maths state this should be less likely than more likely. Notwithstanding sometimes we have selective memory only seeing and recall the unusual, ignoring the usual.

I will confess that for several years I have applied fairly extensively at both the Baccarat and Roulette tables, expected equilibrium stats. Generally based on or around 12 decisions, which has a 77.4% expectation (from the onset) not to be in equilibrium. Non-Equilibrium was easily ahead in all sessions, as to be expected. This has no bearing whatsoever on placed won vs lost bets, which at best would be 50%. Hence noticing shoes in equilibrium after 50, 60 70 hands. Once you've dabbled with something, such events tend to continue stick out when you notice them.

Quote: CyrusV

was interested in expanding my understanding of why I'm noticing many shoes in equilibrium after 50, 60 hands when the maths state this should be less likely than more likely.

your 11% maybe correct at say 50
but over 72 rounds and 36 possible 'equals' in my example

that average of 5.83 times per shoe also carries with a standard deviation of 4.5

in one simulation 7 times or less happened ONLY 68% of the time
that means 32% of the time (about 1 in 3) an 8 deck shoe showed at least 8 'equals'

these are very large numbers applied to a series of outcomes (when one thinks maybe 0 or 1 is more likely)
and not just one outcome.

Quote: CyrusV

Once you've dabbled with something, such events tend to continue stick out when you notice them.

yes,stick out they do.
just watch out for 'confirmation bias'