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[alrelax]

Can anyone figure out how many possible outcomes exist in a shoe of baccarat? 

You know, just the possibilities of what can happen in a bac shoe are in the multi billions, IMO. 

That is staggering if you really clear your head, sit down and think about it.

I could not even think of how to set up that math equation, maybe one of the math gurus here can??

8 decks of cards, remove the first 2 to 11 as the burn cards, cut off the last 15 or so.  416 cards minus, say 25 or so.  How many possibilities on a declining scale does a player actually face?  Huge amounts!  Especially when you are not looking to have optional draws like BJ, etc.

[AsymBacGuy]

Yes, but a large part of the possible results are equivalent in terms of outcomes.

Of course the baccarat player wouldn't want to know what precisely happens for each hand, just the distribution of the results.

For example, the probability to get two shoes in a row not forming at least a couple of  P singles in a row is almost not existent. The same about not having a Banker streak of at least 3 and so on.

Each shoe is just a minuscule part of the entire picture. No one bj player would expect to get a possible mathematical advantage per every shoe played (such probability is just around 12-13%), why a baccarat player should expect or find favourable situations per every shoe played?

as.   


 

[alrelax]

The answer I posted in another section is in the quadrillions. But that is why I raised the point, that anything anyone can come up with that systemic you're fighting against such a large field of possibilities, it's impossible to match up what the presentments are going to be, against what you are wagering for according to a mechanical systematic scheduled plan of wagering.

[Johno-Egalite]

Can anyone figure out how many possible outcomes exist in a shoe of baccarat? 

For a 70 hand shoe, not including TIES

1,180,591,620,717,410,000,000

[BEAT-THE-WHEEL]

Gentlemen,
The ourcome is aka PERMUTATIONS,
Thus, say, next 70hands,
The best/worst  probability for Banker, = 70B in a row, or 70PLAYER in a row,
Which we will never see in our life time...

The 2nd best=a single lose somewhere in the streak.
3rd best=2 losses in the streak...
4th best=3losses...

.all the way, to...
Worst=70losses in a streak....

That trillions of permutations!
Thus they said, "ANYTHING could happen !"

Thus, a good way, is to ability to adapt to take advantage of every possible permutations.

[BEAT-THE-WHEEL]

Unfortunately, there no method that could adapt to every permutation....

[alrelax]

Gentlemen,
The ourcome is aka PERMUTATIONS,
Thus, say, next 70hands,
The best/worst  probability for Banker, = 70B in a row, or 70PLAYER in a row,
Which we will never see in our life time...

The 2nd best=a single lose somewhere in the streak.
3rd best=2 losses in the streak...
4th best=3losses...

.all the way, to...
Worst=70losses in a streak....

That trillions of permutations!
Thus they said, "ANYTHING could happen !"

Thus, a good way, is to ability to adapt to take advantage of every possible permutations.

Exactly.  Thanks, Glen

[TheMagician]

Gentlemen,
The ourcome is aka PERMUTATIONS,


That trillions of permutations!
Thus they said, "ANYTHING could happen !"

Thus, a good way, is to ability to adapt to take advantage of every possible permutations.

You cannot adapt to SHEER Uncertainty.

You mentioned Trillions. That number my friend is as far apart, in the difference between quadrillions (true amount of permutations in 8 decks of Bac) and Trillions, as a Pound is from 1,000 Pound.  You may be able to lift the former, and even at times joggle with it, but the weight of the latter you cannot move an inch, however much you try.

I posted (https://betselection.cc/math-statistics/how-many-possibilities-in-a-baccarat-shoe-exist/msg64160/#msg64160) the actual numbers of any given Bac permutation earlier and it measures close to 60 Quadrillion.

Another way to give you a hint how much that is in terms of stars in a galaxy. Our own galaxy has 250 Billion (+/- 150 Billion stars).  60 Quadrillion stars would be close to 2.4 Million such Galaxies!  Can you honestly say you can fathom such a number of galaxies and even worse, the number of stars in them? I think not.

Do you get now why I mentioned the words "You cannot adapt to SHEER Uncertainty above?"

What can you do then? (Obs, rhetorical Q)

You can most certainly develop a way to measure your bet strategy/selection against the shoe by implementing a variance graph that shows the trend of your made bets, and use said graph to bet according to that trend, but then I suspect such an attempt would eventually make the whole thing, considering the poor payout, a zero-sum game.

Bac is not my game,  and I believe Glen might have his own well-tested strategies worth taking a look at, should you still feel brave enough to challenge such a volatile game of uncertainty.

[alrelax]

"Bac is not my game,  and I believe Glen might have his own well-tested strategies worth taking a look at, should you still feel brave enough to challenge such a volatile game of uncertainty."  I appreciate that comment Magician.

"Unfortunately, there no method that could adapt to every permutation...."  By:  BEAT-THE-WHEEL.

Absolutely! 

Winning, losing and pushing.  That is the only 3 things a player can do at the casino table.  There are no other outcomes.

The results that you experience at the table will not and cannot follow any sort of governed or stable distribution of presentments or results from the shoe.  Because the possibilities as we already established are far too great to narrow down to a certain section of 80 hands or a cumulative total of 160 or 320 or 640 or 5,000 hands, and so on, that will produce what we all are seeking, winning hands.  So many people will combat just that with their defense of Martingale or their application of any one of the numerous theorems or systems that they read about or believe in. 

Seriously people, the only way to profit is to smack the casino real hard and outweigh your losses in the attempt to get to that point, each time or at least every 2, 3 or 4 times you attempt playing.  IMO, there is no other way.  Unlike paper, the computer, trials, running tests, etc., you have finite capital, period.  No two ways about it.  The casino does not. 

Let's look at that for just one paragraph here.  You have a certain amount of money to risk losing in order to win some.  Period.  So you have a very short period of time in order to accomplish that during each session.  No matter how much that figure is, it is limited.  The casino does not.  The casino has massive amounts of capital in chips and the cash within the premises by state law, ready to pay every chip displayed on the floor.  FYI, every chip on every table no matter if open or closed, the casino has the green cash within their vaults or the chips would not be on the tables.  So, you cannot out play them by repeated buy ins with additional money, thinking you will turn things around in your favor and turn their lights out.  As well, stamina, energy, focus, motivation, vision, and everything else along those lines are also working against you.  The casino rotates its dealers every 20 mins or so, not just to avoid collusion with players, but also for exactly the same reasons I just mentioned.  Sitting in either one or two spots for a period of several hours is hard both physically and mentality in so many ways, especially with the focusing and thought process.  Then when things go bad for a player, he believes taking a break is great, but his mind is convinced he will miss that section of presentments yet to come with his winning hands, etc.  That starts a mean cycle and a cycle that is not very good for the player, great for the casino thou. 

Then we have the fact what we have discussed in detail so many times.  A negative game with a negative expectation.  IMO and my proven experience, if you have the proper risk capital and mind-frame along with a governed buy in that is a partial amount of your bank roll, coupled with the knowledge and the experience to manage your winnings into numerous chances that benefit yourself rather than the casino, then you have a chance to play numerous sessions and win money. 

But, IMO you have to master a way to hold wins, perform positive progressions and parlays, yet be able to risk without emotion or distress while walking away losing your buy in which has to be a partial amount of your bank roll, without it effecting you to the point that you regret it and dwell upon the loss.

The myths and the fallacies that exist on the internet regarding baccarat as well as casino gambling are astronomical!  People become delusional to their own thoughts.  They provide themselves no advantage to make themselves a sequence of wagering selections which they really believe they have.  They actually afford themselves no advantage and they limit their options by doing just that.  That is the sad part, all that learning and researching only convinced themselves of numerous ways to beat the casino, when none actually exist.  Especially in mathematical and statistical adherence.  Period. 

At this point so many will still believe and attempt to count the cards, keep track of the banker, the player, ties and other events the shoe produces.  Simply, if it worked like that, the casino would not offer cards, pens and the newer electronic scoreboards.  It does not, at least for the extreme upper 90% of the time you are there, if you employ it as a protocol for wagering or not wagering.  Will there be sections where the equaling out, or certain events happen because there was a deficiency of them prior to that?  Sure.  However, just as important and what becomes devastating, are the times and the sections that those very things were supposed to, or yet believed would come out and did not.  And, that my friend will happen a greater amount of times in the casino's favor, rather than the players advantage.  That is the reason why and the only reason why the casino provides you the equipment and the permission to track, score, calculate and take notes all you desire at the baccarat table. 

So what is one to do?  You have to develop a unique boldness or an advantage in select wagering when the presentments of the shoe offer the chance to win hands that will allow yourself to outweigh your losses in the attempt to win money.  There is really a chance for the player, once you figure that out and forget about the wager for such and such, because so and so just happened, or did not happen, type of play.  And, your boldness or advantage has to work on well less than 50% of your wagers and most importantly, on those that win!  That is why to myself, flat betting and negative progressions are not going to do anything for you, it will require far too many for any kind of stability whatsoever.  Read that once more, your unique boldness and your advantage has to work for you with small sections of shoe presentments, that will only occur in less than 50% of your wagers.

No matter what creative or Holy Grail angle you think you found, you will not bring it to the baccarat table and repeatedly beat the casino at the game.  No matter how perfect your counting is, no matter how perfect your data analyzation and tracking methods become, no matter how perfect you can sense something, etc.  If you continue to wager on any one or several types of wagers because of your expectation, that the presentment will match any type of theorem or system schedule, you are dead wrong and will be on a continuous basis.  Simply because the numbers of possible outcomes have too many possibilities for anything stable or predictable to happen on a consistent basis, whether that is in one shoe or multiple shoes of baccarat.  That is, if you continue playing past your first time anyway. 

You don't have to change yourself.  Or stop believing, or stop gambling, or stop questioning or stop applying yourself.  The whole trick to what will help you, is being totally conscious and putting yourself into a neutral state of playing, a natural state of focus, vision and mind frame.  Not even in the belief that a certain 'betselection' process will prevail over another. 

It is about progressions, parlays and accumulating that amount each time or during a cumulative amount of times, that outweighs the variance, the house edge, your own default rate, etc., that you engage yourself in.  You have to figure out how each $100 you play with, will allow you to win after you lose a certain amount.  And IMO, experience and everything else combined, I found a certain way to be able to win at baccarat.  And that is to realize time, money, emotional, psychological and frame of mind all combined will determine how your decision making process allows you to accumulate and allocated your wins and how you manage the losses that will happen.  Those that think and believe everything I just mentioned does not apply to them, are just wasting their time being here anyway.

[Johno-Egalite]

I'm d_u_m_b founded by some of the responses in this thread.

These in particular stand out for me;

You cannot adapt to SHEER Uncertainty.

Unfortunately, there no method that could adapt to every permutation....

That trillions of permutations!
Thus they said, "ANYTHING could happen !"

But that is why I raised the point, that anything anyone can come up with that systemic you're fighting against such a large field of possibilities, it's impossible to match up what the presentments are going to be

The results that you experience at the table will not and cannot follow any sort of governed or stable distribution of presentments or results from the shoe.  Because the possibilities as we already established are far too great to narrow down to a certain section of 80 hands or a cumulative total of 160 or 320 or 640 or 5,000 hands, and so on

You get the drift, naive, clueless on how to combat 1,180,591,620,717,410,000,000 different permutations.

Firstly, you don't.  Break the game up into manageable segments, you are no longer trying to fight 1.1E23, rather something a tad more manageable such as; 64/1 or 128/1 or 256/1 (64/2, 128/2, 256/2).  Instead of trying to puzzle over a non-correlated game by predicting randomness (WTF), pre-decide what results in 3LIAR or 4LIAR or whatever.  Make the possibility of that occurring as slim (mathematical) as possible, so you can focus solely on the wagering aspect of your game.  It is the opposite of pattern capturing, it is defining the pattern that results in LAIRS and will keep you in any game longer than all the other silly second guessing nonsense that you witness at tables around the world, from the casino floors to VIP rooms, either that of just give the game up as a lost cause and hold on to your hard earned cash. 

 

[alrelax]

That is right Lugi.  IMO, sections and turning points, playing in in reverse of what everyone classically thinks, etc.,  I went into a lot of it elsewhere.  Good little summation thou!  I just concentrate on what is happening with little thought to other presentments as a general rule.   Thanks.

[TheMagician]

I'm d_u_m_b founded by some of the responses in this thread.

Having read some of your posts, it is easy to assess you are not the sharpest knife in the drawer, so I can understand "dumbfounded" LOL

You get the drift, naive, clueless on how to combat 1,180,591,620,717,410,000,000 different permutations.

Wrong! The correct figure is found on this post I made. https://betselection.cc/math-statistics/how-many-possibilities-in-a-baccarat-shoe-exist/msg64160/#msg64160     There is a vast difference between the quadrillions you see in my posted data and your Sextillions you got from holding a whiskey glass in one hand and drunk fingers hitting a number keyboard with the other. When did you stop learning math? Elementary school?

Firstly, you don't.  Break the game up into manageable segments, you are no longer trying to fight 1.1E23, rather something a tad more manageable such as; 64/1 or 128/1 or 256/1 (64/2, 128/2, 256/2).  Instead of trying to puzzle over a non-correlated game by predicting randomness (WTF), pre-decide what results in 3LIAR or 4LIAR or whatever.

Oh yeah, right...and hows that been working out for you so far? I mean if Bac were so simple you should be swimming in Casino profits so far and basically being barred from most Landbased Casinos. But then you are not, because, if its one thing Casinos love, it is self-deceiving dummies like yourself.

[alrelax]

Wrong! The correct figure is found on this post I made. https://betselection.cc/math-statistics/how-many-possibilities-in-a-baccarat-shoe-exist/msg64160/#msg64160     There is a vast difference between the quadrillions you see in my posted data and your Sextillions you got from holding a whiskey glass in one hand and drunk fingers hitting a number keyboard with the other. When did you stop learning math? Elementary school?

Oh yeah, right...and hows that been working out for you so far? I mean if Bac were so simple you should be swimming in Casino profits so far and basically being barred from most Landbased Casinos. But then you are not, because, if its one thing Casinos love, it is self-deceiving dummies like yourself.

First, we all are welcomed here and all might or might not have things of interest to others, some or all.  But since a message board is not a school or an intense only seminar class, etc., things said are sometimes spot-on and other times, depending on whom is reading it, off the mark by huge distance.  With that said............

Second, it is not always eye-to-eye or the same meaning and understanding level when something is written by one person and read by another.  But I did interpret the part about sections or narrowing down that Lugi said, as something useful and something that I have been focusing on "SOMEWHAT" over time now. 

It does to me and many others make 'some' sense, at least giving us a section, whether false or not, to get into the groove, sort of vision and concentration.  And it does not matter what that section does, that to myself, is why so many misunderstand what I say.
What is going to happen will happen.  But the extra key is, you have to know or follow what the shoe is presenting rather than basing your wagering on what you need, attempting to recoup and what you desire. 

I wrote about 'sections and turning points' and I can do better paying attention to and concentrating on sections rather than the whole shoe many times over.  It is a control and an emotional issue that gets almost all players from continually profiting at the game, as far as sitting there playing it governed by their buy-in and bank rolls that are finite.  They successfully do most everything else in their life's as sections with turning points, but most all refuse to apply that very same thing to baccarat. 

[Johno-Egalite]

Oh yeah, right...and hows that been working out for you so far? I mean if Bac were so simple you should be swimming in Casino profits so far and basically being barred from most Landbased Casinos.

Ever heard of players being barred from the Baccarat tables? Playing Baccarat has financed a few global trotting VIP trips for me, how about you?

There is a vast difference between the quadrillions you see in my posted data and your Sextillions

Are you sure about that??  LOL

I didn't steal my figures from the Wizard's site, BTW it's elementary maths, a 70 hand  shoe = 2^70 (type =2^70 into Excel and see what figure is returned) Now what do you say?  Being smart is not the same as pretending to be smart!   

A 80 hand shoe = 1,208,925,819,614,630,000,000,000 or =2^80  (again type that into Excel to confirm the correct answer).

Maybe you think some Microsoft programmer had a glass of Whiskey in their hand when they programmed the formula?? 

IMO, sections and turning points, playing in in reverse of what everyone classically thinks, etc.,  I went into a lot of it elsewhere.  Good little summation thou!  I just concentrate on what is happening with little thought to other presentments as a general rule.   Thanks.

This is not what I am referring to in the slightest. All you are suggesting is taking sections of a shoe, forming some opinion to what you think / assume is occurring and basing your bet placement upon whatever you see and how you interpret it, which itself is subjective. 

This is pure gamblers fallacy, the fallacy is that prior results have some bearing on future hands in a game of non-correlated trials. Just because a shoe may be producing some perceived pattern, one side producing singles, streaks, chops, repeating streak lengths, one-side repeating, cards drawn, winning hand totals and all that other voodoo nonsense. You notice, you react (after the event).  It's gamblers fallacy, never worked before and still doesn't in the long term.

Having dabbled with all these "what is the shoe doing now" theories over the years, they do not work period.

 
Let me give you an small over-view on far superior ways to approach a games of chance were prior hands have no bearing on predicting future hands and studying the score board is as useful as a coin toss.

Expected Streak length distribution;  We I'm sure are already are familiar with these figures.  However just to prove I do not have a whisky glass in my hand, a quick recap.

Series 1 = 50% of the time (yes I know, anything can and will happen & results are not evenly distributed in the short term, so please spare me all that).  Streaks of 2 = 25%, streaks of 3 = 12.5%, streaks of 4's = 6.5%, streaks of 5 = 3.25% and so on.

Yes we are all aware of these figures, they have floated around on the GG site for over a decade. Because we can't predict, they don't really help us do they?    Well actually they can, while we can't predict any occurrence of any streak length, we certainly can appreciate we are going to see a hell of a lot more streaks of 1's, 2's, 3's, 4's than say 5's in the short term, the is no disputing that.


What if we combined the "expected" steak lengths v's one exact streak length?

Let's take a streak of 5 (BBBBB or PPPPP).

All other streak lengths would for argument sake give a combined expectation of 50%+25%+12.5%+6.5%+1.625% and so on.  Or an easier way to view it;  If a 5 streak has an expectation of occurrence 3.25% of the time, then all other streak lengths (includes singles) should occur 96.75% of the time.

Hold on to your chips, I haven't finished just yet, having played easily over 50,0000 shoes, we all know repeating 5 streaks can happen, a 5 by 5 by 5 or a five streak occurs several times in the same shoe, this is what games of random chance can throw at us.

So we need to be a little more smarter, let's make ourselves amour proof as much as we possibly can. How about making some of those occurrences of streaks of 5 work TO OUR FAVOUR?  HUH?

What if we won against all streaks lengths and 86% of streaks of 5 and lost against only 14% of streaks of 5?  Or to be more precisely, snared a winning bet against all streak lengths no matter what what length, except against streaks of 5 only 14% of the time! 

Could you assume to have a rock-solid approach to the game, or would it just be the Whiskey talking? Or would you like some maths to back things up?  Just to reiterate, Baccarat is like a coin flip, prior hands have no bearing on future hands, staring at the score board does you no favours whatsoever, your time is better spent tracking your bet amounts. 

Let us consider combination tables. For the example I have given, the nemesis is 14% of any 5 streak.  Any experienced player should by now deduced that this can be viewed as a very "rare event".  Which can happen, which can repeat, yet would not be expected to repeat with any great frequency to inflict undue stress on the players bankroll.

The exact mathematical nemesis is 1/64, on average we expect to get hit once in 64 trials.  Yet for any given 70 hand shoe there exist only 10 trials. So all things being equal (which they are not), we would expect to get hit once every 6 shoes.  Wow


Let me break this down for anybody having difficulty following this.

We are playing a game of chance and we fully appreciate prior hands have no bearing on future hands and we can't predict jack sh1t, so therefore don't even bother looking at the score board. Instead we choose to put into play maths that have an expectation of producing our pre-chosen nemesis pattern once every 64 trials, of which, there can only be 10 in a average Baccarat shoe.  The entire concept here is controlling the LIAR's (losses in a row), the frequency of our losing bets are short and manageable, nearly all of the time. 

Yes the naysayers may think, what is to stop you getting hit in the first shoe, or it happens more than once? Of course that can happen, yet when you are using a easily proven mathematically expectation of once per 64 trials, rest assured you will not encounter repeated disaster or shoes from hell often or generally more than once in any given session.


The top three aspects of successful Baccarat play IMO are:

1 - Money Management
2 - Patience & Discipline
3 - Bet Selection

In that precise order.  MM over-rides absolutely everything, we don't gamble for stats, or hit rates, rather to make tax-free cash.  So considering what I have outlined above, without some semblance of a staking plan, you might get lucky, but in the long term you simply will not survive.  So even though the strategy I have provided the bare bones for, without a suitable staking plan, you would struggle and yes you do have to be creative.

Patience and Discipline, the strategy above requires patience.   So you've been hit, no big deal, the more shoes you play, the less often you will be hit, think about that for a moment, it's simple maths!!  1/64 chance of being smacked, 10 trials per shoe, how many bet selections have you ever seen / read about can make such a bold statement and be true??

Finally Bet Selection, nope the strategy above will not give you more winning hands per shoe than losing hands (it might but that would depend on luck and we don't want to rely on luck whilst gambling).  It will however give you great confidence of controlling losses in a row and subsequently betting into the abyss, or IF that were to occur, confidence that it shouldn't really occur too often, because it will only happen 14% of the time against any streak of 5.


(Again before anybody mentions it, I am well aware that our true odds are reflective on the number of actual bets placed, no matter how or when we place decide to place them).

I used streaks of 5 for this example, I could have easily used streak of 4 (get hit more frequently), or streaks of 6 (even more bullet proof), however I must stress, the more robust you make your game the more difficult (but not impossible) staking plan becomes.


Here are some other mathematical possibilities;

Let's say we chose streaks of 6 as our nemesis, as opposed to streaks of 5.  Streaks of 6 occur 1.625% of the time, with a little manipulation we can narrow that to 12.5% of given 6 streak, meaning 87.5% of the time when a 6 streak occurs, we will snare a win. The odds of being hit are 1/128 trials, of which there are less than 9 trials per shoe, so IF things were equal, we should expect to get hit once per 16 shoes.


Let's go a bit more extreme;

And make Streaks of 7's our nemesis; a streak of 7 only happens??  Well it's 0.8% of the time, again with a little bit of massaging, only 11% of streaks of 7 hurt us, meaning 89% of streaks of 7 will return a win. We should expect to lose an entire trial once every 33 shoes, once per week /fortnight maybe? 

Bet Selection~wise, a strategy that mathematically is expected to fail once every 33 shoes, one could say the game is practically beaten bet selection~wise.  While it is an extreme approach, it is also extremely difficult to design a betting strategy for such play, but not impossible if you used virtual losses to make it viable and referring to aspect #2 two (patience), you would require that by the bucket load. 

Anyway, I've waffled on more than I intended.  I just wanted to provide insight to alternative ways to consider games of chance and how the figure of 70^2 ( 1,180,591,620,717,410,000,000 ) is irrelevant and nothing to be concerned or fazed about.

[AsymBacGuy]

Series 1 = 50% of the time (yes I know, anything can and will happen & results are not evenly distributed in the short term, so please spare me all that).  Streaks of 2 = 25%, streaks of 3 = 12.5%, streaks of 4's = 6.5%, streaks of 5 = 3.25% and so on.

Taking for grant that baccarat is a 50/50 game (and of course it isn't) , streaks of 4s have a 6.25% probability to appear and not 6.5%. The same about streaks of 5s.
Itlr a 0.25% difference means a lot. 

as.