When you guys tried to design baccarat system, what are your considerations?

Here's mine:

In 8 decks baccarat, there are 8*52 = 416 cards, which means there are 416! (416 factorial = 416*415*414*etc until 1) possible card arrangements or let say, 416! type of shoes. If we are only interested in Player and Banker, there are around 2^75 possible results. (which is PBPBPPBB etc assuming an average of 75 hands per shoe).

Now if you understand about pigeonhole principle you can assume that there are 416! pigeons to fit into 2^75 pigeonholes. Now this means that there will be at least one pigeonhole that contains more than one pigeon. Or probably a lot more considering that the ratio of pigeons/pigeonholes is very very big.

If, let say, we play all the 416! shoes (pigeon) and put then into respective shoe result (pigeon hole) we would know which pigeon holes that has the most number of pigeon, ie which type of shoe result is common, then we would be able to design a system which will win these shoes. But then if most of the pigeon holes contains about the same number of pigeon than probably whatever system it is, it can't beat baccarat.

galo,

Very-good insight. (What galo is wondering is are there some orderings of the "PB..." outcomes which are inherently more likely given the standard shoe, and the rules of determining those outcomes from the played cards.)

I'm not a combinatorics (& otimization) or permutations expert, but my guess is that the pigeons will be evenly distributed in their holes. Looking at the extreme case first, there're plenty of ways to arrange the shoe to produce only P's or B's. (As there are plenty for the other permutations of P and B taken together.)

Please let us know what YOU further discover here. Off hand i can't think of anything to add which might rule out some of the pigeons. But now after thinking a bit more, one could rule out the shoes, and shoes near to, which are the 8 decks (unwashed) one on the other; and the related families of orders, such as any produced by the (7 possible) perfect riffle shuffles of that shoe. Because... wouldn't be possible for the standard shufflers to physically make enough passes in a shift to make those specific shoe orders reappear even if not by chance.

Mark.

Probably if the distribution of pigeon in their holes follows the normal distribution ie bell shaped curve, we could take the center shoes and design a system based on that. In that way, the system would win more shoes than it lose. But I don't know if that will be the case

And by center shoes I mean those shoes with the most pigeons

Hi Galo

The out come of 75 hand of a shoe is : ( 2^75 = 2^75/2 win side+2^75/2 lose side ).

If you are going to use this out come to design your system it something like you only need 1$ to go to super market buy a chewing gum but you bring 1billion $ along! Anyway it work!!!!

Mikewin

galo,

With many problems of this nature, a small further complication often helps unravel it. The thing which makes this one easy is the cutting of the cards after being shuffled (, which in a fair shuffle is actually already done). Then, the 416! possible resultant card arrangements can be reduced by a factor of 416, when each is viewed as "wrapped" around on itself. Each "wrap" from the shuffler becomes a "linear" shoe only after the cut decides its start/end (, of which there's 416 possibilities. The number of possible "wrap" arrangements of n different objects is therefore n! / n ; as opposed to n! arrangements of the objects in a line.)

Take any given "wrap", doesn't matter which. Start dealing out baccarat games at an arbitrary card termed card 0; and note the outcome as X. Then by instead starting (as by the cutting at a different spot) some number of cards between and including four or six earlier, say at card -5, the outcome X happens as the second outcome. Continuing thusly, the outcome X can be made to occur at any position in the scoreboard (of PBBPPPPB...). Generalizing, the entire set of that family of outcomes can be made to advance in the scoreboard sequence, thus averaging each other out.

Of course had the start been card 1, then a different family of outcomes would be generated. But there can be from only four to six possible families; and each averaged w/i itself as before.

Whether all the cards are played out after some start card n selected; some cards remain unusable on the very end; or some cards are "burned", this proof (by procession) still holds.

***** Clarification: Of course we already know that there's more outcomes of BBB...B all the way down to fewer outcomes of PPP...P because of the slightly greater (starting) chance of a B, which usually changes very little from outcome to outcome; that's why the "generally-accepted" strategy is to bet only the banker. Of all the other sets of 80 or so then-possible shoe outcomes we just can't say where any set will begin in play; nor even which of the possible P-B arrangements of each particular combination (set) will occur. One may say the last game or two's cards remaining forces those results then, but in a "wrap-around" (over-all) consideration of the cards any game's outcome may be considered forced on the end (, or none depending on how one wants to look at it.)*****




As for my idea that after the "wash" we know at least one arrangement (or family of that) the cards aren't, ie the original, i tried a few games.

Using a scaled-down deck from K, Q, to ace (, and "wrapping" the ace around to the K,) one can try all the outcomes starting from the K, then the Q, etc. That produces 9 P's and 4 B's. But with that deck turned around, the result is inverted. And, so far, with larger decks slightly varied from the smallest one, the results also tend to balance out. Except for the ties, which seem to increase in frequency with either deck for the larger deck sizes. Which could indicate fewer ties by ("parallel-like") "washed" shoes.

***** Clarification: If extreme deck compositions produce extreme outcomes, then perhaps in live play the P-B, and even T-, outcomes are less streaky. *****

Has anyone done such an analysis with the existing live data? I often ask the regular dealers about that. When i do get an answer, it's usually that they see more P's than B's.

Anyway, nothing of this suggests the method tried above has anything to do with choppiness/streaking. That is just too far removed from the reasoning here. (Don't get your hopes up again Ellis.)

Hey garnabby

That's a good idea. I think I've read somewhere about the inverted results. Don't know if it still holds after shuffle. But then again, every casino has different type of shuffle style or maybe shuffle machine. But if it is, this information would be very valuable. Does anyone know is there any simulator that simulates card shuffle as they are in the real world?

There are a few for blackjack but not for baccarat. In most cases you have to design your own. But for baccarat it has been shown that standard shuffle tracking does not produce any useable information. There are no recognizable patterns or favorable packet compositions that can be accurately tracked by the standard methods. Advanced methods like sequencing, glimpsing and cutting/steering can be effective but most forms of shuffle tracking are too vague to give useful information in baccarat.

Just as a bit of an aside here... when one starts (and ends) with something scientific-by-design, there is always a way to know when a given series of plays: [works because of skill and luck; or because of no skill, and luck]; or [fails because of skill and no luck; or no skill, and no luck.]

Afterall, luck is the predominant short-term factor with these sorts of games. (Unlike pool, or chess, which are more about hustling... and in the short-term only.)

Eg, a card counter can always determine did the counted-upon cards actually show (more than often), and lead to favorable outcomes or not; or did those not show but end well or not anyway.

And it's a psychological "boost", at least, to lose to bad luck; or even to win by chance, alone. Maybe that's what some mean by "losing/winning gracefully".



"Sometimes grain of luck worth more than whole field of knowledge." (Charlie Chan.)

I’ve also heard the famous “I’d rather be lucky than good” quote thrown around by many gamblers. Personally, I’d rather be good everyday than lucky for just one day. As you pointed out, it all depends on whether your goals are short-term or long-term. Some people are willing to risk everything for a big score while others would rather safely build their wealth gradually over time. There are certainly plenty of ways to pursue either goal. Only the individual player can decide which approach is best for his needs.

Hey G, I couldn't resist this one. So the game of chess is about hustling, huh? Well knock me over with a feather! First time I heard of it. I been a chess fan for centuries. I reckon I need more data and context on that one...

K,

Glad you didn't ask me to explain bluffing in mini-baccarat.

People hustle each other in a lot of ways all the time. I mean it gets sort of boring after a while. Doesn't every thing come down to strength, even bluffing. Even when the stronger isn't readily apparent (, as in hustling,) it's still there all along. That's why i sometimes prefer to look beyond all that.

Anyway, i'm going to pull an ex off the web for you because you seem a bit skeptical on this.

In Street Chess Games, a Pedigreed Pastime Becomes a Gritty Sideline


A man known as Russian Paul says he has been playing chess in the streets for 15 years. He says he does not play for money but gives lessons for $45 an hour.


By DYLAN LOEB McCLAIN
Published: September 17, 2007
September is a time of rebirth for chess. With schools back in session, students are returning to their chess clubs.



For regular chess players in Union Square Park, the game is a speedy (and sometimes lucrative) one.


A group of players set up in Union Square Park this month.

Some of those students may be dreaming of vying for the title, now held by a Russian named Vladimir Kramnik.
More likely is that they will someday vie for a few dollars in Union Square Park in Lower Manhattan against the likes of a man known as Russian Paul.
One recent night, Paul was studying the board before him, not far from the subway entrance. With close-cropped gray hair, arms covered with tattoos, heavy bags under his eyes and a faded and slightly tattered green T-shirt covering his paunch, he seemed out of place playing a game with such an intellectual pedigree.
But after a few seconds, Paul made a move and touched his side of the chess clock. His opponent quickly replied, and soon their hands were flying across the board, knocking over pieces and slapping the clock’s buttons.
Finally, Paul gestured at his opponent’s side of the clock, which was flashing a set of dashes, meaning his time had expired. He had lost. Paul’s side of the clock showed only seconds remaining. The players reset the board and the clock, and repeated the scene over and over, with Paul usually winning, well into the night.
Paul is one of a small legion of chess players in places like Union Square Park, Washington Square Park and St. Nicholas Avenue and 141st Street who make a living, or at least some pocket money, from hustling. Like basketball, chess hustling is a city game — fast and gritty and played on street corners and in parks with the throb of street life as a backdrop.
At the top levels it is polished, with high stakes. While the World Chess Championship, which began on Thursday, has $1.3 million in prize money, on the street the bets are usually $5 a game, and the quality of the opposition is unknown.
Another hustler, whose first name is Kenny and whose street name is Little Daddy (he is 5 feet 3 inches tall), said he could always tell how good his opponent was in the first couple of moves. For example, he said, if someone moves quickly but fumbles the pieces, or uses one hand to move the pieces and the other to hit the clock, which is against the normal rules of speed chess, then the person is not experienced.
Little Daddy, who said he started playing street chess in 1976, said he won about 80 percent of the time. A crucial part of the game is not to win too quickly, he said.
“You make the games close,” he said. “You don’t want to crush them. You want to leave their ego intact, because you want to keep them coming back.”
Russian Paul, who displayed the opening knowledge, speed and tactical ability of a master (but not the much higher grandmaster), said he had been playing in the streets for about 15 years and always tried to win. “If they get scared away, it is not my problem,” he said.
Like bartenders, the chess hustlers have names for people who keep coming back and coughing up money: regulars, or customers.
Little Daddy said that every hustler — there are about a dozen in Union Square, although the number fluctuates during the day — had at least a couple of regulars.
On this particular night, Carl Neblett, a regular, was taking on Junior, who always wears a baseball cap and keeps up a running commentary as he chain-smokes his way through games.
Mr. Neblett, who said he was an ambulette driver, said that playing against the hustlers helped him improve his game and that he had no illusions about his skill.
“Everybody here is adults; they know what they are getting into,” Mr. Neblett said, adding: “I like to think that I am smart. After losing $10, I pretty much shut it down. And sometimes you get lucky and you take these guys.”
Technically, playing chess for money is unlawful gambling, according to Jama Adams, a spokeswoman for the city’s parks department.
But a police officer at Union Square, who would not give his name because he was not authorized to speak for the department, said that he was not so sure, because the hustlers were not taking a cut of the stakes, which is how illegal gaming houses break the law. Even if what the hustlers are doing is illegal, he added, it would be hard to prove unless you watched them carefully and saw the money changing hands.
Hustlers said they had almost never had trouble with the police. Still, most were reluctant to give their full names, and were cagey when asked about their street earnings. Most said that on a good night, they might earn $150 to $200, but a slow night could produce as little as $30.
Russian Paul said he usually did not play for money. Instead, as he described it, he gives lessons for $45 an hour.
Paul is in his early 40s, younger than he appears, and is not actually Russian; he’s from Ukraine. And though by association his nickname would suggest a childhood spent hunched over a board, he said he picked up the game only after coming to the United States when he was 15.
He said he had a couple of jobs teaching chess in schools in the past, but he does not teach formally now. Fortunately, he said, he lives in a rent-stabilized apartment not far from the park, and he has no children, so his needs are minimal. Six years ago, he said, he and his wife “went separate ways.”
Not all the players give so much of their lives to the game. Leonard Rock (which he said was his real name; his chess name is Master Rock) said he worked in the billing department at Manhattan Total Health and sometimes played after work.
But for others, playing chess in the streets leaves room for nothing else.
“Chess is my life,” Little Daddy said. “You can’t play chess and have a girlfriend, because they don’t want you playing chess all night.”

The ultimate result per hand is what matters. Whether we have a B or P with 4,5 or 6 cards isn't the issue, it is the P or B.

Most 8 deck shoes will have 70 to 80 hands. Remember there is a cut and some are burned.

Lets take 70 hands. There are 2^70 possible combinations from all Ps to all Bs - this isn't including ties. This is 1.18059162 x 10^21 possible outcomes.

I think it would be better to find where a pattern breaks down in the short term most readily. I would offer it is around 6 to 12 along a path of similar results.

IE - PPBPBPPBBPBP if we see after this PPBPBP we could be ready to expect a change soon from the immediate past results that continued as PBBPBP we would prepare to bet BPPBPB until we won with a progression of some sort.

There are systems that incoporate this methodology.

I have found with craps that there is a sort of breaking point with FIELD bets where after NO FIELD for 5 or 6 rolls, there should be a FIELD. It appears to be at a standard deviation point where it is more likely to hit after 5 or 6 misses than it is to go to 7 and beyond.

This pattern break method is exactly the same as betting against a streak of P or B.

Age-old thoughts have often been "this has to change" when we see PPPPPPPP or BBBBBBBB

It is no different to expect PBPPBBP to not be expected to be PBPPBBPPBPPBBP.

The difference is that there are more occurences of varying patterns than the two obvious ones: PPPPP.... or BBBBBBB.....

So to attack those when they appear after 6 to 12 or some key number around there, we could expect to be right MOST of the time. How much of the time and so on is what would need to be calculated.

I call shoe with different cards combinations Card Order Shoe and shoe displaying PBPB... results Result Shoes. For a 8-deck shoe disregarding tie, there are average 72 hands, so the Result Shoes number is 2^72=4.722E+21. In fact the number for Card Order Shoe is much less than 416! because you have to exclude the effect of suits. My calculation for Card Order Shoe is 1.649E+376. So there should be 3.492E+354 pigeons go into one pigeon-cage.

I have repeated these figures on different posts merely want to let you guys know two things. 1)the figure E+376 is beyond the capability of the current computer. Given you the fastest computer in the world that can test E+20 shoes a day, you still need almost a year to complete. The problem is that you don't have such a computer; 2)even you can test the entire shoes, the probabilities for next hand are still approx. the same.

I am optimistic that one day either this game will be disappeared or casino has to increase the commission because in future when we have more powerful computer we can beat the game with computer aid.

This is a good thought galo. So far we don't know if the distribution obeys the Gauss curve. The topic about relationsihp between pigeon and pegion-cage is too challenging. Even this is the case, the figure 3.492E+354 pigeons to 1 pigeon-cage is still a horrible number, however that figure is just a average one. There are still 4.73E+21 times of that figure of shoes out there, i.e. on average for every 4.73E+21 shoes you will play the same shoe or the same pigeon-cage. This probability is even less less than hit the lottery (about 1/E+10 of the odds of Mega Lottory, right?).

If you want to find out if it's a Gauss curve try work on 1-deck shoe. I think the computer can handle that if not try half deck.

I can show you some statistics on 1-deck and half-deck shoe here:

(1) Total 500,000 shoes (1-deck):
Total hands: 5075866 (10.15/shoe)
Player: 2268293(44.688%) Banker: 2332781(45.958%) Tie: 474792(9.354%)
Total Shoes: 1.459E+42

(2) Total 500,000 shoes (half-deck):
Total hands: 2450623 (4.90/shoe)
Player: 1093333(44.614%) Banker: 1130165(46.117%) Tie: 227125(9.268%)
Total Shoes: 1.954E+19