System Test Thread: Summary with Statistics on Various Systems

[Archer]

Yes they can ayuinca. The STRONGEST trend usually survives. Fortunately the game is not about always, its about USUALLY.

This is pretty simple to prove or disprove Ellis. Pick a trend, locate it in a number of shoes and calculate the results. I know you prefer anecdotes to real Baccarat discussion but I would like to challenge you to pick a trend.

We can then put it against real or RNG shoes or both to see if there are differences. I would think everyone would like to see such a study. Am I wrong? Can we have a show of hands?

Since you proposed the theory Ellis, you have the honors of choosing any trend you want.

Archer

[Archer]

You know, I often have high rollers at my table. They are up $70,000 one day and down $140,000 the next. They are far and away the biggest bettor at the table. I seldom see the pit boss watching over THEIR shoulder. He already KNOWS how its going to end. No, he's watching over MY shoulder and I'm only playing quarters. But he knows how THAT is going to end also.

Hehehhehehehe, lol. Garnabby you should really start an Ellis archive! The above is the best post Ellis has written. You gotta love this stuff! Ellis, please don't abandon us!

I can see it all now.

"All the dealers look up and notice as I, the great E. Clifton Davis enter the casino. They all nod in acknowledgement to the best Bacc and BJ player ever as I walk by and sit at "my" $5.00 Bacc table! It's the Gold Strike, Tunica (could be Horseshoe, Tunica or Gold Coast, LV, I'm not sure - low rent districts). (Afterall, isn't that where the high rollers are?)"

"I can see the pit critters gather around me. Even the forhead on the Pit Boss himself begins to beat with perspiration as I win unit after unit---betting 2hi! Soon, I am up $200.00 - nay, 300 -400! I've won 16 green!!!!!! Pretty soon the phone rings in the pit. The eye in the sky is watching me. I can just feel it. Better leave or I will get barred! Ha, never mind the guy next to me who is up $70,000.00. He'll be back! He'll lose it all back and then some! But I. . . . "

"Ellis, Ellis!, sweetheart, your were dreaming, wake up, wake up. You were dreaming again! What were you dreamiing about? Here, dear, have some warm milk! Now go back to sleep."

Archer>>>----------------------------> OUCH!

[ayuinca]

You are so entertaining Archer.

[pitty1]

Prediction vs probabilities..Hi ayunica..can u model the probabilities of a rotated dealer..at for a instant call the next hand a number 4 tie and it occurs?
even if it's a luck call what are the odds?..to me that would be in the lightning strike range..what do you think? o yeah no cheating allowed.

[ayuinca]

Pitty1, what is a rotated dealer? Yes, I can calculate the probability(pb) of next hand Tie 4, given the remaining cards in the shoe. So what's the point if you know the pb for that? Only when you count in the pay-odds(8:1) and find the house for tie is a positive number, you have advantage to play. But such condition is pretty rare.

[ayuinca]

Baccarat Counting to Win Strategy by Peter Wu 7/7/2007
http://baccaratforums.com/groups/7/discussion-25/

I find this one interesting so give it a try. Here is 10,000 shoes:

Total Shoe Net Win: -13484.85 (-1.35/shoe)
Shoe Range Occurrence(% of total shoes)
------------------------------------------
70~ 75 - ( -%)
65~ 70 - ( -%)
60~ 65 - ( -%)
55~ 60 - ( -%)
50~ 55 1 ( 0.01%)
45~ 50 5 ( 0.05%)
40~ 45 12 ( 0.12%)
35~ 40 33 ( 0.33%)
30~ 35 86 ( 0.86%)
25~ 30 212 ( 2.12%)
20~ 25 374 ( 3.74%)
15~ 20 598 ( 5.98%)
10~ 15 883 ( 8.83%)
5~ 10 1080 (10.80%)
0~ 5 1333 (13.33%)
-5~ 0 1386 (13.86%)
-10~ -5 1265 (12.65%)
-15~ -10 1014 (10.14%)
-20~ -15 730 ( 7.30%)
-25~ -20 447 ( 4.47%)
-30~ -25 277 ( 2.77%)
-35~ -30 150 ( 1.50%)
-40~ -35 74 ( 0.74%)
-45~ -40 31 ( 0.31%)
-50~ -45 5 ( 0.05%)
-55~ -50 3 ( 0.03%)
-60~ -55 1 ( 0.01%)
-65~ -60 - ( -%)
-70~ -65 - ( -%)
-75~ -70 - ( -%)
Positive Shoes: 4617 (46.17%)
------------------------------------------

[pitty1]

Hi ayuinca..excuse me..dealer rotation i meant a dealer change during a session.I have yet to see a single dealer last a full shoe in a live casino..must be a standard operating procedure..(unless theres a DS advantage with bac play..lol..).No need for (pb) with the play i gave..just proof statistics don't matter to get a win in the game..yeah sure 50,000 hands indicates u have a better chance to hit a 1peat 2peat or 3peat..but u still don't know when it will occur in a shoe.. thus strategies are developed..human elements and instinct still rules to win.Statisics are scary..U know the thousand of possibilities for a 2 card draw? Say can u come up with the odds of a whole shoe duplicating itself?(with 10k,20k,50k shoes) I mean with the same B/P decisions..extra credit for same card count..thanks.

[Ellis]

Ayuinca, you seem to be hoplessly brain washed beyond repair. I don't see how you could ever beat a casino with any consistency with such a negative attitude. There is only one way to win and you denounce it out of hand leaving yourself no way to win. You MUST play the shoe at hand. That is what I teach.

You are right! EVERYONE is looking for a single mechanical Holy Grail that wins. No such system exists or ever will. Such a system is a mathematical impossibility. I've been teaching that for 30 years.

Nearly All truly experienced players recognize the existence of trends in some simplistic form. Most table conversation is about chop vs streak. That is only 2/3 of one trend. The other third is when there is no disparity between chop and streak - when a table is running about even. But there are playable trends OTHER than chop vs streak.

In my simple free public systems there is a streak system and a chop system. I tell the public that you MUST find either the streakiest or the chopiest table to win with these systems. "OTHERWISE they are break even systems." I tell them that up front. But most of the public, such as yourself, does not bother with the write-up, they go straight to the systems with no clue of when to play which system or how to change the system from chop to streak. Therefore they lose just as I warned them they would.

But those who DO differentiate win and often use those winnings to pay for their private subscription.

Do they all win? No, some simply never get the idea of playing the shoe at hand. They continue to play the same way they played before they were members. They simply find new systems to make the same mistakes with and can't be bothered with instructions. I can only lead a horse to water.

But MOST do finally get it and when they do they start winning every trip or close to it. And they do this betting much smaller than the way they were betting. I mention AD only because he came to my forum from this forum. So some from here know of him. But AD is winning very nicely now and has said so on this forum only to be called a liar by certain members here who don't know any better. But there are a lot of ADs on my private forum.

Which brings us to deleting posts. We almost never delete anyone's post and haven't deleted anyone's post in years. I don't recall ever deleting any of your posts but I'll take your word for it. We don't allow trashing other players on my forum. The very few that were deleted were deleted for this reason. We also don't allow the posting of Martingale systems on my forum because they are dangerous and suicidal and can only hurt unsuspecting, inexperienced players. We also delete sales pitches for such systems. But we have noticed no such posts in a long time.

Yes, we delete Garnabby out of hand because he NEVER posts anything the least bit constructive on any forum including this one. To him its all a big name calling contest. We want adults only.

No, I don't think you should join my forum. You are still on a quest for the Holy Grail. Until you get over that I don't think you have the discipline to play our way. Maybe one day you 'll come to the realization that our way is the only way that wins consistently. And maybe not.

I am not the enemy. I do my best to teach students how to win. Its a lot of work. Most get it, but not all.

[thegeorgiahurricane]

I must side with Ellis on this one. Math and statistics have their place in the game-- but in the end you must play the shoe at hand. Therefore, you MUST play the game by being ready to adjust to the shoe at hand. Any method OWN ITS OWN will not stand up to the mathmatical tests to which they are subjected. Only the knowledge of MANY METHODS and an INDIVIDUAL STYLE of PLAY can win in the long run-- and this can't be run through a computer program. It's the human element. Ellis stated you can lead a horse to water, but you can't make him drink. I agree. But in this case you might say you can teach a player many winning methods, but you can't make them a winner.

[Ellis]

I must side with Ellis on this one.

Ha, you're in big trouble now!

Just trying to head em off at the pass. Probably won't work. Too many at the pass.

[ayuinca]

Forget that Ellis, I am not the one will believe you until you are willing or able to show your data, at least your shoes records.

Whether hopeless or not, it's not necessary I have to gamble. I have not played for a while. I do have a system can win statistically but it needs computer aid so is not feasible at casino.

Any way, don't try to make me believe your "trend theory" Ellis. I am not buying that.

[ayuinca]

I must side with Ellis on this one. Math and statistics have their place in the game-- but in the end you must play the shoe at hand. Therefore, you MUST play the game by being ready to adjust to the shoe at hand. Any method OWN ITS OWN will not stand up to the mathmatical tests to which they are subjected. Only the knowledge of MANY METHODS and an INDIVIDUAL STYLE of PLAY can win in the long run-- and this can't be run through a computer program. It's the human element. Ellis stated you can lead a horse to water, but you can't make him drink. I agree. But in this case you might say you can teach a player many winning methods, but you can't make them a winner.

Yes, hurricane, what you advised can be concluded into two points. 1)shoe prediction; 2)subjuctive play factor.

No matter what Ellis or other people say, it would not take you too long to find out how many shoes you predict are correct and how many are inccorrect. I did as Ellis said find the streakest or choppest shoe to play, in a long run the predictions were no more than 50-50 to me. I also tested the SAP with real shoes, it turns out same 50-50. So Ellis, leave me alone here don't try to post and repeat your stuff for me. I was once get into your private forum (I didn't know why I could, maybe you people put me in the wrong list) and surprised; and thanked you for that and promised I would pay you the entrance fee since you already let me in. Guess what happened next day? You guy just kicked me out. So bunch of your guys are just business man fooling around people. That's how I learned your SAP. If any one wants it I can upload it here.

As to the subjective factor, individaul style, whatever you call it. I can not program it and I am not 100% confident with my own subjective guess or my play style so I do not play. Well, people with their own styles can win are their businesses. I am not lucky I don't have the style and I am not going to train that.

[ayuinca]

Hi ayuinca..excuse me..dealer rotation i meant a dealer change during a session.I have yet to see a single dealer last a full shoe in a live casino..must be a standard operating procedure..(unless theres a DS advantage with bac play..lol..).No need for (pb) with the play i gave..just proof statistics don't matter to get a win in the game..yeah sure 50,000 hands indicates u have a better chance to hit a 1peat 2peat or 3peat..but u still don't know when it will occur in a shoe.. thus strategies are developed..human elements and instinct still rules to win.Statisics are scary..U know the thousand of possibilities for a 2 card draw? Say can u come up with the odds of a whole shoe duplicating itself?(with 10k,20k,50k shoes) I mean with the same B/P decisions..extra credit for same card count..thanks.

So far I can only calculate the next hand pb. If a pb for player is 45%, each time you bet when it's 45%, on average you will hit it 2.2 times out of 10. Of course you can choose a higher pb to play instead of 45%. So it won't take 50,000 hands to hit a 2S. I know human elements & instinct are ways to win but I can't rely on them in a long run. The odds for a duplicate result shoe is 2^72(disregard tie), right?

[Archer]

I must side with Ellis on this one. Math and statistics have their place in the game-- but in the end you must play the shoe at hand. Therefore, you MUST play the game by being ready to adjust to the shoe at hand. Any method OWN ITS OWN will not stand up to the mathmatical tests to which they are subjected. Only the knowledge of MANY METHODS and an INDIVIDUAL STYLE of PLAY can win in the long run-- and this can't be run through a computer program. It's the human element. Ellis stated you can lead a horse to water, but you can't make him drink. I agree. But in this case you might say you can teach a player many winning methods, but you can't make them a winner.

What exactly are you agreeing with? Did you quit your day job? Ellis didn't!

It's true that most players use some kind of trend method.

It is not necessarily true that no method will stand up on it's own to mthematical tests. That is your opinion and you are certainly entitled to it.

No you can't make a player a winner. Ellis can't either. His guess methods are playing a 50/50 game. Ellis' advantage is that we, as players play a small number of hands or shoes. As Ayuinca has pointed out, half will win and half will lose. Without a pure mathematical advantage all are just guessing. Why do you think Ellis sells rather than plays?

Archer

[Plasia]

ayuinca said:
I also tested the SAP with real shoes, it turns out same 50-50.

Considering that you ignored things like table selection and just tested it on a bunch of shoes, you probably would have tested on a bunch of shoes that SAP would never be played on. One of the things about Ellis' systems is that you don't go blindly into a shoe playing a system, like you did in your tests, you evaluate the tables at the casino and play the one that has the strongest trend. Hence your results are invalid.

[thegeorgiahurricane]

I agree with Ellis that there is no single holy grail system. I believe it to be impossible or impracticle to put into play. I believe trending is a useful tool in the short run--and every individual shoe is in the short run. I don't care who comes up with an idea--be it Ellis, Garnabby, John1234, or Archer--if it has merit it has merit. And if I can adopt it into my individual style of play I will. I will be in the casino for the next three days--I will post my observations(for anyone interested) upon my return. I want to see if any of my new learning has improved my play.

[thegeorgiahurricane]

And yes--we are just guessing in my opinion--or maybe better stated wagering. It is a commonly accepted fact that each hand is a individual statistical event. And every hand is for all practical reasons an unknown. But it is undeniable that certain shoes or parts of those shoes will trend. IMO exploiting these trends are the best way to make a profit.I dont care if it trends back to 50-50-- as long as the majority of my wagers are on the winning 50 side. I dont care if banker has an overall advantage if the shoe im currently playing is heavy player--I'm going to stick with player until the shoe tells me otherwise. And im going to to play the streak and chop and TT's and whatever else until the shoe tells me otherwise. And with proper money management and a little discipline--and yes-- a little luck I will turn a profit.

[ayuinca]

I played SAP according to the SAP rules, sum up the event of 1S, 2S, 3S, 4S and >=5S; and C/S. After 10 events it'a bout 1/3 of the shoe and then start to play with a progression like 212 or 123 or else; adjust the progression after every 10 events. The idea of SAP is to follow the trend of the last 10, 20, 30... events and adjust the progression in order to have the progrssion lost as less as possible or lost to the least event. I manually tested with real shoes and have the results no better than 50/50.

Maybe now you have newer SAP rules but please don't avoid to answer that: how often the table trend you selected will carry on in the rest of the same shoe? I am very ready to believe this if you can show me your records on a few hundred shoes or just 100 shoes from a land casino indicating the trend you select will remain end shoe. I will not jump to any conclusions before I have data either from RNG test or real shoes test. All my over 2000 real shoes from land casinos give me no advantage on any of Ellis' system.

Please type your records here, don't just talk-talk. I will be really appreciated if you have data that can convince me.

[Archer]

ayuinca said:
I also tested the SAP with real shoes, it turns out same 50-50.

Considering that you ignored things like table selection and just tested it on a bunch of shoes, you probably would have tested on a bunch of shoes that SAP would never be played on. One of the things about Ellis' systems is that you don't go blindly into a shoe playing a system, like you did in your tests, you evaluate the tables at the casino and play the one that has the strongest trend. Hence your results are invalid.

You are absolutely right, Plasia. By your standards Ayuinca's results are invalid. Though it wasn't a "bunch" of shoes. It was thousands. No matter. Table selection is a simple theory that assumes a certain trend or observed pattern previously seen will repeat. It is really not that complicated. Pick ANY trend you want then pick ANY method that will defeat it and test it against individual "biased" shoes ANYwhere that trend appears in the shoe. Record the results. What do you get?

Now Ellis is trying to tell people that it is necessary to find a "table" that shows such a "bias" "every shoe." When will all this nonsense end?

Archer

[Archer]

And yes--we are just guessing in my opinion--or maybe better stated wagering. It is a commonly accepted fact that each hand is a individual statistical event. And every hand is for all practical reasons an unknown. But it is undeniable that certain shoes or parts of those shoes will trend. IMO exploiting these trends are the best way to make a profit.I dont care if it trends back to 50-50-- as long as the majority of my wagers are on the winning 50 side. I dont care if banker has an overall advantage if the shoe im currently playing is heavy player--I'm going to stick with player until the shoe tells me otherwise. And im going to to play the streak and chop and TT's and whatever else until the shoe tells me otherwise. And with proper money management and a little discipline--and yes-- a little luck I will turn a profit.

Exactly right. With a little luck you will turn a profit. I can show you a string of 100 shoes that show a profit - but when tested against 2000 REAL shoes using the same parameters it breaks down.

But please let's not start using the term 50/50 as a trend phenomenon. It is a 50/50 game ALL THE TIME AT EVERY DECISION.

A

[ayuinca]

And yes--we are just guessing in my opinion--or maybe better stated wagering. It is a commonly accepted fact that each hand is a individual statistical event. And every hand is for all practical reasons an unknown. But it is undeniable that certain shoes or parts of those shoes will trend. IMO exploiting these trends are the best way to make a profit.I dont care if it trends back to 50-50-- as long as the majority of my wagers are on the winning 50 side. I dont care if banker has an overall advantage if the shoe im currently playing is heavy player--I'm going to stick with player until the shoe tells me otherwise. And im going to to play the streak and chop and TT's and whatever else until the shoe tells me otherwise. And with proper money management and a little discipline--and yes-- a little luck I will turn a profit.

I understand that hurricane. It's all up to individual style. I also agree that following the trend is certainly a way to play. It's same as you invest money into stock in term of following trend. But everything in the university is all about probability. The pb of buying stock when the 5-day or 10-day curve is going up results in profit will be much higher 50% because all the history data, charts there have the proof; but following the trend of shoe and the trend I believe so far is barely 50/50 because all my tests and real shoes data have the proof of 50/50 too.

As I have said I can win once or twice depending on any subjective decision and luck but if I want to win in a long term I could not do it without knowing the statistics.

Casino is against me with statistcs so I can't fight with them just with luck for few decades (well if I am going to play Bac until my 60s).

[Archer]

ayuinca said:
I also tested the SAP with real shoes, it turns out same 50-50.

Considering that you ignored things like table selection and just tested it on a bunch of shoes, you probably would have tested on a bunch of shoes that SAP would never be played on. One of the things about Ellis' systems is that you don't go blindly into a shoe playing a system, like you did in your tests, you evaluate the tables at the casino and play the one that has the strongest trend. Hence your results are invalid.

OH, I almost forgot. Plasia, Ellis has stated on this forum that SAP turns a profit when played mechanically. That is probably why Ayuinca used it for a computer test. Ellis has also sold other systems (I'm thinking of "The System") that play mechanically and win Baccarat (Craps AND Roulette, too, LOL).

I am not against playing trends and trying to win. I deplore Ellis for selling nearly worthless methods and concepts that are no better than what anyone else on this forum has proposed.

Ellis is still playing green! Some pro, huh? How many shoes do you think Ellis plays a year? I bet he plays no more than 20 shoes a year!

A

[edwardng]

Frankly speaking there is no sure win mechanical system within the present min max bet of any casino, if there is any the principle would have been out by now. Casino's building would have been delepitated state. However, the occasional small wins from casino keeps us moving and as greed takes over our emotion, when the tide turn against us, we will lose all the earlier winnings and perhaps including the capital. We have a saying in chinese, the casino is not afraid you win, but, they are afraid you win and never return. Forget about making a living through gambling

[SRTZEE]

Just because a shoe strats chop or streak does not guarantee it will finish that way. Previous results have no bearing on future results especially in baccarat.

[Archer]

I have been reading this forum for a while. Been playing bac full time for the past 15 years, I thought I can't really agree with you, Ellis.

You mean the pit boss is watching over you because of your play??? You must be joking unless you are Kerry Packer, who can affect the P&L of the casino with his wealth and play.

The casino is not worry about your play. They are just afraid you don't go. And if you are really good and playing for the past 30 or so years full time, I guess your fortune is big enough and seriously, you should be retired by now and won't bother about the $50 dollar monthly that you are trying to squeeze out from fellow bac player.

Just my 2 cents.

Didn't see this until now. Of course you are correct, Bryan. This is where the rubber meets the road. But Ellis rarely actually plays. By his own testimony Ellis has only played twice in the last 6 mos or so.

Archer

[Archer]

Just because a shoe strats chop or streak does not guarantee it will finish that way. Previous results have no bearing on future results especially in baccarat.

That's right. As I stated below this would be a pretty easy thiing for Ellis to prove if he dared to. But this would rin his income stream!

A

[Plasia]

P231523211
B61215311
P33311113

Above is a Black Orchid shoe that I made a decent profit on (over half my buy in). I decided on play 12 what the trend was and played to play 49.

Here's another one where I made over 150% of my bankroll.

B12413225
P1315113113
P412212

I'll let you know when my winning streak ends (and it will, don't worry). The thing is that to make a loss overall I'd have to lose quite a few shoes in a row (more than I've won).

I'm sorry ayuinca that I cannot provide 100s of shoes for you to analyse. May I ask how you think trending works though? For instance in the above 2 shoes, what trends have you recognised, by when and what conclusions did you come to?

[ayuinca]

For any kind of system I have tested, no matter in what form the trend is, the statistics do not indicate any advantage of following the trend.

Regarding to the system you might played with that 2 shoes, I will not feel safe to jump to any conclusion after only a very samll sample.

I believe in this way you guys might understand the 'merit' of trend. For example, there are 2 systems, one is Sys1 and the other is Sys2. Now there is a shoe play half. Sys1 finds a trend like Trend1 and Sys2 finds a trend calls Trend2. Unfortunately Trend1 is opposite to Trend2. So tell me now in what reason do you believe your trend, say Trend1, is representing the truth of the rest of shoe?

There are thousands of systems out there, but let me assume in a land casino there are tens of them are being played by different people in frond of a table. So, these system sys1, sys2, sys3,.... sysn they all can find a trend in term of its own pattern. It is always that all systems there can be classified into 2 groups that one group will play against the other. Same question, how can you know which group is representing the correct direction? Well, maybe yours is the one because it's Ellis' system... If you can tell there the shoe is going with my trend, I guess everyone there will respond nothing but a sigh: one more idiot.

Play with the trend isn't incorrect but I believe you want to know how often the trend will work. This is a very basic question any still-have-a-mind people will think about. For some people they will think they are all random events and there is no even a trend at all in just a short period.

If we have different understanding of trend I think we can end such discussion.

[ayuinca]

Shanghai System

This one is also interesting because it plays to break the pattern 1-2-3 (e.g. P-BB-PPP). During the course it has the potential to get over on a streak or zig-zag run so the wins might be good. Before I will repeat the rules of this system (some of you may already know this system) let me run a program RNG shoes test to find out how often this pattern 1-2-3 will appear because the max. lost on the pattern is 6 units if flat bet.

Taken B/P as 50/50, for 6 hands in a row, the probability is 2^7=128. I expect there will be 0.56 such pattern in a shoe which have 72 hands.

Here is the statistics from 10,000 RNG shoes:

Total 1-2-3 Patterns: 5426 (0.5426/shoe)

Ptn Amnt. Shoes
0________5690
1________3330
2_________837
3_________124
4___________9
5___________1
6___________0
7___________0

I can see there are 5690 shoes do not have a 1-2-3 pattern and there are total 5426 1-2-3 patterns that make 0.5426 per shoe; that is 0.5426*6=3.26 unit lost per shoe but not count in the win yet. Next one I will code in the rules to explore how capable the system is to win.

[Archer]

Shanghai System

This one is also interesting because it plays to break the pattern 1-2-3 (e.g. P-BB-PPP). During the course it has the potential to get over on a streak or zig-zag run so the wins might be good. Before I will repeat the rules of this system (some of you may already know this system) let me run a program RNG shoes test to find out how often this pattern 1-2-3 will appear because the max. lost on the pattern is 6 units if flat bet.

Taken B/P as 50/50, for 6 hands in a row, the probability is 2^7=128. I expect there will be 0.56 such pattern in a shoe which have 72 hands.

Here is the statistics from 10,000 RNG shoes:

Total 1-2-3 Patterns: 5426 (0.5426/shoe)

Ptn Amnt. Shoes
0________5690
1________3330
2_________837
3_________124
4___________9
5___________1
6___________0
7___________0

I can see there are 5690 shoes do not have a 1-2-3 pattern and there are total 5426 1-2-3 patterns that make 0.5426 per shoe; that is 0.5426*6=3.26 unit lost per shoe but not count in the win yet. Next one I will code in the rules to explore how capable the system is to win.

Does it matter what the order of the pattern is?

Also, these kinds of tests ARE important. Ellis emphatically states that this kind of testing is a waste of time. Not so. Diffferent bet placement methods will perform differently. Some better than others (why else would Ellis have a zillion different methods?) No matter how you play it would be best to use the most efficient bet placment possible.

A