Baccarat is beatable statistically

Quote: wz60

This is also the answer to ThatDonGuy:

Doing the test from a player's perspective:

You are going to a Casino and you are going to do Baccarat for 250k shoes, shoe by shoe. Ignoring all ties, you start from hand #9 to the end of the shoe. When you see the previous 8 hands are BPPPPPPP then you bet B. You win if it turns out to be B and you loss if P. You record all your bets and the results of wins and losses then you have the result for all 250k shoes.

Does this make sense?

I think so...
wild-goose chase : An impractical and ill-advised search for something nonexistent or unobtainable; a foolish and useless quest; a futile or hopeless enterprise. Originally, a wild-goose chase was a horse race where the second and all succeeding horses had to follow the leader at definite intervals, thus resembling wild geese in flight. Since the second horse was not allowed to overtake the first, it would become exhausted in its futile chase. It has alternately been suggested that wild-goose chase may refer to the difficulty of capturing a wild goose, implying that even if caught, the prize is of little value.

Is that what you mean by bpppppppb?

Quote: wz60

Let me make this clear: I am willing to admit that I am wrong if anyone can prove that I am wrong.

Your own results have already demonstrated that you are wrong. You just don't see it. Here's what you wrote:

Quote:

Shoe Size (k)/B-Win-Chance after 7P:
1 55.55556 %
5 53.05085
10 52.00507

To put that in plainer English, you are hunting for an extremely rare event: a bank win followed by 7 player wins, and then your theory is that the next non-tie outcome will favor bank significantly more than the expected overall probability.
After 1000 shoes, the observed conditional probability of a bank win after the rare event was 55.55556%.
After 5000 shoes, the observed conditional probability of a bank win after the rare event was 53.05085%.
After 10000 shoes, the observed conditional probability of a bank win after the rare event was 52.00507%.

As a result, the 4000 shoes subsequent to the first 1000 demonstrated an average conditional probability of 52.42467%.
Further, while the first 5000 shoes showed 53.05085%, the second 5000 demonstrated a conditional probability of 50.95929%.

So clearly the "win chance" of your target play isn't 55.555% after 1000 shoes. That happened to be what you observed for those particular 1000 shoes, but how many times did the event happen during those shoes anyway? A dozen or two? If so, your sample size is far too small. If you were looking at 9 total occurrences of the rare event, your most likely number of successes afterwards would either be 4 or 5, leading to 44.44% or 55.55%. The latter is what you observed. Like I said before, your methodology is like tossing a coin a few dozen times, observing that heads occurred 51.3% of the time, and then confidently concluding that the probability of heads for all coin flips is 51.3%. It might feel like it, especially if you've got money on the line, but it's just superstition and confirmation bias messing with your head. I was playing craps earlier this week and had a terrible run: I was betting continuous-come and rolling a lot of numbers but few repeaters. Without fail, every time I got the bases loaded, the shooter would 7-out within 3 rolls. Usually it was after just rolling one more number. Now, if I were superstitious or didn't understand math, I might have concluded that having all the numbers covered increases the likelihood of rolling a 7. That isn't actually true, but it sure seemed like it that day.

You're doing exactly the same thing with your baccarat pattern analysis. If you want to persist in hunting the wumpus, you should fix your data collection so you can see the effects of random variation on your process. Rather than adding your results together in a long running average, which is a really bad way to gather data, you should gather the data in a distribution. For each 1000 shoes, collect (a) the frequency of the rare event, and (b) the win probability after the rare event. Then plot those on a histogram. You'll see the distribution and be able to understand the variance and the mean, as well as how infrequent the rare event is to begin with.

Quote: wz60

This is also the answer to ThatDonGuy:

Doing the test from a player's perspective:

You are going to a Casino and you are going to do Baccarat for 250k shoes, shoe by shoe. Ignoring all ties, you start from hand #9 to the end of the shoe. When you see the previous 8 hands are BPPPPPPP then you bet B. You win if it turns out to be B and you loss if P. You record all your bets and the results of wins and losses then you have the result for all 250k shoes.

Does this make sense?

Yes, and as I already said, I did this 40 times (just to clarify: 40 runs of 250,000 shoes each). The win percentages ranged from 50.3591% to 51.1366%. I also did this for a single run of 200 million shoes and got 50.700%.

Quote: wz60

Let me make this clear: I am willing to admit that I am wrong if anyone can prove that I am wrong.

I don't care whether you admit that you are wrong. However, I will gladly write code to generate data and analyze your claims. At the end, you can have the code and the results. My rate is $500 per hour. Cash up front, of course.

Quote: AxiomOfChoice

I don't care whether you admit that you are wrong. However, I will gladly write code to generate data and analyze your claims. At the end, you can have the code and the results. My rate is $500 per hour. Cash up front, of course.

That's a decent price. Do your results come with a happy ending? (Jk)

Quote: ThatDonGuy

Yes, and as I already said, I did this 40 times (just to clarify: 40 runs of 250,000 shoes each). The win percentages ranged from 50.3591% to 51.1366%. I also did this for a single run of 200 million shoes and got 50.700%.

But you haven't give your result for the same 250k data I used, did I miss it?

Quote: wz60

But you haven't give your result for the same 250k data I used, did I miss it?

You understand that 250k shoes is nowhere near enough data, right?

The problem is that you're only betting around 1 hand every 3 shoes. You can't expect to get consistent results, down to a few decimal places, from only 80k bets. That's why Don's numbers vary so much from shoe to shoe.

Quote: Dracula

That's a decent price. Do your results come with a happy ending? (Jk)

I am fairly sure that he will not be happy with the results :)

Quote: wz60

But you haven't give your result for the same 250k data I used, did I miss it?

We need to confirm:
Num of total bets you did out of this 250k shoe
Num of wins
Num of losses

Quote: wz60

We need to confirm:
Num of total bets you did out of this 250k shoe
Num of wins
Num of losses

If we don't conform results for same data, how do I trust your calculations you trust my calculations?

Quote: MathExtremist

Your own results have already demonstrated that you are wrong. You just don't see it. Here's what you wrote:

To put that in plainer English, you are hunting for an extremely rare event: a bank win followed by 7 player wins, and then your theory is that the next non-tie outcome will favor bank significantly more than the expected overall probability.
After 1000 shoes, the observed conditional probability of a bank win after the rare event was 55.55556%.
After 5000 shoes, the observed conditional probability of a bank win after the rare event was 53.05085%.
After 10000 shoes, the observed conditional probability of a bank win after the rare event was 52.00507%.

As a result, the 4000 shoes subsequent to the first 1000 demonstrated an average conditional probability of 52.42467%.
Further, while the first 5000 shoes showed 53.05085%, the second 5000 demonstrated a conditional probability of 50.95929%.

Thus showing the law of large numbers in effect.

Quote: wz60

But you haven't give your result for the same 250k data I used, did I miss it?

No - but I already said that I don't see any purpose in it, since I don't see why my results with your data would not match yours.

If there is another reason why you want me to do it, then let me know. Otherwise, I trust your calculations from your data. (It's not your calculations that are being questioned; it's the hypothesis that, somehow, that one set of 250K shoes leads to a conclusion that applies in general to all 8-deck shoe baccarat games.)

Quote: ThatDonGuy

No - but I already said that I don't see any purpose in it, since I don't see why my results with your data would not match yours.

If there is another reason why you want me to do it, then let me know. Otherwise, I trust your calculations from your data. (It's not your calculations that are being questioned; it's the hypothesis that, somehow, that one set of 250K shoes leads to a conclusion that applies in general to all 8-deck shoe baccarat games.)

The reason is that I am suspicious of your results that 250k data can swing from 50.3591 to 51.1366.

Quote: wz60

The reason is that I am suspicious of your results that 250k data can swing from 50.3591 to 51.1366.

How is my comparing the number of times B,P,P,P,P,P,P,P,P and B,P,P,P,P,P,P,P,B appear in those 10 files (which is exactly what you are asking me to do, right?) going to make your confidence in my numbers any better, since I obviously have to use an entirely different method for counting those shoes than I did for generating and counting the ones I used?

Quote: ThatDonGuy

How is my comparing the number of times B,P,P,P,P,P,P,P,P and B,P,P,P,P,P,P,P,B appear in those 10 files (which is exactly what you are asking me to do, right?) going to make your confidence in my numbers any better, since I obviously have to use an entirely different method for counting those shoes than I did for generating and counting the ones I used?

That is exactly the point: the correct answer for same data should be only one. You and me are using different methods but we should get same numbers. Without knowing this I don't trust your results.

Quote: wz60

The reason is that I am suspicious of your results that 250k data can swing from 50.3591 to 51.1366.

When one has no concept of variance, anything and everything looks suspicious
250k is such a small sample size you must agree.

What is the average between 50.3591 to 51.1366?
about 50.74785
much closer to 50.6825 when we consider variance.

But we should really start at all your first post claims.

Quote: wz60

I want to share my findings and I want anyone who can do modeling to challenge me.

there should not be any challenge.
Scientific study is about finding out the truth and maybe having more than one arriving at the same conclusions.

Quote: wz60

can some bet selections provide higher edge and even >51.28 so a statistically win can be achieved?

The answer is yes and some selections do provide much better edges.

I say the answer is NO.
here you now must show all your data that made you arrive at this conclusion to say yes.
Only after that can another agree or disagree with your conclusions

Quote: wz60

Here are some examples:

1 You should not bet B after B --- continuation is always bad bet in Baccarat statistically, although each one has slightly different statistical expectation, e.g. bet 5B to continue is much better than 6B to continue (50.18 vs 49.28).

where is your proof

Quote: wz60

3 Lets back to bet B strategy, here is a winning one:
bet B every time after first P appears, this will give us a 51.41% edge, it is a winner since it is >51.28.
If you bet B after 2P, you will get a 51.24% edge
If you bet B after 3P, you will get 51.27% ---- very close to even
If you bet B after 8P, you have a big edge at 52.5%

I am sure that there are other B-betting selections that will also provide winning statistics.

where is the proof?

Quote: wz60

The bottom line is: the widely recognized 1.06% house edge for Baccarat is very misleading compared with BJ ----- BJ’s number is after applying some strategies while the Baccarat 1.06% number is flat overall number.
It can be reduced significantly by some good betting selections.

"good betting selections"
all talk and no show
where is your proof?

I would claim that variance made you to conclude these statements after you looked over a data sample, and a very small one at that.
But this has already been pointed out.

Show all your proof and forever change the game of Casino Baccarat
show no proof and continue to waste time and efforts.

Sally

Quote: wz60

That is exactly the point: the correct answer for same data should be only one. You and me are using different methods but we should get same numbers. Without knowing this I don't trust your results.

yes the same expected value when considering variance.
Oh, what is variance?

I always get 50 heads and 50 tails when I flip 100 fair coins.
always
Sally

Quote: wz60

The reason is that I am suspicious of your results that 250k data can swing from 50.3591 to 51.1366.

What was the numerator in your fraction, and what was the denominator, that lead to your reported result? You may have looked through 250,000 shoes, but how many times did you actually observe the pattern you're seeking, and how many times did banker win on the next hand? A few hundred times, perhaps a few thousand?

Quote: MathExtremist

What was the numerator in your fraction, and what was the denominator, that lead to your reported result? You may have looked through 250,000 shoes, but how many times did you actually observe the pattern you're seeking, and how many times did banker win on the next hand? A few hundred times, perhaps a few thousand?

That is exactly we need to know (and I have mine to share) to confirm that different calculations reach same results. Then we can talk about other things.

Quote: ThatDonGuy

How is my comparing the number of times B,P,P,P,P,P,P,P,P and B,P,P,P,P,P,P,P,B appear in those 10 files (which is exactly what you are asking me to do, right?) going to make your confidence in my numbers any better, since I obviously have to use an entirely different method for counting those shoes than I did for generating and counting the ones I used?

Did you filter out all T's before calculation? Without filtering out all T's then the swings in the results are understandable.

Quote: wz60

Did you filter out all T's before calculation? Without filtering out all T's then the swings in the results are understandable.

I filter out the Ts in my numbers. Why wouldn't different sets of 250,000 shoes have different numbers even with the Ts removed? Remember, 250,000 shoes and 250,000 occurrences of BPPPPPPP are two entirely different things.

Question: are you including PPPPPPPB and PPPPPPPP at the start of a shoe (after Ts are removed, of course) in your counts?

Quote: wz60

The reason is that I am suspicious of your results that 250k data can swing from 50.3591 to 51.1366.

That is what happens when you use such a ridiculously tiny sample size.

Quote: wz60

That is exactly we need to know (and I have mine to share) to confirm that different calculations reach same results. Then we can talk about other things.

But you're not actually sharing your data, just the ratio. So let's try this another way: run your simulations until you have observed 250,000 instances of your rare event, and then report the sample probability of winning events.

Quote: wz60

Can you run a simulation for following 2 cases to see if my results on 250000-k shoes are in line with yours:
a) Bet 5P to stop (BPPPPPB vs BPPPPPP) I got B has only 50.62% edge
b) Bet 7P to stop (BPPPPPPPB vs BPPPPPPPP) I got B has 51.10% edge

In the B5P case, I counted 125851 BPPPPPB and 122787 BPPPPPP = 50.61616%

In the B7P case, I counted 30019 BPPPPPPB and 28724 BPPPPPPP (yes, after removing all ties) = 51.10226%.

In both cases, I match your numbers - using the 250,000 shoes you used.

Now, how does this make any of my numbers invalid?

I just ran 20 million shoes to count how many times B7P was followed by B, and how many times it was followed by P.
Here is what I got - the columns indicate how many shoes had been dealt, the combined number of times B7PB and B8P appeared (after ties were removed), and what percentage of those times it was B7PB instead of B8P:

Shoes	B7Ps	% B7PB
50000	11781	50.3692386045
100000	23592	50.5595116989
150000	35328	50.3708106884
200000	47261	50.3607625738
250000	59190	50.4730528806
300000	70836	50.6098593935
350000	82637	50.6322833598
400000	94449	50.7024955267
450000	106199	50.685034699
500000	118001	50.6351641088
550000	129780	50.7004160888
600000	141628	50.7088993702
650000	153427	50.6990295059
700000	165117	50.6501450487
750000	176879	50.6804086409
800000	188700	50.7546369899
850000	200357	50.7519078445
900000	212176	50.7309969082
950000	224019	50.7198050165
1000000	235705	50.7473324707
1050000	247407	50.7511913568
1100000	259137	50.7642675496
1150000	270948	50.7632460841
1200000	282913	50.7937068993
1250000	294431	50.7735258855
1300000	306169	50.7791448514
1350000	318118	50.792787582
1400000	329941	50.7893835565
1450000	341757	50.8083228727
1500000	353603	50.8030192052
1550000	365293	50.8077077853
1600000	377157	50.8149126226
1650000	388964	50.8026449749
1700000	400861	50.8098817296
1750000	412723	50.7919355112
1800000	424672	50.7886086203
1850000	436345	50.7905441795
1900000	448132	50.7843671061
1950000	459949	50.7738901487
2000000	471844	50.7523673078
2050000	483644	50.7437288584
2100000	495493	50.7417864632
2150000	507195	50.7461627185
2200000	518994	50.7518391349
2250000	530840	50.7473061563
2300000	542486	50.7587292575
2350000	554226	50.7812697347
2400000	565912	50.7748554546
2450000	577878	50.7835563908
2500000	589588	50.768841971
...
3000000	707902	50.7307508666
3500000	825548	50.7022002355
4000000	943861	50.7266430121
4500000	1061190	50.7562265004
5000000	1179832	50.7578197574
5500000	1297880	50.7683298918
6000000	1415693	50.7721659993
6500000	1533597	50.7513381938
7000000	1651097	50.7452923723
7500000	1768879	50.7338828716
8000000	1886884	50.7212950028
8500000	2004329	50.7206152283
9000000	2121967	50.7254354097
9500000	2239648	50.711495735
10000000	2357297	50.6985755295
10500000	2475310	50.6986599658
11000000	2593342	50.7006403321
11500000	2710711	50.691903342
12000000	2828572	50.6928584459
12500000	2946644	50.6971999332
13000000	3064195	50.7036595256
13500000	3181743	50.704880941
14000000	3299348	50.7064426062
14500000	3417089	50.7052933067
15000000	3534732	50.6948758774
15500000	3652441	50.6875812641
16000000	3770016	50.6842411279
16500000	3887558	50.6897131824
17000000	4005103	50.6891832744
17500000	4122836	50.6880215463
18000000	4240243	50.6843829469
18500000	4358269	50.6864078376
19000000	4475925	50.6873551277
19500000	4593968	50.6896434629
20000000	4710900	50.6924366894
...
21000000	4947160	50.6967431819
22000000	5182656	50.6951840909
23000000	5418798	50.694877351
24000000	5654539	50.6889597896
25000000	5890306	50.6824772771
26000000	6125475	50.6852774683
27000000	6361443	50.6788318311
28000000	6597680	50.6801936438
29000000	6833633	50.6854406726
30000000	7069958	50.685506194
31000000	7305542	50.6873001346
32000000	7540713	50.6876471761
33000000	7775968	50.6870655846
34000000	8011583	50.6847398323
35000000	8247267	50.6831657081
36000000	8483523	50.68206923
37000000	8718994	50.6792870829
38000000	8954520	50.6777136016
39000000	9190386	50.6725615224
40000000	9426322	50.676605361
41000000	9662257	50.673150176
42000000	9897254	50.6758743385
43000000	10133447	50.6767440536
44000000	10369121	50.6747775438
45000000	10604553	50.6736116081
46000000	10840398	50.6722815897
47000000	11076347	50.6749653112
48000000	11311559	50.6776652095
49000000	11546898	50.6776538599
50000000	11781561	50.6800414648
55000000	12958964	50.6825699956
60000000	14136853	50.6840171571
65000000	15315290	50.683062482
70000000	16493208	50.6875072454
75000000	17670666	50.6844337389
80000000	18850461	50.6802724878
85000000	20027584	50.6791583049
90000000	21205488	50.6827383553
95000000	22383243	50.6787287258
100000000	23561206	50.6803599103
105000000	24741013	50.6821406221
110000000	25918129	50.6830064778
115000000	27095230	50.6819871985
120000000	28273926	50.6804148812
125000000	29450216	50.6833905734
130000000	30627787	50.6837206358
135000000	31805195	50.6819027521
140000000	32983082	50.6791269536
145000000	34161518	50.6792906568
150000000	35337668	50.6827586925
155000000	36514940	50.6796533145
160000000	37693418	50.6793812119
165000000	38873213	50.6820081993
170000000	40051711	50.6809509337
175000000	41229026	50.679310251
180000000	42408288	50.6785206703
185000000	43585188	50.6804352892
190000000	44762722	50.6802848138
195000000	45943430	50.6809439347
200000000	47119619	50.6801105501

This reminds me of a clip -

http://m.youtube.com/watch?v=KX5jNnDMfxA

Quote: RS

I don't follow the logic. What's the point of squaring either of the RC or the tag values? A third of the deck remaining.....means 66% pen? Or they cut off 1/3 of a deck (Ie 17 cards)? How many decks?

I have no knowledge on this topic. Ask someone knowledgeable on the topic if you are interested in details about quadratics. I am changing my preferences to filter your posts, which is remarkably unfortunate.

Quote: ThatDonGuy

I just ran 20 million shoes to count how many times B7P was followed by B, and how many times it was followed by P.
Here is what I got - the columns indicate how many shoes had been dealt, the combined number of times B7PB and B8P appeared (after ties were removed), and what percentage of those times it was B7PB instead of B8P:

Shoes	B7Ps	% B7PB
50000	11781	50.3692386045
100000	23592	50.5595116989
150000	35328	50.3708106884
200000	47261	50.3607625738
250000	59190	50.4730528806
300000	70836	50.6098593935
350000	82637	50.6322833598
400000	94449	50.7024955267
450000	106199	50.685034699
500000	118001	50.6351641088
550000	129780	50.7004160888
600000	141628	50.7088993702
650000	153427	50.6990295059
700000	165117	50.6501450487
750000	176879	50.6804086409
800000	188700	50.7546369899
850000	200357	50.7519078445
900000	212176	50.7309969082
950000	224019	50.7198050165
1000000	235705	50.7473324707
1050000	247407	50.7511913568
1100000	259137	50.7642675496
1150000	270948	50.7632460841
1200000	282913	50.7937068993
1250000	294431	50.7735258855
1300000	306169	50.7791448514
1350000	318118	50.792787582
1400000	329941	50.7893835565
1450000	341757	50.8083228727
1500000	353603	50.8030192052
1550000	365293	50.8077077853
1600000	377157	50.8149126226
1650000	388964	50.8026449749
1700000	400861	50.8098817296
1750000	412723	50.7919355112
1800000	424672	50.7886086203
1850000	436345	50.7905441795
1900000	448132	50.7843671061
1950000	459949	50.7738901487
2000000	471844	50.7523673078
2050000	483644	50.7437288584
2100000	495493	50.7417864632
2150000	507195	50.7461627185
2200000	518994	50.7518391349
2250000	530840	50.7473061563
2300000	542486	50.7587292575
2350000	554226	50.7812697347
2400000	565912	50.7748554546
2450000	577878	50.7835563908
2500000	589588	50.768841971
...
3000000	707902	50.7307508666
3500000	825548	50.7022002355
4000000	943861	50.7266430121
4500000	1061190	50.7562265004
5000000	1179832	50.7578197574
5500000	1297880	50.7683298918
6000000	1415693	50.7721659993
6500000	1533597	50.7513381938
7000000	1651097	50.7452923723
7500000	1768879	50.7338828716
8000000	1886884	50.7212950028
8500000	2004329	50.7206152283
9000000	2121967	50.7254354097
9500000	2239648	50.711495735
10000000	2357297	50.6985755295
10500000	2475310	50.6986599658
11000000	2593342	50.7006403321
11500000	2710711	50.691903342
12000000	2828572	50.6928584459
12500000	2946644	50.6971999332
13000000	3064195	50.7036595256
13500000	3181743	50.704880941
14000000	3299348	50.7064426062
14500000	3417089	50.7052933067
15000000	3534732	50.6948758774
15500000	3652441	50.6875812641
16000000	3770016	50.6842411279
16500000	3887558	50.6897131824
17000000	4005103	50.6891832744
17500000	4122836	50.6880215463
18000000	4240243	50.6843829469
18500000	4358269	50.6864078376
19000000	4475925	50.6873551277
19500000	4593968	50.6896434629
20000000	4710900	50.6924366894
...
21000000	4947160	50.6967431819
22000000	5182656	50.6951840909
23000000	5418798	50.694877351
24000000	5654539	50.6889597896
25000000	5890306	50.6824772771
26000000	6125475	50.6852774683
27000000	6361443	50.6788318311
28000000	6597680	50.6801936438
29000000	6833633	50.6854406726
30000000	7069958	50.685506194
31000000	7305542	50.6873001346
32000000	7540713	50.6876471761
33000000	7775968	50.6870655846
34000000	8011583	50.6847398323
35000000	8247267	50.6831657081
36000000	8483523	50.68206923
37000000	8718994	50.6792870829
38000000	8954520	50.6777136016
39000000	9190386	50.6725615224
40000000	9426322	50.676605361
41000000	9662257	50.673150176
42000000	9897254	50.6758743385
43000000	10133447	50.6767440536
44000000	10369121	50.6747775438
45000000	10604553	50.6736116081
46000000	10840398	50.6722815897
47000000	11076347	50.6749653112
48000000	11311559	50.6776652095
49000000	11546898	50.6776538599
50000000	11781561	50.6800414648
55000000	12958964	50.6825699956
60000000	14136853	50.6840171571
65000000	15315290	50.683062482
70000000	16493208	50.6875072454
75000000	17670666	50.6844337389
80000000	18850461	50.6802724878
85000000	20027584	50.6791583049
90000000	21205488	50.6827383553
95000000	22383243	50.6787287258
100000000	23561206	50.6803599103
105000000	24741013	50.6821406221
110000000	25918129	50.6830064778
115000000	27095230	50.6819871985
120000000	28273926	50.6804148812
125000000	29450216	50.6833905734
130000000	30627787	50.6837206358
135000000	31805195	50.6819027521
140000000	32983082	50.6791269536
145000000	34161518	50.6792906568
150000000	35337668	50.6827586925
155000000	36514940	50.6796533145
160000000	37693418	50.6793812119
165000000	38873213	50.6820081993
170000000	40051711	50.6809509337
175000000	41229026	50.679310251
180000000	42408288	50.6785206703
185000000	43585188	50.6804352892
190000000	44762722	50.6802848138
195000000	45943430	50.6809439347
200000000	47119619	50.6801105501

Thx, I was wrong to think that 250 k data is large enough to produce insignificant swings from statistic expectation.

Quote: wz60

Let me make this clear: I am willing to admit that I am wrong if anyone can prove that I am wrong.

The problem is, what do you call a proof ? When you get one, you disregard it.

Quote: wz60

Well then lets wait others to check this data. You cannot convince me without presenting your results for same data I used.

Actually, you are not asking for proof, but "to be convinced". That's different; I cannot convince someone who does not understand mathematical proof. What you ask is not proof, it is sample results, which never proved anything. And then when you get some new sample analysis, you claim the samples are not good and yours is the only one that can be used. Highly unscientific. Compels me to ask, What exactly was your job at the engineering company?... Marketing and advertisement, probably. They like data-mining and are accustomed to believe in their own cowdung.

On another point: at one moment you compare sequences of BPP and BPB and claim one is more frequent. Did you (correctly) cut up your sample into sequences of three (INCLUDING ties), then check for the BP- pattern and check the frequency of third-place B and P? Or did you pick up every such sequence appearing in the list? In the latter case, it is logical that the frequency differs. Some patterns overlapped (e.g. BPBPP) but that can't happen the other way round.

Quote: wz60

This is also the answer to ThatDonGuy:

Doing the test from a player's perspective:

You are going to a Casino and you are going to do Baccarat for 250k shoes, shoe by shoe. Ignoring all ties, you start from hand #9 to the end of the shoe. When you see the previous 8 hands are BPPPPPPP then you bet B. You win if it turns out to be B and you loss if P. You record all your bets and the results of wins and losses then you have the result for all 250k shoes.

Does this make sense?

This is preposterous. Why is this thread still alive? Yes, bet the opposite of what won last hand because it is due. No one ever thought of that before.

Quote: Sonuvabish

This is preposterous. Why is this thread still alive? Yes, bet the opposite of what won last hand because it is due. No one ever thought of that before.

BRB withdrawing my life savings and driving to the nearest store.

Quote: Sonuvabish

This is preposterous. Why is this thread still alive?

Because people like us are responding to it. The OP admitted his mistake in his most recent post (see his response at the bottom of that list of numbers). Sometimes, it just takes sheer numbers to get the point across.