Silver Tiger Baccarat Strategy

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  • Roulette Analysis
  • Miscellaneous

Introduction

The Gambler's Fallacy is the mistaken belief that if an independent event has not happened in a long time, then it becomes overdue and more likely. It is also equally incorrect that if an outcome has happened a disproportionate number of times lately, compared to statistical expectations, then it becomes overheated and less likely to occur the next time. An example of this fallacious thinking might be that if the number 23 hasn't been drawn in a 6-49 lottery the last 100 games, then it becomes more likely to be drawn during the next drawing.

Many worthless betting strategies and systems are based on belief in the Gambler's Fallacy. I got the idea for writing about this after reading an 888 online roulette article by Frank Scoblete entitled How to Take Advantage of Roulette Hot Spots. In that article, Scoblete recommends taking a count of each outcome for 3,700 spins in single-zero roulette and 3,800 spins in double-zero roulette in the hunt for 'hot numbers.' Never mind that this would take about 100 hours to make this many observations, assuming the industry standard of 38 spins per hour.

Some casinos are kind enough to give you, on a silver platter, the number of times in the last 300 spins the four 'hottest' and 'coolest' numbers occurred. The image at the top of the page shows an example taken on a double-zero wheel at the Venetian. Free Slot Tournament Strategy. There is no physical thing you can do to get the maximum number of spins or change the results on the spinning reels beside to keep pressing the spin as fast as you. Having a word with Lady Luck might also help because you are going to need the luck to be on your side.

Before going further, let me say that I strongly believe modern roulette wheels made by top brands like Cammegh are extremely precise and any bias would be minuscule compared to the house advantage. Thus, testing a modern roulette for bias would be a total waste of time. Now, testing a 30-year-old hand-me-down wheel in a banana republic might be another story. However, you're on your own if you win a lot of money from said casino and try to leave with it.

That said, if you track 3,800 outcomes in single-zero roulette, the average number of times any number will hit is 3800/38=100. I ran a simulation of over 1.3 trillion spins, counting how many times each number was hit, sorting the outcomes to find the most frequent number and how many times it was observed, and keeping a count of how many times the most frequent number in each simulation was seen.

Hottest Number in 3,800 Spins of Double-Zero Roulette

As a former actuary, I hate to use a layman's term like the 'hottest number,' but that is how gamblers talk so will go with that. That said, following are the results of the count of the hottest number in millions of 3800-spin simulations.

Count of the Hottest Number in 3,800 Spins on Double-Zero Wheel

StatisticValue
Mean122.02
Median121
Mode120
90th Percentile128
95th Percentile131
99th Percentile136
99.9th Percentile142
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Here is what the table above means in plain simple English.

  • The mean, or average, count of the hottest number is 122.02.
  • The median count of the most frequent number is 121. This means that over 50% of time the most frequent number appeared 121 times or less, as well as 121 times or more. This is possible because the probability of 121 observations is in both groups.
  • The mode, or most count of the hottest number is 120, which happens 8.29% of the time.
  • The 90th percentile is the smallest number such that the probability the count of the hottest number is at least 90% .
  • The 95th percentile is the smallest number such that the probability the count of the hottest number is at least 95%.
  • The 99th percentile is the smallest number such that the probability the count of the hottest number is at least 99%.
  • The 99.9th percentile is the smallest number such that the probability the count of the hottest number is at least 99.9%.

Hottest Number in 3,700 Spins of Single-Zero Roulette

The results are very similar with 3,700 spins tracked on a single-zero wheel. Following is a summary of the results.

Count of the Hottest Number in 3,700 Spins on Single-Zero Wheel

StatisticValue
Mean121.90
Median121
Mode120
90th Percentile128
95th Percentile131
99th Percentile136
99.9th Percentile142

The following table shows the full results of the simulation on both wheels. The two commulative columns show the probability that the count of the hottest number is the number on the left column or more. For example, the probability the hottest number in 3,700 spins of single-zero roulette is 130 or more is 0.072044.

Summary of the Count of the Hottest Number in 3,700 Spins of Single-Zero Roulette and 3,800 spins of Double-Zero Roulette

CountProbability
Single Zero
Cummulative
Single Zero
Probability
Double Zero
Cummulative
Double Zero
160 or More0.0000010.0000010.0000010.000001
1590.0000000.0000010.0000000.000001
1580.0000010.0000010.0000010.000001
1570.0000010.0000020.0000010.000002
1560.0000010.0000030.0000010.000003
1550.0000020.0000050.0000020.000005
1540.0000030.0000090.0000030.000008
1530.0000050.0000130.0000050.000013
1520.0000070.0000200.0000080.000021
1510.0000120.0000320.0000120.000033
1500.0000170.0000490.0000180.000051
1490.0000260.0000750.0000270.000077
1480.0000380.0001140.0000410.000118
1470.0000600.0001740.0000620.000180
1460.0000910.0002650.0000920.000273
1450.0001320.0003970.0001370.000409
1440.0001950.0005920.0001990.000608
1430.0002820.0008740.0002890.000898
1420.0004090.0012830.0004210.001319
1410.0005800.0018630.0006060.001925
1400.0008330.0026960.0008600.002784
1390.0011860.0038820.0012150.003999
1380.0016520.0055340.0017040.005703
1370.0023150.0078490.0023740.008077
1360.0031750.0110230.0032860.011363
1350.0043550.0153780.0044890.015852
1340.0059160.0212950.0060880.021940
1330.0079390.0292330.0081960.030136
1320.0106010.0398340.0109080.041044
1310.0139910.0538240.0143840.055428
1300.0182200.0720440.0187570.074185
1290.0234980.0955420.0241140.098299
1280.0298660.1254080.0306030.128901
1270.0372880.1626960.0382280.167130
1260.0457710.2084670.0468980.214027
1250.0551650.2636320.0563100.270337
1240.0648530.3284850.0660200.336357
1230.0741780.4026620.0752360.411593
1220.0819290.4845910.0828850.494479
1210.0871580.5717500.0876960.582174
1200.0885200.6602690.0885590.670734
1190.0849820.7452520.0844060.755140
1180.0764540.8217050.0752450.830385
1170.0636060.8853120.0618510.892236
1160.0480690.9333810.0461110.938347
1150.0324320.9658130.0306040.968952
1140.0191170.9849300.0176640.986616
1130.0095670.9944960.0086140.995230
1120.0038940.9983900.0034200.998650
1110.0012570.9996470.0010650.999715
1100.0002970.9999440.0002430.999958
1090.0000500.9999940.0000380.999996
108 or Less0.0000061.0000000.0000041.000000

Count of the Hottest Numbers in 300 Spins in Double-Zero Roulette

What if you don't want to spend 100 hours gathering data on a single wheel? Some casinos are kind enough to give you, on a silver platter, the number of times in the last 300 spins the four 'hottest' and 'coolest' numbers occurred. The image at the top of the page shows an example taken on a double-zero wheel at the Venetian.

In 300 spins, the average number of wins on a double-zero wheel for any number is 300/38=7.9. As you can see from the image above, the four hottest numbers were 20, 5, 29, and 2, which occurred 15, 14, 13, and 12 times respectively. Is this unusual? No. In a simulation of over 80 billion spins, the most frequent number, in 300-spin experiments, appeared most frequently at 14 times with a probability of 27.4%. The most likely total of the second, third, and fourth most frequent numbers was 13, 12, and 12 times respectively, with probabilities of 37.9%, 46.5%, and 45.8%. So the results of the 'hottest' numbers in the image above were a little more flat than average.

The following table shows the probabilities of the four hottest numbers in 300 spins of double-zero roulette. For example, the probability the third most frequent number happens 15 times is 0.009210.

Count of the Hottest Four Numbers in 300 Spins on a Double-Zero Wheel

ObservationsProbability
Most Frequent
Probability Second
Most Frequent
Probability Third
Most Frequent
Probability Fourth
Most Frequent
25 or More0.0000220.0000000.0000000.000000
240.0000510.0000000.0000000.000000
230.0001660.0000000.0000000.000000
220.0005090.0000000.0000000.000000
210.0014940.0000010.0000000.000000
200.0041200.0000090.0000000.000000
190.0108060.0000750.0000000.000000
180.0265990.0005320.0000030.000000
170.0605260.0032630.0000600.000001
160.1235640.0169880.0008520.000020
150.2126990.0712620.0092100.000598
140.2741180.2150250.0682420.011476
130.2127810.3790970.2837680.117786
120.0679130.2707470.4647480.457655
110.0046150.0425520.1682850.383900
100.0000170.0004480.0048300.028544
90.0000000.0000000.0000010.000020
Total1.0000001.0000001.0000001.000000

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth hottest numbers in millions of 300-spin simulations of double-zero roulette.

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Summary of the Count of the Four Most Frequent Numbers in 300 Spins of Double-Zero Wheel

OrderMeanMedianMode
First14.481414
Second13.071313
Third12.271212
Fourth11.701212

Count of the Coolest Numbers in 300 Spins in Double-Zero Roulette

The next table shows the probability of each count of the four collest numbers in 300 spins of double-zero roulette.

Count of the Coolest Four Numbers in 300 Spins on a Double-Zero Wheel

ObservationsProbability Least
Frequent
Probability Second
Least Frequent
Probability Third
Least Frequent
Probability Fourth
Least Frequent
00.0126790.0000630.0000000.000000
10.0980300.0051750.0001350.000002
20.3158840.0885090.0120410.001006
30.4162540.4204910.2053030.063065
40.1502200.4326380.5951390.522489
50.0069240.0529450.1855050.401903
60.0000080.0001800.0018780.011534
Total1.0000001.0000001.0000001.000000

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth coolest numbers in the 300-spin simulations of double-zero roulette.

Summary of the count of the Four Least Frequent Numbers on a Double-Zero Wheel

OrderMeanMedianMode
Least2.6133
Second Least3.4434
Third Least3.9644
Fourth Least4.3644

Count of the Hottest Numbers in 300 Spins of Single-Zero Roulette

In 300 spins, the average number of wins on a single-zero wheel for any number is 300/37=8.11. The next table shows the probability of each count of the four coolest numbers in 300 spins of double-zero roulette. For example, the probability the third most frequent number happens 15 times is 0.015727.

Count of the Hottest Four Numbers in 300 Spins on a Single-Zero Wheel

ObservationsProbability
Most Frequent
Probability Second
Most Frequent
Probability Third
Most Frequent
Probability Fourth
Most Frequent
25 or More0.0000340.0000000.0000000.000000
240.0000780.0000000.0000000.000000
230.0002450.0000000.0000000.000000
220.0007280.0000000.0000000.000000
210.0020690.0000020.0000000.000000
200.0055700.0000180.0000000.000000
190.0141910.0001350.0000000.000000
180.0338330.0009050.0000080.000000
170.0742350.0052020.0001250.000001
160.1444900.0252860.0016240.000050
150.2324290.0970460.0157270.001286
140.2697350.2593600.1012590.021054
130.1772160.3824320.3471020.175177
120.0432660.2081370.4297150.508292
110.0018790.0213730.1029790.283088
100.0000030.0001030.0014610.011049
90.0000000.0000000.0000000.000002
Total1.0000001.0000001.0000001.000000

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth hottest numbers in millions of 300-spin simulations of double-zero roulette.

Summary — Count of the Four Hottest Numbers — Double-Zero Wheel

OrderMeanMedianMode
First14.741514
Second13.301313
Third12.501212
Fourth11.921212

Count of the Coolest Numbers in 300 Spins in Single-Zero Roulette

The next table shows the probability of each count of the four coolest numbers in 300 spins of double-zero roulette. For example, the probability the third coolest numbers will be observed five times is 0.287435.

Count of the Coolest Four Numbers in 300 Spins on a Double-Zero Wheel

ObservationsProbability Least
Frequent
Probability Second
Least Frequent
Probability Third
Least Frequent
Probability Fourth
Least Frequent
00.0099260.0000380.0000000.000000
10.0796540.0033240.0000680.000001
20.2752260.0623920.0067910.000448
30.4193840.3504080.1401730.034850
40.2001960.4843570.5579070.406702
50.0155630.0985470.2874350.521238
60.0000500.0009330.0076260.036748
70.0000000.0000000.0000010.000013
Total1.0000001.0000001.0000001.000000

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth coolest numbers in the 300-spin simulations of single-zero roulette.

Summary of the count of the Four Least Frequent Numbers on a Single-Zero Wheel

OrderMeanMedianMode
Least2.7733
Second Least3.6244
Third Least4.1544
Fourth Least4.5655

The least I hope you have learned from this article is it is to be expected that certain numbers will come up more than others. To put it in other words, it is natural that some numbers will be 'hot' and some 'cool.' In fact, such differences from the mean are highly predictable. Unfortunately, for roulette players, we don't know which numbers will be 'hot,' just that some of them almost certainly will be. I would also like to emphasize, contrary to the Gambler's Fallacy, that on a fair roulette wheel that every number is equally likely every spin and it makes no difference what has happened in the past.

Finally, it should not be interpreted that we give an endorsement to the 888 Casino, which we linked to earlier. I am very bothered by this rule in their rule 6.2.B. Before getting to that, let me preface with a quote from rule 6.1, which I'm fine with.

'If we reasonably determine that you are engaging in or have engaged in fraudulent or unlawful activity or conducted any prohibited transaction (including money laundering) under the laws of any jurisdiction that applies to you (examples of which are set out at section 6.2 below), any such act will be considered as a material breach of this User Agreement by you. In such case we may close your account and terminate the User Agreement in accordance with section 14 below and we are under no obligation to refund to you any deposits, winnings or funds in your account.' -- Rule 6.1

Let's go further now:

The following are some examples of 'fraudulent or unlawful activity' -- Rule 6.2

Next, here is one of many examples listed as rule 6.2.B

'Unfair Betting Techniques: Utilising any recognised betting techniques to circumvent the standard house edge in our games, which includes but is not limited to martingale betting strategies, card counting as well as low risk betting in roulette such as betting on red/black in equal amounts.' -- Rule 6.2.B

Let me make it perfectly clear that all betting systems, including the Martingale, not only can't circumvent the house edge, they can't even dent it. It is very mathematically ignorant on the part of the casino to fear any betting system. Why would any player trust this casino when the casino can seize all their money under the reason that the player was using a betting system? Any form of betting could be called a betting system, including flat betting. Casino 888 normally has a pretty good reputation, so I'm surprised they would lower themselves to this kind of rogue rule.


Written by: Michael Shackleford

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