This is a message from Grabb regarding his calculator.
Thanks to him for so kindly taking the time to reply and forward it for the benefit of the roulette community. It is greatly appreciated.
Victor
To all users of the "HIT OR SLEEP CALCULATOR"
To understand what the calculator shows, you have to understand the
question you ask and the PURPOSE of the calculator.
Now,
You use it if you want to know the chances...
* to "hit exactly once"
and
* to "hit more than once"
* (in other words to "hit at least once")
and
* that the number/s will "sleep all spins"
...when you're GOING TO record AND/OR bet one or more numbers for some
TOTAL of future spins.
(A "hit" in this case is to see the number/s regardless of betting or
not)
*** That is the PURPOSE of the calculator.
>>> ALL RESULTS BELOW ARE CALCULATED FOR A DOUBLE-ZERO WHEEL! <<<
(For a single-zero wheel, the results will be slightly different.)
BASICS:
For example you enter...
...a "1" for "How many numbers" and
...a "100" for "How many spins".
*** Now you asked the QUESTION "What are the chances for 1 number in
100 future spins?"
The result will be:
Spins Probability % to...
...hit at least once ...hit exactly once ...hit more than
once ...sleep all spins
1 2.631578947368425 2.631578947368425
0 97.36842105263158
2 5.19390581717451 5.124653739612188
0.06925207756232243 94.80609418282549
....
99 92.86498948353507 19.090974084595356
73.77401539893971 7.135010516464933
100 93.05275291817888 18.776343464381405
74.27640945379747 6.947247081821119
Your four answers are found in the BOTTOM line 100 (you asked for
"100" spins):
* There's an 18.7763% chance to find your number "exactly once" DURING
those 100 spins (at spin 1 or spin 100 - you don't know).
* There's a 74.2764% chance that your number will come up "more than
once" during those 100 spins (maybe one hit at spin 1, another hit at
spin 2 and perhaps yet another one at spin 100 - you don't know).
* Added together there's a 93.0527% chance that your number will show
"at least once" during those 100 spins that you record and/or bet.
* Finally, you'll also find that there's a 6.9472% chance that your
number will "sleep all spins" during those 100 spins.
All of this DURING 100 spins. No more and no less. 100 spins.
>>>> That's the answer to the question that was asked ("What are the
chances for 1 number in 100 future spins?").
>>>> That's the purpose of the calculator.
So why are there 99 OTHER lines?
The other lines (1 - 99) are only for "service"...
Now you don't have to make a second calculation because you want to
know the chances for, say, 4 spins. You simply have to look at line 4
because it's already been calculated for you:
4 10.118045057972225 9.71696810184084 0.4010769561313854
89.88195494202778
10.1% chance to be seen at least once (=9.7% chance to be seen exactly
once PLUS 0.4% to be seen more than once) and 89.9% chance to sleep,
within a TOTAL OF FOUR SPINS. No more - no less.
The reason I show these results is just because the formula can be
used in an iteration, so why not...?
Maybe it would have been more clear if I had put line 100 at the top,
titled "Result/Answer", and the rest of the table is titled
"Additional results for your convenience"?
ADVANCED:
(No, not really
)
Now, suppose you want to RECORD 100 spins and IF you have NOT seen
your number, you'll BET it for 20 spins.
Look: Here's a CONDITION! An IF-clause.
IMPORTANT: This is NOT added to 120 spins - it is 100 spins in one
sequence and when you HAVE SEEN IT - not before, right? - you start
the NEXT sequence that is 20 bets.
So you calculate:
The chance for a sleeper for 100 (yes one hundred - no more) spins is
approximately 6.95% (check the table, line 100).
So there's a close-to 7% chance that you'll get your betting signal.
Not very high because it's a high probability that your number has
already hit during those 100 spins.
And when you start to bet you'll have a 58.66% chance to lose ALL 20
bets (check the table, line 20).
You can't use line 120 because you've already seen 100 spins before
your next sequence (20 bets) begins and all those calculations show
results for UN-SEEN AND FUTURE spins/bets.
*** When there are CONDITIONS for you to continue, you'll have to make
ONE calculation for EACH condition.
The condition probably says something like "if you don't SEE..." or
"if you have SEEN...", making it obvious that those first 100 spins
are ALREADY RECORDED or seen when the next sequence (maybe betting)
BEGINS.
So they have to be excluded from the second calculation.
Likewise; the last 20 (bets) are excluded from the first calculation
because the first calculation is regarding a 100-sleeper. Nothing
else, less or more.
There are two "groups" of spins (100 and 20) in this case, and each
"group" is ALWAYS calculated individually.
(And Yes: You WILL have the same chance for those 20 bets regardless
the number you bet - your selected number or any else - or how long
you wait before you do it.
)
OOOH...
If you find it hard to believe that a number that hasn't hit for, say,
120 spins has the same chance to hit as the latest number...
To be blunt: Your way of thinking is flawed; it's a "Gambler's Fallacy".
And you can easily check it:
Just look at a spin-sample of a good size.
The Hamburg or Wiesbaden spins for example. Or your own records if you
have enough of them.
Set ANY point in time where you say that "from here the sleeping
number has a better chance to hit than the rest". Maybe 120 spins but
12 or 1200 will do just as fine - the result is actually the same.
Always (given a good sample-size). I know this...
The chance for one number to sleep 120 spins is 4.075% (check the
table, line 120). This means that, in average, in four of 100 120-
spins sequences your number will not be found.
(You have to look for one and the same number in all sequences, of
course)
I'd say; get yourself some 10,000 sequences with 122 (!) spins and
look for one and the same number in the first 120 spins of all those
sequences - I did just like that (more in a minute)!
You'll find that approximately 407 (4.075%) sequences will lack your
number in the first 120 spins.
Now check spin number 121 in those 407 sequences for that same number.
You'll find approximately 11 sequences (10.71) with a hit. That's
actually 1/38...
There's 396 sequences that have had no hit for 121 spins...
Now check spin number 122 in those 396 sequences and you'll find the
hit in approximately 10 of them (10.42) = 1/38.
So in total you'll have 386 sequences that have slept all 122 spins,
right?
This WILL be so - I promise you. Check it!
Now use the table:
The chance for 1 number to sleep for 120 spins is 4.075%
The chance for 1 number to sleep for 121 spins is 3.968% or 37/38 of
4.075%. And 3.968% of 10,000 = approximately 396 sequences, compare to
above.
The chance for 1 number to sleep for 122 spins is 3.864% or 37/38 of
3.968%. And 3.864% of 10,000 = approximately 386 sequences, compare to
above.
NOW: If the chance to "sleep one more spin" is ALWAYS 37/38 of the
previous chance, the chance to hit is - of course - always 1/38.
If you check the table you'll find that in ALL cases the % adds up to
100% and the sleeper result is always 37/38 of the previous one.
(OK, maybe you'll find some rounding-errors in the last decimals
)
And this is...
*** NOT ONLY IN THEORY ***
I have done live-spins checking (Hamburg) myself and I published the
results at my old site.
Everything showed exactly what I tell you.
Live Wheel Hamburg Spins.
(Unfortunately I haven't got those tables saved and when the site was
taken down by the provider the tables were gone.)
But if you do this test yourself you'll get the same results. Everyone
will. And all tests done to date show the same:
The chance for any number to hit at the next spin is always 1/38
regardless of how long it's been sleeping.
(If there's nothing wrong with the wheel of course)
And if the chance to HIT is always 1/38 and you are always PAYED 35x
your bet...
You don't have to find it hard to believe this. Just check it!
Or ask a friend to check it for you if you don't have the means, tools
or skills. There are millions of live-wheel spins out there just
waiting to be checked.
Simple, really.
I'm sorry (truly) but the truth is:
The ONLY reason that the sleeping sequence eventually MAY end is that
there are enough trials for the selected number to hit.
I say "may end" - not "will end" - because there's still a whopping
37/38 chance to MISS your number... each and every spin.
AND a last thing before you ask it (and it's also in regards to the
last paragraph):
"Why are there no reports about one number hitting 10 times in
sequence on ANY double-zero wheel if probability says it's possible?"
And the simple answer is: "Not enough trials. Yet."
The probability for one number to repeat 9 times after the first hit
is (1/38)^9...
You want that figure?
ONE CHANCE IN 165,216,101,262,848 spins (00-wheel)
Say there are 1,000,000 double-zero tables in the world.
Say they are spun every minute 24 hours 365 days a year. That's
525,600 spins per wheel per year.
That's a total of 525,600,000,000 spins per year.
So it will happen ONCE in the TOTAL DATA from approximately 314 YEARS
of 1,000,000 wheels spinning every minute 24/365.
AND you have to check for the 10-sequence using the data as one
continous, concatenated, sequence!
That is; in reality there may be some of the 10 in the end of one
wheel-data sequence and the rest in the beginning of the next (after
you concatenated them).
* So the casino/s involved maybe WOULDN'T EVEN BE AWARE of it (9/10
chance, actually)!
I am sure there are not 1,000,000 roulette-wheels, of any kind or even
added, in the world and they have not all been spun every minute
24/365 for the last 314 years...
Maybe we'll have to wait for a little longer before it happens...
Now, if there's ANYTHING of what I've said above that you don't believe:
Either...
* Check it yourself with live spins, and you'll find that I'm telling
the truth - both math- and "reality"-wise
OR
* Have someone who knows how and is able, to check live spins for you,
and you'll find that I'm telling the truth - both math- and "reality"-
wise
OR
* Ask some math- and/or statistics knowledgeable member of this board
(or maybe a maths forum), and you'll find that I'm telling the truth -
both math- and "reality"-wise
But don't claim I'm wrong BEFORE you have the answer.
This is my last post. I can do nothing more.
GrabbPS.
A number that has slept for any amount of spins, may sleep for one
more spin.
This is both probable and possible.
And a number that has hit any number of times in sequence, may hit
again at the next spin.
This is also both probable and possible.
But maybe none of it is very likely...
April 10, 2008, 05:25:34 AM