Introduction

Trivially, when a fair coin is tossed, ad infinitum:

a) Any arbitrarily-long sequence of consecutive heads
will occur, eventually.
So, for example, the probability that a googolplex-long
sequence of consecutive heads will occur is 1.

b) The sequence will occur infinitely often.

a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.

Trivial, as I said - which should make what follows also
trivial:

The Challenge

The coin starts off being fair, i.e. p_1 = 0.5

Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
So:
p_2 = 0.5 / B
p_3 = 0.5 / B^2
..
p_n = 0.5 / B^(n-1)

Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.

QUESTION:
Find the range of values (B,k) for which P_B,k = 1

HINT
P_k = 1 for all B>1, k>0 is not the answer.

On 10/16/2022 1:28 PM, Perrti Lounesto Jr. wrote:
> Introduction
>
> Trivially, when a fair coin is tossed, ad infinitum:
>
> a) Any arbitrarily-long sequence of consecutive heads
> will occur, eventually.
> So, for example, the probability that a googolplex-long
> sequence of consecutive heads will occur is 1.
[...]

I can see that for a googolplex-long sequence is not infinite.

On 10/16/2022 3:28 PM, Perrti Lounesto Jr. wrote:
> Introduction
>
> Trivially, when a fair coin is tossed, ad infinitum:
>
> a) Any arbitrarily-long sequence of consecutive heads
> will occur, eventually.
> So, for example, the probability that a googolplex-long
> sequence of consecutive heads will occur is 1.

no, probability is an event.

the probability of it occurring is simply 0.5^(10^10^100)

which means if you flipped your coin a million times a second, it would not occur in several lifetimes of the universe.

>
> b) The sequence will occur infinitely often.

no one would ever know, no record could last several lifetimes of the universe...

>
> a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.
>
> Trivial, as I said - which should make what follows also
> trivial:
>
>
>
> The Challenge
>
> The coin starts off being fair, i.e. p_1 = 0.5
>
> Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
> So:
> p_2 = 0.5 / B
> p_3 = 0.5 / B^2
> ..
> p_n = 0.5 / B^(n-1)
>
> Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.
>
> QUESTION:
> Find the range of values (B,k) for which P_B,k = 1
>
> HINT
> P_k = 1 for all B>1, k>0 is not the answer.
>

On Sunday, October 16, 2022 at 1:31:41 PM UTC-7, Perrti Lounesto Jr. wrote:
> Introduction
>
> Trivially, when a fair coin is tossed, ad infinitum:
>
> a) Any arbitrarily-long sequence of consecutive heads
> will occur, eventually.
> So, for example, the probability that a googolplex-long
> sequence of consecutive heads will occur is 1.
>
> b) The sequence will occur infinitely often.
>
> a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.
>
> Trivial, as I said - which should make what follows also
> trivial:
>
>
>
> The Challenge
>
> The coin starts off being fair, i.e. p_1 = 0.5
>
> Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
> So:
> p_2 = 0.5 / B
> p_3 = 0.5 / B^2
> ..
> p_n = 0.5 / B^(n-1)
>
> Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.
>
> QUESTION:
> Find the range of values (B,k) for which P_B,k = 1
>
> HINT
> P_k = 1 for all B>1, k>0 is not the answer.

Each time you sample a next digit, it both refines the previous
sample, and, starts a new sample.

So, it's absolutely improbable to get infinitely many heads,
but, then it's also infinitely many samples of same.

This also helps explain why most samples are infinitely many
different irrationals, each, but, the rationals have
much more, weight.

What's AI? Something that can explain, not just go with the flow.

On Sunday, October 16, 2022 at 4:46:25 PM UTC-4, Sergi o wrote:
> On 10/16/2022 3:28 PM, Perrti Lounesto Jr. wrote:
> > Introduction
> >
> > Trivially, when a fair coin is tossed, ad infinitum:
> >
> > a) Any arbitrarily-long sequence of consecutive heads
> > will occur, eventually.
> > So, for example, the probability that a googolplex-long
> > sequence of consecutive heads will occur is 1.
> no, probability is an event.
>
> the probability of it occurring is simply 0.5^(10^10^100)
>
> which means if you flipped your coin a million times a second, it would not occur in several lifetimes of the universe.
> >
> > b) The sequence will occur infinitely often.
> no one would ever know, no record could last several lifetimes of the universe...
> >
> > a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.
> >
> > Trivial, as I said - which should make what follows also
> > trivial:
> >
> >
> >
> > The Challenge
> >
> > The coin starts off being fair, i.e. p_1 = 0.5
> >
> > Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
> > So:
> > p_2 = 0.5 / B
> > p_3 = 0.5 / B^2
> > ..
> > p_n = 0.5 / B^(n-1)
> >
> > Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.
> >
> > QUESTION:
> > Find the range of values (B,k) for which P_B,k = 1
> >
> > HINT
> > P_k = 1 for all B>1, k>0 is not the answer.
> >

I played on a single zero roulette table for free betting $100.00 on each spin
on red, black, red, black, red, black, red, black ... win or loose and after each loss
I doubled the bet, I got up to almost $12,000 after many win loss sessions and
then hit the table limit of $3,000 after 30 spin losses and finally hit on that for
a much smaller loss. I started with $1,000. I ended the session with $11,200 win
minus the starting money
It is like sticking with Red or Black or a coin toss with the zero.
The zero came out many times during my session and is treated as the opposite color
that you are playing,

Try it --
Remember play red, black, red, black ... win or loose.
https://freeroulettedoc.com/

You are going into probability theory, the science of the unknown, yet you dress it all up in "guaranteed knowns". So, the case is you have no problem here, but that you have an unstable mind and rotten logic.

On Sunday, October 16, 2022 at 3:31:41 PM UTC-5, Perrti Lounesto Jr. wrote:
> Introduction
>
> Trivially, when a fair coin is tossed, ad infinitum:
>
> a) Any arbitrarily-long sequence of consecutive heads
> will occur, eventually.
> So, for example, the probability that a googolplex-long
> sequence of consecutive heads will occur is 1.
>
> b) The sequence will occur infinitely often.
>
> a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.
>
> Trivial, as I said - which should make what follows also
> trivial:
>
>
>
> The Challenge
>
> The coin starts off being fair, i.e. p_1 = 0.5
>
> Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
> So:
> p_2 = 0.5 / B
> p_3 = 0.5 / B^2
> ..
> p_n = 0.5 / B^(n-1)
>
> Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.
>
> QUESTION:
> Find the range of values (B,k) for which P_B,k = 1
>
> HINT
> P_k = 1 for all B>1, k>0 is not the answer.

On 10/16/2022 4:54 PM, Dan joyce wrote:
> On Sunday, October 16, 2022 at 4:46:25 PM UTC-4, Sergi o wrote:
>> On 10/16/2022 3:28 PM, Perrti Lounesto Jr. wrote:
>>> Introduction
>>>
>>> Trivially, when a fair coin is tossed, ad infinitum:
>>>
>>> a) Any arbitrarily-long sequence of consecutive heads
>>> will occur, eventually.
>>> So, for example, the probability that a googolplex-long
>>> sequence of consecutive heads will occur is 1.
>> no, probability is an event.
>>
>> the probability of it occurring is simply 0.5^(10^10^100)
>>
>> which means if you flipped your coin a million times a second, it would not occur in several lifetimes of the universe.
>>>
>>> b) The sequence will occur infinitely often.
>> no one would ever know, no record could last several lifetimes of the universe...
>>>
>>> a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.
>>>
>>> Trivial, as I said - which should make what follows also
>>> trivial:
>>>
>>>
>>>
>>> The Challenge
>>>
>>> The coin starts off being fair, i.e. p_1 = 0.5
>>>
>>> Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
>>> So:
>>> p_2 = 0.5 / B
>>> p_3 = 0.5 / B^2
>>> ..
>>> p_n = 0.5 / B^(n-1)
>>>
>>> Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.
>>>
>>> QUESTION:
>>> Find the range of values (B,k) for which P_B,k = 1
>>>
>>> HINT
>>> P_k = 1 for all B>1, k>0 is not the answer.
>>>
>
> I played on a single zero roulette table for free betting $100.00 on each spin
> on red, black, red, black, red, black, red, black ... win or loose and after each loss
> I doubled the bet, I got up to almost $12,000 after many win loss sessions and
> then hit the table limit of $3,000 after 30 spin losses and finally hit on that for
> a much smaller loss. I started with $1,000. I ended the session with $11,200 win
> minus the starting money
> It is like sticking with Red or Black or a coin toss with the zero.
> The zero came out many times during my session and is treated as the opposite color
> that you are playing,
>
> Try it --
> Remember play red, black, red, black ... win or loose.
> https://freeroulettedoc.com/
>

roulette has the worst odds, 2.6% but better than Keno

https://www.casino.org/roulette/odds/

dont play roulette!

Just send the Casino a check and save on the airplane and hotel, save the time, go fishing...

On 10/16/2022 6:32 PM, Sergi o wrote:
> On 10/16/2022 4:54 PM, Dan joyce wrote:
>> On Sunday, October 16, 2022 at 4:46:25 PM UTC-4, Sergi o wrote:
>>> On 10/16/2022 3:28 PM, Perrti Lounesto Jr. wrote:
>>>> Introduction
>>>>
>>>> Trivially, when a fair coin is tossed, ad infinitum:
>>>>
>>>> a) Any arbitrarily-long sequence of consecutive heads
>>>> will occur, eventually.
>>>> So, for example, the probability that a googolplex-long
>>>> sequence of consecutive heads will occur is 1.
>>> no, probability is an event.
>>>
>>> the probability of it occurring is simply 0.5^(10^10^100)
>>>
>>> which means if you flipped your coin a million times a second, it
>>> would not occur in several lifetimes of the universe.
>>>>
>>>> b) The sequence will occur infinitely often.
>>> no one would ever know, no record could last several lifetimes of the
>>> universe...
>>>>
>>>> a) and b) remain true even if the coin is non-fatally loaded/biased,
>>>> i.e., for any probability p > 0 of a toss resulting in a head.
>>>>
>>>> Trivial, as I said - which should make what follows also
>>>> trivial:
>>>>
>>>>
>>>>
>>>> The Challenge
>>>>
>>>> The coin starts off being fair, i.e. p_1 = 0.5
>>>>
>>>> Then, for each successive toss, the coin is progressively biased
>>>> against heads by a constant factor B > 1
>>>> So:
>>>> p_2 = 0.5 / B
>>>> p_3 = 0.5 / B^2
>>>> ..
>>>> p_n = 0.5 / B^(n-1)
>>>>
>>>> Let P_B,k = Probability that somewhere within the infinite sequence
>>>> of toss results there will be at least one occurrence of k > 0
>>>> consecutive heads.
>>>>
>>>> QUESTION:
>>>> Find the range of values (B,k) for which P_B,k = 1
>>>>
>>>> HINT
>>>> P_k = 1 for all B>1, k>0 is not the answer.
>>>>
>>
>> I played on a single zero roulette table for free betting $100.00  on
>> each spin
>> on red, black, red, black, red, black, red, black ... win or loose and
>> after each loss
>> I doubled the bet, I got up to almost $12,000 after many win loss
>> sessions  and
>> then hit the table limit of $3,000 after 30 spin losses and finally
>> hit on that for
>> a much smaller loss. I started with $1,000. I ended the session with
>> $11,200 win
>> minus the starting money
>> It is like sticking with Red or Black or a coin toss with the zero.
>> The zero came out many times during my session and is treated as the
>> opposite color
>> that you are playing,
>>
>> Try it --
>> Remember play red, black, red, black ... win or loose.
>> https://freeroulettedoc.com/
>
> roulette has the worst odds, 2.6%   but better than Keno
>
> https://www.casino.org/roulette/odds/
>
> dont play roulette!
>
>       Just send the Casino a check and save on the airplane and hotel,
> save the time, go fishing...
>

Playing red and black is pretty good odds, green's aside for a moment...

On 10/16/2022 8:25 PM, Chris M. Thomasson wrote:
> On 10/16/2022 6:32 PM, Sergi o wrote:
>> On 10/16/2022 4:54 PM, Dan joyce wrote:
>>> On Sunday, October 16, 2022 at 4:46:25 PM UTC-4, Sergi o wrote:
>>>> On 10/16/2022 3:28 PM, Perrti Lounesto Jr. wrote:
>>>>> Introduction
>>>>>
>>>>> Trivially, when a fair coin is tossed, ad infinitum:
>>>>>
>>>>> a) Any arbitrarily-long sequence of consecutive heads
>>>>> will occur, eventually.
>>>>> So, for example, the probability that a googolplex-long
>>>>> sequence of consecutive heads will occur is 1.
>>>> no, probability is an event.
>>>>
>>>> the probability of it occurring is simply 0.5^(10^10^100)
>>>>
>>>> which means if you flipped your coin a million times a second, it
>>>> would not occur in several lifetimes of the universe.
>>>>>
>>>>> b) The sequence will occur infinitely often.
>>>> no one would ever know, no record could last several lifetimes of
>>>> the universe...
>>>>>
>>>>> a) and b) remain true even if the coin is non-fatally
>>>>> loaded/biased, i.e., for any probability p > 0 of a toss resulting
>>>>> in a head.
>>>>>
>>>>> Trivial, as I said - which should make what follows also
>>>>> trivial:
>>>>>
>>>>>
>>>>>
>>>>> The Challenge
>>>>>
>>>>> The coin starts off being fair, i.e. p_1 = 0.5
>>>>>
>>>>> Then, for each successive toss, the coin is progressively biased
>>>>> against heads by a constant factor B > 1
>>>>> So:
>>>>> p_2 = 0.5 / B
>>>>> p_3 = 0.5 / B^2
>>>>> ..
>>>>> p_n = 0.5 / B^(n-1)
>>>>>
>>>>> Let P_B,k = Probability that somewhere within the infinite sequence
>>>>> of toss results there will be at least one occurrence of k > 0
>>>>> consecutive heads.
>>>>>
>>>>> QUESTION:
>>>>> Find the range of values (B,k) for which P_B,k = 1
>>>>>
>>>>> HINT
>>>>> P_k = 1 for all B>1, k>0 is not the answer.
>>>>>
>>>
>>> I played on a single zero roulette table for free betting $100.00  on
>>> each spin
>>> on red, black, red, black, red, black, red, black ... win or loose
>>> and after each loss
>>> I doubled the bet, I got up to almost $12,000 after many win loss
>>> sessions  and
>>> then hit the table limit of $3,000 after 30 spin losses and finally
>>> hit on that for
>>> a much smaller loss. I started with $1,000. I ended the session with
>>> $11,200 win
>>> minus the starting money
>>> It is like sticking with Red or Black or a coin toss with the zero.
>>> The zero came out many times during my session and is treated as the
>>> opposite color
>>> that you are playing,
>>>
>>> Try it --
>>> Remember play red, black, red, black ... win or loose.
>>> https://freeroulettedoc.com/
>>
>> roulette has the worst odds, 2.6%   but better than Keno
>>
>> https://www.casino.org/roulette/odds/
>>
>> dont play roulette!
>>
>>        Just send the Casino a check and save on the airplane and
>> hotel, save the time, go fishing...
>>
>
> Playing red and black is pretty good odds, green's aside for a moment...

I should say, red or black. Actually, one time I saw somebody betting on
both red and black. Then a green came up and he got pissed off for some
reason. Too funny. It was at harveys in south lake tahoe.

On 10/16/2022 10:28 PM, Chris M. Thomasson wrote:
> On 10/16/2022 8:25 PM, Chris M. Thomasson wrote:
>> On 10/16/2022 6:32 PM, Sergi o wrote:
>>> On 10/16/2022 4:54 PM, Dan joyce wrote:
>>>> On Sunday, October 16, 2022 at 4:46:25 PM UTC-4, Sergi o wrote:
>>>>> On 10/16/2022 3:28 PM, Perrti Lounesto Jr. wrote:
>>>>>> Introduction
>>>>>>
>>>>>> Trivially, when a fair coin is tossed, ad infinitum:
>>>>>>
>>>>>> a) Any arbitrarily-long sequence of consecutive heads
>>>>>> will occur, eventually.
>>>>>> So, for example, the probability that a googolplex-long
>>>>>> sequence of consecutive heads will occur is 1.
>>>>> no, probability is an event.
>>>>>
>>>>> the probability of it occurring is simply 0.5^(10^10^100)
>>>>>
>>>>> which means if you flipped your coin a million times a second, it would not occur in several lifetimes of the universe.
>>>>>>
>>>>>> b) The sequence will occur infinitely often.
>>>>> no one would ever know, no record could last several lifetimes of the universe...
>>>>>>
>>>>>> a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.
>>>>>>
>>>>>> Trivial, as I said - which should make what follows also
>>>>>> trivial:
>>>>>>
>>>>>>
>>>>>>
>>>>>> The Challenge
>>>>>>
>>>>>> The coin starts off being fair, i.e. p_1 = 0.5
>>>>>>
>>>>>> Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
>>>>>> So:
>>>>>> p_2 = 0.5 / B
>>>>>> p_3 = 0.5 / B^2
>>>>>> ..
>>>>>> p_n = 0.5 / B^(n-1)
>>>>>>
>>>>>> Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.
>>>>>>
>>>>>> QUESTION:
>>>>>> Find the range of values (B,k) for which P_B,k = 1
>>>>>>
>>>>>> HINT
>>>>>> P_k = 1 for all B>1, k>0 is not the answer.
>>>>>>
>>>>
>>>> I played on a single zero roulette table for free betting $100.00  on each spin
>>>> on red, black, red, black, red, black, red, black ... win or loose and after each loss
>>>> I doubled the bet, I got up to almost $12,000 after many win loss sessions  and
>>>> then hit the table limit of $3,000 after 30 spin losses and finally hit on that for
>>>> a much smaller loss. I started with $1,000. I ended the session with $11,200 win
>>>> minus the starting money
>>>> It is like sticking with Red or Black or a coin toss with the zero.
>>>> The zero came out many times during my session and is treated as the opposite color
>>>> that you are playing,
>>>>
>>>> Try it --
>>>> Remember play red, black, red, black ... win or loose.
>>>> https://freeroulettedoc.com/
>>>
>>> roulette has the worst odds, 2.6%   but better than Keno
>>>
>>> https://www.casino.org/roulette/odds/
>>>
>>> dont play roulette!
>>>
>>>        Just send the Casino a check and save on the airplane and hotel, save the time, go fishing...
>>>
>>
>> Playing red and black is pretty good odds, green's aside for a moment...
>
> I should say, red or black. Actually, one time I saw somebody betting on both red and black. Then a green came up and he got pissed off for some reason.
> Too funny. It was at harveys in south lake tahoe.

I was just up at an Indian Casino in Seattle, and wondering what type of algorithum(s) they have now on the new slot machines.
inputs they have are bet size (5 buttons), a re-bet same key, total you have deposited, they are connected by internet, they can determine the amount of
time between key presses, an overall timer, they may have a sensor to detect if you are sitting in front, most all machines are made in china, most of
the graphics is interchangable (HW and most SW stay the same) and there is an optional key card you can use, which they could track you from machine to
machine. Anyhow, won 50 lost 50, and I got to see flashing lights and some tones. The machine emits tones on you bet size, muffeled low for small
bets, crisp brite tones for large bets...

On 10/17/2022 6:42 AM, Sergi o wrote:
> On 10/16/2022 10:28 PM, Chris M. Thomasson wrote:
>> On 10/16/2022 8:25 PM, Chris M. Thomasson wrote:
>>> On 10/16/2022 6:32 PM, Sergi o wrote:
>>>> On 10/16/2022 4:54 PM, Dan joyce wrote:
>>>>> On Sunday, October 16, 2022 at 4:46:25 PM UTC-4, Sergi o wrote:
>>>>>> On 10/16/2022 3:28 PM, Perrti Lounesto Jr. wrote:
>>>>>>> Introduction
>>>>>>>
>>>>>>> Trivially, when a fair coin is tossed, ad infinitum:
>>>>>>>
>>>>>>> a) Any arbitrarily-long sequence of consecutive heads
>>>>>>> will occur, eventually.
>>>>>>> So, for example, the probability that a googolplex-long
>>>>>>> sequence of consecutive heads will occur is 1.
>>>>>> no, probability is an event.
>>>>>>
>>>>>> the probability of it occurring is simply 0.5^(10^10^100)
>>>>>>
>>>>>> which means if you flipped your coin a million times a second, it
>>>>>> would not occur in several lifetimes of the universe.
>>>>>>>
>>>>>>> b) The sequence will occur infinitely often.
>>>>>> no one would ever know, no record could last several lifetimes of
>>>>>> the universe...
>>>>>>>
>>>>>>> a) and b) remain true even if the coin is non-fatally
>>>>>>> loaded/biased, i.e., for any probability p > 0 of a toss
>>>>>>> resulting in a head.
>>>>>>>
>>>>>>> Trivial, as I said - which should make what follows also
>>>>>>> trivial:
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> The Challenge
>>>>>>>
>>>>>>> The coin starts off being fair, i.e. p_1 = 0.5
>>>>>>>
>>>>>>> Then, for each successive toss, the coin is progressively biased
>>>>>>> against heads by a constant factor B > 1
>>>>>>> So:
>>>>>>> p_2 = 0.5 / B
>>>>>>> p_3 = 0.5 / B^2
>>>>>>> ..
>>>>>>> p_n = 0.5 / B^(n-1)
>>>>>>>
>>>>>>> Let P_B,k = Probability that somewhere within the infinite
>>>>>>> sequence of toss results there will be at least one occurrence of
>>>>>>> k > 0 consecutive heads.
>>>>>>>
>>>>>>> QUESTION:
>>>>>>> Find the range of values (B,k) for which P_B,k = 1
>>>>>>>
>>>>>>> HINT
>>>>>>> P_k = 1 for all B>1, k>0 is not the answer.
>>>>>>>
>>>>>
>>>>> I played on a single zero roulette table for free betting $100.00
>>>>> on each spin
>>>>> on red, black, red, black, red, black, red, black ... win or loose
>>>>> and after each loss
>>>>> I doubled the bet, I got up to almost $12,000 after many win loss
>>>>> sessions  and
>>>>> then hit the table limit of $3,000 after 30 spin losses and finally
>>>>> hit on that for
>>>>> a much smaller loss. I started with $1,000. I ended the session
>>>>> with $11,200 win
>>>>> minus the starting money
>>>>> It is like sticking with Red or Black or a coin toss with the zero.
>>>>> The zero came out many times during my session and is treated as
>>>>> the opposite color
>>>>> that you are playing,
>>>>>
>>>>> Try it --
>>>>> Remember play red, black, red, black ... win or loose.
>>>>> https://freeroulettedoc.com/
>>>>
>>>> roulette has the worst odds, 2.6%   but better than Keno
>>>>
>>>> https://www.casino.org/roulette/odds/
>>>>
>>>> dont play roulette!
>>>>
>>>>        Just send the Casino a check and save on the airplane and
>>>> hotel, save the time, go fishing...
>>>>
>>>
>>> Playing red and black is pretty good odds, green's aside for a moment...
>>
>> I should say, red or black. Actually, one time I saw somebody betting
>> on both red and black. Then a green came up and he got pissed off for
>> some reason. Too funny. It was at harveys in south lake tahoe.
>
> I was just up at an Indian Casino in Seattle, and wondering what type of
> algorithum(s) they have now on the new slot machines.
> inputs they have are bet size (5 buttons), a re-bet same key, total you
> have deposited, they are connected by internet, they can determine the
> amount of time between key presses, an overall timer, they may have a
> sensor to detect if you are sitting in front, most all machines are made
> in china, most of the graphics is interchangable (HW and most SW stay
> the same) and there is an optional key card you can use, which they
> could track you from machine to machine.  Anyhow, won 50 lost 50, and I
> got to see flashing lights and some tones.  The machine emits tones on
> you bet size, muffeled low for small bets, crisp brite tones for large
> bets...

Humm... This reminds me of another time I saw one of the progressive
machines that have a guaranteed hit when the total gets to a certain
amount. It was guaranteed to hit a progressive at 20$ and the counter
was at 19.90. So, I sat down, and played minimum bet, 50 cents a pull.
The progressive would increase one penny per pull. So, 10 pulls at 50
cents each would get it to 20.00. 10 * .5 = 5 so I put in five bucks.
Sure enough, it rolled over to 20, I won 20 dollars, a 15 dollar profit.
Nice! Iirc, it was a coyote moon progressive.

There was another story about some russian hacker who was able to get
insight into the PRNG of Aristocrat machines:

https://www.wired.com/story/meet-alex-the-russian-casino-hacker-who-makes-millions-targeting-slot-machines/

On Monday, October 17, 2022 at 9:42:19 AM UTC-4, Sergi o wrote:
> On 10/16/2022 10:28 PM, Chris M. Thomasson wrote:
> > On 10/16/2022 8:25 PM, Chris M. Thomasson wrote:
> >> On 10/16/2022 6:32 PM, Sergi o wrote:
> >>> On 10/16/2022 4:54 PM, Dan joyce wrote:
> >>>> On Sunday, October 16, 2022 at 4:46:25 PM UTC-4, Sergi o wrote:
> >>>>> On 10/16/2022 3:28 PM, Perrti Lounesto Jr. wrote:
> >>>>>> Introduction
> >>>>>>
> >>>>>> Trivially, when a fair coin is tossed, ad infinitum:
> >>>>>>
> >>>>>> a) Any arbitrarily-long sequence of consecutive heads
> >>>>>> will occur, eventually.
> >>>>>> So, for example, the probability that a googolplex-long
> >>>>>> sequence of consecutive heads will occur is 1.
> >>>>> no, probability is an event.
> >>>>>
> >>>>> the probability of it occurring is simply 0.5^(10^10^100)
> >>>>>
> >>>>> which means if you flipped your coin a million times a second, it would not occur in several lifetimes of the universe.
> >>>>>>
> >>>>>> b) The sequence will occur infinitely often.
> >>>>> no one would ever know, no record could last several lifetimes of the universe...
> >>>>>>
> >>>>>> a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.
> >>>>>>
> >>>>>> Trivial, as I said - which should make what follows also
> >>>>>> trivial:
> >>>>>>
> >>>>>>
> >>>>>>
> >>>>>> The Challenge
> >>>>>>
> >>>>>> The coin starts off being fair, i.e. p_1 = 0.5
> >>>>>>
> >>>>>> Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
> >>>>>> So:
> >>>>>> p_2 = 0.5 / B
> >>>>>> p_3 = 0.5 / B^2
> >>>>>> ..
> >>>>>> p_n = 0.5 / B^(n-1)
> >>>>>>
> >>>>>> Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.
> >>>>>>
> >>>>>> QUESTION:
> >>>>>> Find the range of values (B,k) for which P_B,k = 1
> >>>>>>
> >>>>>> HINT
> >>>>>> P_k = 1 for all B>1, k>0 is not the answer.
> >>>>>>
> >>>>
> >>>> I played on a single zero roulette table for free betting $100.00 on each spin
> >>>> on red, black, red, black, red, black, red, black ... win or loose and after each loss
> >>>> I doubled the bet, I got up to almost $12,000 after many win loss sessions and
> >>>> then hit the table limit of $3,000 after 30 spin losses and finally hit on that for
> >>>> a much smaller loss. I started with $1,000. I ended the session with $11,200 win
> >>>> minus the starting money
> >>>> It is like sticking with Red or Black or a coin toss with the zero.
> >>>> The zero came out many times during my session and is treated as the opposite color
> >>>> that you are playing,
> >>>>
> >>>> Try it --
> >>>> Remember play red, black, red, black ... win or loose.
> >>>> https://freeroulettedoc.com/
> >>>
> >>> roulette has the worst odds, 2.6% but better than Keno
> >>>
> >>> https://www.casino.org/roulette/odds/
> >>>
> >>> dont play roulette!
> >>>
> >>> Just send the Casino a check and save on the airplane and hotel, save the time, go fishing...
> >>>
> >>
> >> Playing red and black is pretty good odds, green's aside for a moment...
> >
> > I should say, red or black. Actually, one time I saw somebody betting on both red and black. Then a green came up and he got pissed off for some reason.
> > Too funny. It was at harveys in south lake tahoe.
> I was just up at an Indian Casino in Seattle, and wondering what type of algorithum(s) they have now on the new slot machines.
> inputs they have are bet size (5 buttons), a re-bet same key, total you have deposited, they are connected by internet, they can determine the amount of
> time between key presses, an overall timer, they may have a sensor to detect if you are sitting in front, most all machines are made in china, most of
> the graphics is interchangable (HW and most SW stay the same) and there is an optional key card you can use, which they could track you from machine to
> machine. Anyhow, won 50 lost 50, and I got to see flashing lights and some tones. The machine emits tones on you bet size, muffeled low for small
> bets, crisp brite tones for large bets...

Odds of winning at the slots are much worse then even the American double zero roulette tables.

On 10/17/2022 7:08 PM, Dan joyce wrote:
> On Monday, October 17, 2022 at 9:42:19 AM UTC-4, Sergi o wrote:
>> On 10/16/2022 10:28 PM, Chris M. Thomasson wrote:
>>> On 10/16/2022 8:25 PM, Chris M. Thomasson wrote:
>>>> On 10/16/2022 6:32 PM, Sergi o wrote:
>>>>> On 10/16/2022 4:54 PM, Dan joyce wrote:
>>>>>> On Sunday, October 16, 2022 at 4:46:25 PM UTC-4, Sergi o wrote:
>>>>>>> On 10/16/2022 3:28 PM, Perrti Lounesto Jr. wrote:
>>>>>>>> Introduction
>>>>>>>>
>>>>>>>> Trivially, when a fair coin is tossed, ad infinitum:
>>>>>>>>
>>>>>>>> a) Any arbitrarily-long sequence of consecutive heads
>>>>>>>> will occur, eventually.
>>>>>>>> So, for example, the probability that a googolplex-long
>>>>>>>> sequence of consecutive heads will occur is 1.
>>>>>>> no, probability is an event.
>>>>>>>
>>>>>>> the probability of it occurring is simply 0.5^(10^10^100)
>>>>>>>
>>>>>>> which means if you flipped your coin a million times a second, it would not occur in several lifetimes of the universe.
>>>>>>>>
>>>>>>>> b) The sequence will occur infinitely often.
>>>>>>> no one would ever know, no record could last several lifetimes of the universe...
>>>>>>>>
>>>>>>>> a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.
>>>>>>>>
>>>>>>>> Trivial, as I said - which should make what follows also
>>>>>>>> trivial:
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> The Challenge
>>>>>>>>
>>>>>>>> The coin starts off being fair, i.e. p_1 = 0.5
>>>>>>>>
>>>>>>>> Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
>>>>>>>> So:
>>>>>>>> p_2 = 0.5 / B
>>>>>>>> p_3 = 0.5 / B^2
>>>>>>>> ..
>>>>>>>> p_n = 0.5 / B^(n-1)
>>>>>>>>
>>>>>>>> Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.
>>>>>>>>
>>>>>>>> QUESTION:
>>>>>>>> Find the range of values (B,k) for which P_B,k = 1
>>>>>>>>
>>>>>>>> HINT
>>>>>>>> P_k = 1 for all B>1, k>0 is not the answer.
>>>>>>>>
>>>>>>
>>>>>> I played on a single zero roulette table for free betting $100.00 on each spin
>>>>>> on red, black, red, black, red, black, red, black ... win or loose and after each loss
>>>>>> I doubled the bet, I got up to almost $12,000 after many win loss sessions and
>>>>>> then hit the table limit of $3,000 after 30 spin losses and finally hit on that for
>>>>>> a much smaller loss. I started with $1,000. I ended the session with $11,200 win
>>>>>> minus the starting money
>>>>>> It is like sticking with Red or Black or a coin toss with the zero.
>>>>>> The zero came out many times during my session and is treated as the opposite color
>>>>>> that you are playing,
>>>>>>
>>>>>> Try it --
>>>>>> Remember play red, black, red, black ... win or loose.
>>>>>> https://freeroulettedoc.com/
>>>>>
>>>>> roulette has the worst odds, 2.6% but better than Keno
>>>>>
>>>>> https://www.casino.org/roulette/odds/
>>>>>
>>>>> dont play roulette!
>>>>>
>>>>> Just send the Casino a check and save on the airplane and hotel, save the time, go fishing...
>>>>>
>>>>
>>>> Playing red and black is pretty good odds, green's aside for a moment...
>>>
>>> I should say, red or black. Actually, one time I saw somebody betting on both red and black. Then a green came up and he got pissed off for some reason.
>>> Too funny. It was at harveys in south lake tahoe.
>> I was just up at an Indian Casino in Seattle, and wondering what type of algorithum(s) they have now on the new slot machines.
>> inputs they have are bet size (5 buttons), a re-bet same key, total you have deposited, they are connected by internet, they can determine the amount of
>> time between key presses, an overall timer, they may have a sensor to detect if you are sitting in front, most all machines are made in china, most of
>> the graphics is interchangable (HW and most SW stay the same) and there is an optional key card you can use, which they could track you from machine to
>> machine. Anyhow, won 50 lost 50, and I got to see flashing lights and some tones. The machine emits tones on you bet size, muffeled low for small
>> bets, crisp brite tones for large bets...
>
> Odds of winning at the slots are much worse then even the American double zero roulette tables.
>

what about that EU game Baccarat or Banco ? (I dont know anything about these games)

from the wiki "About 91% of total income from Macau casinos in 2014 came from punto banco.[13]"

On 16/10/2022 21:28, Perrti Lounesto Jr. wrote:
> Introduction
>
> Trivially, when a fair coin is tossed, ad infinitum:
>
> a) Any arbitrarily-long sequence of consecutive heads
> will occur, eventually.
> So, for example, the probability that a googolplex-long
> sequence of consecutive heads will occur is 1.
>
> b) The sequence will occur infinitely often.
>
> a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.
>
> Trivial, as I said - which should make what follows also
> trivial:
>
>
>
> The Challenge
>
> The coin starts off being fair, i.e. p_1 = 0.5
>
> Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
> So:
> p_2 = 0.5 / B
> p_3 = 0.5 / B^2
> ..
> p_n = 0.5 / B^(n-1)
>
> Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.
>
> QUESTION:
> Find the range of values (B,k) for which P_B,k = 1
>
> HINT
> P_k = 1 for all B>1, k>0 is not the answer.
>

I'll try k=1 first, as that looks easier.

If P_B,1 = 1 then that is to say P(at least one head) = 1, i.e. P(no heads) = 0.

i.e. 0 = Product[n=0..oo] (1 - p_n).

There is a standard result for such infinite products: the product diverges to zero iff
Sum[n=0..oo](p_n) diverges. BUT in our example, p_n = 0.5 / B^(n-1), so we have a convergent
geometric series for any B > 1.

Conclusion: P(no heads) > 0, so P_B,1 < 1 for all B > 1.

Having got this result, the more complicated cases become obvious too. Basically, the probability
of 2 or more heads in a row occuring somewhere are always less than the probability of just 1 head
occuring somewhere, and since this last probability is already shown to be strictly less than 1, the
same applies for the cases k > 1.

Well, I'd have to admit I'm out of practice with this sort of thing, so I could have misunderstood,
or just gone off the rails somewhere :) But it matches what my intuitive guess would have been -
applying an exponential decay on the probability of getting a head is a pretty strong constraint...

Regards,
Mike.