On Saturday, February 9, 2019 at 12:45:25 AM UTC+2, Ion Saliu wrote:
> On Friday, February 8, 2019 at 2:04:01 PM UTC-5, Ion Saliu wrote:
> > On Saturday, May 22, 2004 at 2:43:13 PM UTC-4, Ion Saliu wrote:
>
> • Point of Relative Certainty
>
> There is no absolute certainty if we are to abide by the rules of Reason…absolutely! Go to the Saliu site and search for 'reason, certainty, randomness.'
>
> This is a more mundane problem. It is a parlor favorite. It is also a favourite reason to put up a fight. Just ask Kotskarr, or Shobolun, or Kulai Parakelsus; or just ask yourself, or myself…
>
> The question goes "If heads did not appear in 10 consecutive coin tosses, is it more likely to come out in the 11th toss?" Many will answer, I mean will shout right away "NOT! NOT! The probability of heads is always ½ or 0.5 or 50%!" Indeed, the probability for heads is always ½ or 0.5 or 50%. But that parameter simply represents the number of expected successes in ONE trial; or, the number of favorite cases over total cases.
>
> There is a lot more to a phenomenon such as ‘coin tossing'. For starters, we can analyze coin tossing by calculating the ‘probability of the normal distribution'. The ‘probability of the normal distribution' refers to ‘EXACTLY M successes in N trials'. In this particular case: what is the probability of exactly 0 heads in 10 tosses? What is the probability of exactly 0 heads in 11 tosses?
>
> You don't need to do all those calculations manually. My probability software SuperFormula.EXE ( https://saliu.com/formula.html ) is a very convenient tool. Select option L (‘At Least' M Successes in N Trials). Select next option 1, since we know the probability p (p=0.5). Type 0 for number of successes M, and 10 for number of trials N. The program responds:
> The binomial probability of 0 successes in 10 trials
> for an event of individual probability p = .5 is:
> BDF = .0009765625
> or .09765625 %
> or 1 in 1024
>
> Thus, the probability of zero heads in 10 tosses is 1 in 1024. So we missed heads 10 times in a row. What is the probability to miss heads in the very next toss? That is equivalent to missing heads 11 times in a row!
>
> The binomial probability of 0 successes in 11 trials
> for an event of individual probability p = .5 is:
> BDF = .00048828125
> or .04882812 %
> or 1 in 2048
> We always use the constant p = .5, but the CHANCE to miss heads worsens with the number of tosses! Tell you what, Krushbeck. Those casino consultants, and game designers, and executives are not damn idiots!
>
> Remember last time you lost all your money at the slot machines? You remember that every time you won a flashy-snazzy prompt asked you to "Double your win". Why would the casinos offer you a good chance to double your wins? Isn't the probability the same from one spin to the next? Of course it is. But your chance (degree of certainty) to win consecutively is lower.
>
> The casinos offer you the "opportunity" to double your player's disadvantage. That is, one method for the casino to double the house advantage! That's mathematics. Read more:
> • https://saliu.com/keywords/casino.htm
>
> OK. We missed, this rare time, 11 consecutive tosses. What is the degree of certainty to miss heads consecutively in 12 tosses?
>
> The binomial probability of 0 successes in 12 trials
> for an event of individual probability p = .5 is:
> BDF = .000244140625
> or .02441406 %
> or 1 in 4096
>
> If you will, the odds against missing heads in consecutive tosses doubles with each toss. Those casino consultants, and game designers, and executives are not damn idiots! They know how to boost their wealth. They even pay pocket change to all kinds of ghiolbans and tirtans to debate in every conceivable public place. The ghiolbans and tirtans "debate" with ardor that no matter how many times in a row an event has skipped, your odds will remain eternally the same!
>
> If you are stubborn and don't believe the ghiolbans and tirtans, guess what? Them casino consultants, and game designers, and executives (who are not damn idiots, ever!) will even offer players free "gambling systems"! Ever heard of the "Turnaround" system? Read more:
> • https://saliu.com/bbs/messages/733.html
>
> I've heard many times that heads can hit an infinity of times in a row; or, miss an infinite number of consecutive tosses! My honest question is, when does that infinity start? I wanna see a beginning, if I were to believe in a certain end. Certain? Say what?
>
> • "For only Almighty Number is exactly the same, and at least the same, and at most the same, and randomly the same. May Its Almighty grant us in our testy day the righteous proportion of being at most unlikely the same and at least likely different. For our strength is in our inequities."
>
> Ion Saliu (royalty-name Parpaluck),
> Founder of Gambling Mathematics
> > >
> > > edd...@hotmail.com (Raymond Baldwin) wrote in message news:<2571f6f8.04051...@posting.google.com>...
> > > > Hi Everyone,
> > > >
> > > > I understand that there is a fascinating formula on sleeper expectations for roulette, baccarat, craps, keno, lotteries; meaning that after a specific number of no-show outcomes then the due number is most likely to appear.
> > > >
> > > > Has anyone heard about an ostensible physics law called 'Point of Certainty'?
> > > >
> > > > Thanks in advance for your kind replies-
> > > > RB
> >
>
> • The true idiots always boast this characteristic: “The Lizard of Odds Syndrome”. In a nutshell, the syndrome states that “the probability of getting 200 ‘heads’ in a row is always equal to the probability of getting 1 'heads' in a row”. Read more on how you can detect the bullish idiots:
>
> • https://saliu.com/bbs/messages/204.html
> • Wizard of Odds, Wizard of Vegas: Fallacy, Idiocy, Mysticism.
>
> The undeniable universal Law (the famed FFG) states:
>
> • The ‘degree of certainty DC’ rises exponentially with the increase in the ‘number of trials N’ while the ‘probability p’ is always the same or constant.
>
> • N = log (1 - DC) / log (1 - p)
> or
> • DC = 1 – (1 – p) ^ N
>
>
> Best of luck from Parpaluck!
>
> Ion Saliu,
> Founder of Mathematics of Odds

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