Therefore, lotteries are a form of taxation - the governments must tell the truth to their constituents... Let's go all the way to the last column: p=1/1,000. He uses the term Black Swan’s to represent events that were unforeseeable in advance, obvious in hindsight, extremely rare verging on unprecedented. A common use of these calculations is to understand what is the chance the next sample is above the highest seen so far. With dice and coin problems the observable possibilities are finite and known. Examples. The certainty and uncertainty a researcher has in his or her results presents another critical area to probe. If the story recounted is accurate, the researchers had secured two tanks. Four equal possibilities each with a 25% chance. Key points and tips discussed in this chapter:  In statistics, a percentage isn’t represented as 0% and 100%, its represented as 0 and 1 by the coolest kids. My wife is a lawyer, and she would say (and did) that there isn’t enough information to answer that question. As a matter of fact, FFG is applicable to any sort of highly randomized events: lottery, roulette, blackjack, horse racing, sports betting, even stock trading. If the probability is 1/N and we repeat the event N times, the degree of certainty is 1 (1/e), when N tends to infinity. How many observable six-sided dice values are at least 2? “Uncertainty indicates we have limited knowledge about the future and can only represent our understanding with possibilities, and the probability of those possibilities”. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The post-Brexit trade agreement between the UK and EU offers travel retailers ‘a degree of certainty’ regarding new rules, says the UK Travel Retail Forum (UKTRF). No certainties, just that it’s more likely than not that the result falls into the equated probability if run enough times. $2! Many of you said two, the possibilities are heads or tails. Why You Should Be Kind to People You Hate, Let’s Face It. DC = 1 – (1 – p) ^ N Simultaneously, the opposite event, the losing chance , decreases exponentially with an increase in the number of trials. They couldn’t know for sure the serial numbers were sequential, or if the two tanks they procured were from the same manufacturing plant and given close proximity serial numbers. This chapter has shown that to calculate probability, we generate a list of all possible values, or all possible range intervals, and allocate them a proportion of 100%. However, some rare event might disrupt your plans such as an earthquake. Any casino would be a guaranteed loser in a matter of months! By contrast, what they call theory of games is a form of vague mathematics: The formulae are barely vaguely correlated with real life. Certainty grows the more samples we have, and the longer we reliably observe. The probability of an event is expressed as a number 0 and 1, 0 indicates the impossibility and 1 indicates the certainty of an event. This is often a surprise, its assumed hundreds or thousands of samples are required to have any significance. Thus, the individual probability for either event is p = 1/2. With a 95% certainty, 19 of 20 survey samples drawn from the population of interest would lie within the confidence interval.) Actually, it could be even worse: It might take 10 or 11 tosses until heads appear! The Black Swan Theory describes how common knowledge, facts and wisdom known as true to everyone, can sometimes be wrong. Calculating probabilities for range problems requires knowing how many possible interval positions a value could fall between. Even this easiest of the games of chance can lead to sizable losses. If it was easy, I’d suspect people who perform prediction on stage (or on Wall Street) would all be retired and own small islands; And all faith healers would be doctors. Nevertheless, this game is too easy for any player with a few thousand dollars to spare. Sure, they were lucky. If there was one black swan, how many other colors are there? Most of our life decisions and actions are not a matter of certainty vs probability. The width of the distribution represents our degree of certainty in our estimate. Very encouraging, isn't it? The researchers boosted their chances by using the serial numbers from the tank track rubber dolly wheels. When calculating probabilities from sample observations of an unknown range of values, there can be no way of knowing in advance all of the possibilities. The degree of certainty DC is 50% that my number will hit within 692 drawings! In reality, they now pay only $500 for a $1 winning bet!!! Subtract the minimum estimate from the highest to estimate, divide by how many of that component are used on each tank, and you have how many total tanks produced. The upper and lower bounds of this range are based on the desired degree of certainty (for example, a 60 percent or 90 percent degree of certainty). Being unforeseeable in advance makes them challenging to account for. In the digit lotteries, the state commissions enjoy typically an extraordinary 50% house edge!!! With sampling you can never be sure, but you can’t be any surer without sampling. 1 in 6. They are largely a matter of probability alone. The probability and statistical program allows you to calculate the number of trials N for any degree of certainty DC. You may want to know the detailed procedure leading to this numerical relation. Let's try to make sense of those numbers. A step in the Fundamental Formula of Gambling leads to this relation: I tested for N = 100,000,000 N = 500,000,000 N = 1,000,000,000 (one billion) trials. They need what is known as house edge or percentage advantage. Un-observed is important to consider and manage. 1. There is no way of knowing for certain, but the odds are in their favor. Pastel purple, pink or blue? The Internet search on Degree of Certainty, DC yielded one and only one result in 1998: This very Web page (zero results in 1997, for DC was introduced in December of that glorious year, with some beautiful snowy days just before the Global Warming debate started ) For we shall always be mindful that nothing comes in absolute certainty; everything comes in degrees of certainty Never zero, Never absolutely. Never say never; never say forever!. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. Also, the casinos set limits on maximum bets: the players are not allowed to double up indefinitely. Evidently, the same-lotto-game combinations have an equal probability, p always the same but they appear with different statistical frequencies. Fundamental Formula of Gambling: Games Other Than Coin Tossing I might have to go all the way to the 9th toss to have a 99.9% chance that, finally, heads came out! Back in 1982 professor Lazlo used degrees of certainty testing our knowledge in chemistry. Now the odds are 50% heads, 50% tails. Nevertheless, the state lotteries may conduct their business because their hefty profits serve worthy social purposes (helping the seniors, the schools, etc.) Most of our life decisions and actions are not a matter of certainty vs probability. None of these colors are out of the question now we know that not all swans are white. This chapter continues to explore statistical sampling. 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