Curiosities; Meal with Álvaro

    2^n is the formula used for this problem knowing that any kind of papers cant be folded more than 7 times. If we fold it 8 times, the solution will be 256 sheets of paper (thickness) which cant be impossible to fold knowing that it is made from wood. 

Curiosities, Meal with Alvaro

San Petersburg paradox

Mathematics, as well as this blog has been demonstrating, is related to all aspects in our life; this includes probability. However, real life is not always adjusted to what mathematics say. This is the case of the San Petersburg Paradox; this paradox uses probability as its tool. By definition, probability is a measure or estimation of likelihood of occurrence of an event and takes place every time in our day to day, for instance, in every gaming we can find in casinos (roulette, slot machines...). With this post , I am trying to demonstrate why, even though mathematics try to explain one of these games and the chances we have of winning (San Petersburg) it is not adjusted to reality.

• This game consists on betting chains. First of all, you have to bet two euros. A coin will be dropped; If the result is heads, the profit will be the double of the previous bet, in this case, 4 euros. In case you continue obtaining heads, the profit will be continuously multiplied by 2 (2nd round you get heads, profit will be 8, 16 for the 3rd, 32 the forth etc...) On the other hand, (if you get tales), the results will be the same as explained with heads but negative (first of all you will lose 2 euros, then 4, 8 etc...). 
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• This game has been analyzed by mathematicians in order to obtain a "winning formula", but formulas cant describe reality. In fact, maths say that, by minimun the probability is, you can keep winning forever. But real life, as well as we all know, says that there is a moment where luck will turn its back. 
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• In order to find a finite profit (finite value, not infinite as probability would say), the mathematician Bernoulli described this game with the following formula, assigning a finite value to the profit: 

This formula gives an implicit relationship between the gambler's wealth and how much he should be willing to pay to play (specifically, any c that gives a positive expected utility).

Bernoulli

In conclusion, the San Petersburg paradox demonstrate that mathematics cannot be applied for everything in real life, even though it is the most important tool we have nowadays.