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Pop Quiz: Roulette odds


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View Poll Results: Does a series of "black" spins increase the chance the next spin will be "red"?
Yes 1 11.11%
No 8 88.89%
I like cheese 0 0%
Voters: 9. You may not vote on this poll

 
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Pop Quiz: Roulette odds

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  #1 (permalink)
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Please vote above.

The question is:

When watching a roulette wheel in vegas, does a series of consecutive spins that land on "black" increase the chance the next spin will land on "red" ?

Mike

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Big Mike View Post
Please vote above.

The question is:

When watching a roulette wheel in vegas, does a series of consecutive spins that land on "black" increase the chance the next spin will land on "red" ?

Mike

Haha, nice question Mike.


 
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Select the text below to read my answer, so I'm not spoiling this "quiz")
I would say: off course not. Each spin is independent of the previous one, i.e. there is no "memory" for previous outcomes (only your own memory. ). This effect is also know as the Gambler's Fallacy.




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I do not know the answer of course, but I can image different solutions:


Mathematician: It will not increase the odds.

Physicist: If it had a series of spins on black, the wheel is probably a fake.

Economist: I don't have a model to answer the question.

Gambler: Let us try.

Politician: Let us vote.

Professional Trader: Does not watch roulette wheels, but plays Black Jack or Hold'em.


Are you a politician or a trader?



Big Mike View Post
Please vote above.

The question is:

When watching a roulette wheel in vegas, does a series of consecutive spins that land on "black" increase the chance the next spin will land on "red" ?

Mike


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The answer is no.

Just like when flipping a fair coin, the chance of heads vs. tails is always 50/50. It doesn't matter if heads has landed 10 times in a row, the next flip has no better odds of being tails, it is still 50/50. The same is true for the roulette wheel.

This is also why backtesting with insufficient sample size leads to erroneous results. You can imagine that if you flip a coin just ten times, there may not be exactly 5 heads and 5 tails. You can imagine such a thing in backtesting for trading, if you got 6 heads and 4 tails you may think you have a winning strategy, when in fact you simply have insufficient sample size.

Lookup the Law of Large Numbers for more info.

Mike

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You assume that it is an ideal regular wheel. Your statement is correct in case that the wheel is regular and has not been manipulated.

However, in real life (physicists unlike economists have to prove their models empirically) the wheel may well be manipulated. If you have observed a number of events that do not fit the Gaussian distribution, this affects the probability that the wheel was regular. Finally your question did not state that it was a regular wheel, which would produce random result with an expectancy of 9/19 (American Roulette) or 18/37 (French Roulette) for black numbers. So if I do not know, whether the wheel is regular, the ex-post probability that it is a regular wheel changes, once I have observed an unlikely series of black numbers (the physicist knows from experience that models usually do not work in real life).

As a trader I observe markets that are mostly random. Only non-random patterns are tradeable, as they rely on feedback and thus create stochastic dependence between the events of the time series. A regular roulette wheel only produces random patterns with a negative expectancy, so it is of no interest to a seasoned trader. When playing Black Jack, however, you may have a positive expectancy, if you know how to count the cards.

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