Calculating Average for Roulette

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Discussion Overview

The discussion revolves around calculating the average outcome in roulette, specifically addressing how to interpret statistical measures such as mean and variance in the context of the game. Participants explore the implications of different rules and scenarios, including biased roulettes and the significance of outcomes like 0 and 00.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how to calculate the average for roulette, suggesting that 0 and 00 might be treated as numerical zero.
  • Another participant clarifies that the average only makes sense if outcomes can be added, using the example of a die to illustrate expected earnings per roll.
  • A different participant argues that the average of 52.63 mentioned in a text is not a payoff odds but rather a mean, and raises a scenario involving a biased roulette where the average becomes 105.26, questioning how this is derived.
  • Some participants express skepticism about the figure of 52.63, suggesting it seems impossible without further context from the referenced material.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the average in roulette, with some agreeing on the need for clarity regarding game rules, while others contest the validity of the average figures presented. The discussion remains unresolved regarding the correct interpretation and calculation of averages in this context.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the outcomes and the specific rules of the game, as well as the lack of clarity on how averages are derived in different scenarios.

KFC
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In basic statistic, we consider mean, mode and variance. Take a die as example, there are 6 possible values so the average is (1+2+3+4+5+6)/6= 3.5. For a roulette, besides 1 to 36, there are two special sections 0 and 00. So how do we calculate the average? Take 0 and 00 as numerical ZERO?

In one text, it said that for roulette, in 2000 spins, the average is 52.63 and standard derivation is 7.16. But how come it get an average that large?
 
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You have to specify rules of the game

The average only makes sense if you can add outcomes. In case of a die, if you get $1 for each dot that you roll ($1 for 1, $2 for 2, ...) you can add them and you can say that the average (expected earnings per roll) is $3.5.

52.63% is the chance for the casino to win (and for you to lose) if you put money on a color. Say, you bet on red, if the roulette rolls red, you win, if it rolls black or either zero, you lose. The chance to lose is 20/38 = 52.63%.
 
Thanks for reply. But I don't think the average (52.63) is the payoff odds or (rate to lose) because in the context of the book, it mentioned it is the average (mean) which later central limit theorem will be applied. And the author consider the same game on a biased roulette in which 17's appear at the chance 1/19 instead of the 1/38, and the average now becomes 105.26 instead of 52.63. Following your idea to get 52.63, I don't see how to get 105.26 in this case

hamster143 said:
You have to specify rules of the game

The average only makes sense if you can add outcomes. In case of a die, if you get $1 for each dot that you roll ($1 for 1, $2 for 2, ...) you can add them and you can say that the average (expected earnings per roll) is $3.5.

52.63% is the chance for the casino to win (and for you to lose) if you put money on a color. Say, you bet on red, if the roulette rolls red, you win, if it rolls black or either zero, you lose. The chance to lose is 20/38 = 52.63%.
 
KFC said:
In basic statistic, we consider mean, mode and variance. Take a die as example, there are 6 possible values so the average is (1+2+3+4+5+6)/6= 3.5. For a roulette, besides 1 to 36, there are two special sections 0 and 00. So how do we calculate the average? Take 0 and 00 as numerical ZERO?

In one text, it said that for roulette, in 2000 spins, the average is 52.63 and standard derivation is 7.16. But how come it get an average that large?
52.63 is impossible on the face of it. You might want to include more text material from the article or book you are referring to.
 

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