MHB What Are the Odds of Winning or Drawing in Paper Rock Scissors?

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In Paper Rock Scissors, the probability of winning in a single round is one-third, with odds of 1:2 against winning. The odds of drawing are the same, also at 1:2. If the game continues after a draw until a winner is determined, the probability of winning increases to one-half, changing the odds to 1:1. In this scenario, the probability of drawing becomes zero, with odds of 0:1. Understanding these probabilities can enhance strategic gameplay.
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Firstly I apologise for the most basic of questions...

I want to know the odds for the game Paper Rock Scissors.

What are the odds of winning

What are the odds of drawing

Thanks in advance :)
 
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dandare30 said:
Firstly I apologise for the most basic of questions...

I want to know the odds for the game Paper Rock Scissors.

What are the odds of winning

What are the odds of drawing

Thanks in advance :)

Hi dandare30, welcome to MHB! ;)

The probability to win in a single round is $\frac 13$.
The odds of winning in a single round are $1:2$. That is 1 possibility to win versus 2 equally likely possibilities to not-win.
It's the same for drawing.

If we keep going after a draw until someone wins, then the probability to win becomes $\frac 12$, and the odds to win becomes $1:1$.
The probability for drawing becomes $0$, and the odds for drawing becomes $0:1$.
 
I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...

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