Question

Rock-Paper-Scissors, also called Roshambo, is a popular two-player game often used to quickly determine a winner and loser. In the game, each player puts out a fist (rock), a flat hand (paper), or a hand with two fingers extended (scissors). In the game, rock beats scissors which beats paper which beats rock. The question is: Are the three options selected equally often by players? Knowing the relative frequencies with which the options are selected would give a player a significant advantage. A study \(^{10}\) observed 119 people playing Rock-Paper-Scissors. Their choices are shown in Table 2.6 . (a) What is the sample in this case? What is the population? What does the variable measure? (b) Construct a relative frequency table of the results. (c) If we assume that the sample relative frequencies from part (b) are similar for the entire population, which option should you play if you want the odds in your favor? (d) The same study determined that, in repeated plays, a player is more likely to repeat the option just picked than to switch to a different option. If your opponent just played paper, which option should you pick for the next round? $$\begin{array}{lc}\hline \text { Option Selected } & \text { Frequency } \\\\\hline \text { Rock } & 66 \\\\\text { Paper } & 39 \\\\\text { Scissors } & 14 \\\\\hline \text { Total } & 119 \\\\\hline\end{array}$$

Short answer

The sample in this case are the 119 observed people playing Rock-Paper-Scissors. The population refers to all people who play Rock-Paper-Scissors. The variable measures the option that players choose. The relative frequency table shows Rock is chosen in about 55.5% of the games, Paper is chosen approximately 32.8%, and Scissors about 11.8%. To have the odds in your favor, you should play Paper as it would beat Rock which is the most commonly selected option. If the opponent just played Paper, the next option you should pick is Scissors.

Step-by-step solution

Identify Sample, Population and Variable

The sample in this study are the 119 people who were observed playing Rock-Paper-Scissors. The population would be all the people who play Rock-Paper-Scissors. The variable that is measured in this study is the option that players choose (rock, paper, or scissors).

Construct Relative Frequency Table

To calculate the relative frequency, divide the frequency of each option by the total number of observations (119):\[\begin{align*}\text { Relative frequency of Rock: } & \frac{66}{119} = 0.555 \\text { Relative frequency of Paper: } & \frac{39}{119} = 0.328 \\text { Relative frequency of Scissors: } & \frac{14}{119} = 0.118 \\end{align*}\]This means that Rock is chosen in about 55.5% of the games, Paper is chosen in about 32.8% of the games, and Scissors is chosen in about 11.8% of the games.

Determine Strategy

To maximize chances of winning, choose the option that beats the one picked most frequently by players. From the relative frequency table, the most frequently chosen option is Rock, therefore, the best choice would be Paper.

Predict Next Move

Given that a player is more likely to repeat than switch, if your opponent just played Paper in the last round, you should pick Scissors for the next round as it would beat Paper if the opponent repeats their choice.