AboutJason Eisele Expertise I am qualified to answer probability questions through the undergraduate level. I can also assist with the first actuarial exam in probability and explain the roles of probability in applications such as economics and game theory.
I hope to address any topics that I am currently unfamiliar with during my studies as an actuary.
Experience I am beginning employment as an Actuarial Assistant with a major auto insurer. On the side, I have experience applying probability to poker at a highly competitive level.
Organizations Mensa
Education/Credentials University of Rochester Class of 2008:
Bachelor of Arts, Mathematics and Economics
Certificate in Actuarial Studies
Certificate in Mathematical Modeling in Political Science and Economics
Certificate in Management Studies with track in Accounting and Finance
Question Hi Jason. Can you figure the statistical probability that 2 people playing rock,
paper, scissors came up with matching signals every time in the first 5
consecutive times they signaled. The trials were matching rock-rock, scissors-
scissors, rock-rock, paper-paper, scissors-scissors I think.
Thanks so much.
Answer Dr. Lynn,
Thanks for your question! Since there are three different ways Player A can throw, and three different ways Player B can throw, there are 3^2 = 3*3 = 9 possible pairings of throws. The grid below illustrates the interaction of these throws:
R,r R,s R,p
S,r S,s S,p
P,r P,s P,p
The first player chooses a row (represented by capital letters and first entry of each pair) and the second player chooses a column represented by lowercase letters and the second of each pair). The 9 locations in the grid represent the 9 different possible outcomes. So if each player signals rock, we end up in the top left of the grid at "R,r".
Like with many problems in probability and statistics, we have to clarify what assumptions we are making in order to solve the problem. The most practical thing to do with the information given is to assume that each player is choosing at random (ie. 1/3 probability of rock, 1/3 probability of scissors, 1/3 probability of paper), which would set the probability of each row or column equal to 1/3. If we instead had reason to believe that they have some non-random tendencies, we could change these probabilities appropriately.
With each player throwing at random, the probability of seeing any specific pairing of throws (1/3) * (1/3) = (1/9). There are three ways for both players to match (R,r), (S,s), or (P,p), so the probability of a match is 3 * (1/9) = (1/3). This should make sense because whatever one player throws, the other player has a one in three chance of matching when throwing at random.
If both players keep throwing at random we must see this (1/3) chance happen five times in a row. This would have a probability of (1/3)^5 or 1 in 243. A probability like this means you saw something pretty rare, but not completely unheard of if you play a lot of rock, paper, scissors.
I hope you continue to enjoy exploring the mathematical foundations of games like this. Thanks again!
