A tournament for computer programs playing VNM POKER(5,1,1,2) is announced. The tournament is played in the knock-out system, where computer programs, from now on called "robots" play 200 rounds against other robots.
Every student should submit just one robot, and should provide
Most of the games will be executed at the teacher's home computer, but cheating will not occur.
There is a prize for the creator of the winning computer player, maybe a box of self-made brownies, maybe a little book on Mathematics.
Here you can play the game
Here you can select two of these robots and let them play 200 rounds of the game all on their own.
The following table displays the expected payoff of the different pairings when playing 200 rounds. The higher it is, the greener it is, the lower, the reder.
In the next table, the winning probability of the row player in the corresponding pairing is shown (assuming that draws are impossible, meaning that in case of a draw another 200 rounds are played, and so on, until a decision is reached). Again, red means low winning probability, and green means high winning probability. The numbers are somehow related to the number in the previous table, but not directly.
So what are the chances of the different robots of winning a 8-member knock-out tournament of 200 rounds for each pairing? These numbers are obtained by simulating a huge number of possible pairings and multiplying the corresponding winning probabilities. We get
Why does Cantor, who would win each one of the others if the number of rounds being played would be very high (let's say 1,000,000,000 rounds) not have the highest chance of winning the tournament?
If the robots RX-24 and Brains are replaced by the more reasonable versions RX-24rev and Brainsrev, the probabilities that the robots win the whole tournament are:
The (random) pairing was rather favorable for Dake Quinton. With this pairing, the winning probabilities for Dake Quinton increased to 48%. R2-D2 and Cantor still had probabilities for winning the tournament of 28% respectively 23%. All other robots had winning probabilities of 1% or less.
The results in the quarter-final were as follows:
Before playing this semi-final, the winning probabilities changed further. The probabilities for winning the tournament are now 59% for Dake Quinton, 38% for R2-D2, 3% for Jennirafe, and less than 1% for RX-24.
Question: Dake Quinton's chance for winning the tournament was 59% before the semi-final. Dake Quinton won, but still its (his?) winning chance decreased to 55%. How is this possible?