Our Game Report
By Seraphina Kim and Vivian Chou
MDM4U
Doctor D
2025.01.06
Table of Contents:
1. Introduction
2. Theoretical data table and graph
I.
Pachinko game
II.
Lottery (online game)
3. Experimental data table and graph
I.
Pachinko game
II.
Lottery (online game)
4. Calculations of incomes and expenses
5. Comparison between theoretical and experimental data
6. Conclusion
Introduction
Welcome to our exciting games of chances! Here are two games that you are going to play: a
pachinko game and an online lottery game. To play the pachinko game, you will be provided a
pachinko machine. When the machine is handed in, you will need to simply press the button on
the machine to launch a small silver marble into 8 separated areas marked with different
numbers. You will try your luck at landing it in one of the winning slots.
There are four ways to win:
1.
2.
3.
4.
Hitting the ball into the area '5’: Earn a reward of 10rmb.
Hitting the ball into the area '10’: Earn a reward of 5rmb.
Hitting the ball into the area ‘20’ or ‘30’: Earn a reward of 1rmb.
Hitting the ball into the area ‘40’: Earn a reward of 15rmb.
If you miss launching the marble, just try it again until you successfully score any of the
number. Each game will cost 5rmb, so strategize carefully and let the game begin!
Player Population:
This game appeals to fans of pachinko and those interested in exploring probability through
interactive gameplay.
Hypothesis:
If players rely on random outcomes, the expected value per game indicates whether the game is
profitable or results in an average loss.
Besides, to play the lottery game, you will need your phone to get into the site we provided.
Playing is incredibly simple. With just a press of a button, you will receive a random result that
determines whether you win.
There are three ways to win in this game, each offering a reward:
1.
Drawing ‘50’: Win 50rmb as a prize.
2.
Drawing ‘10’: Win 10rmb as a prize.
3.
Drawing ‘1’: Win 1rmb as a prize.
Not getting the amount of money you paid for each game means you lose. Each game costs
10rmb, so it means that if you draw the second option, it is at the breakeven point.
Player Population:
This game is designed for those curious about probability and decision-making strategies, such
as students and casual gamers.
Question: Is this game profitable for the player over time, or is it skewed in favor of the owner?
Theoretical value spreadsheets
Pachinko game:
Theoretical
*E(X) = probability (decimal)*payout
Lottery game:
Theoretical
*E(X) = probability (decimal)*payout
Experimental values spreadsheets
Here are the values resulted from my peers’ gameplays.
Pachinko game:
(Pachinko)
*Experimental Prob =
frequency of winning (each option)/total trials
E(X) =
E(X) = experimental prob(decimal)*payout
(Lottery)
Lottery game:
*Experimental Prob =
frequency of winning (each option)/total trials
E(X) = experimental prob(decimal)*payout
Incomes and expenses:
Pachinko-
Total:
Lottery-
Total: