Keno Simulation

DIRECTORY STRUCTURE:

\Keno Simulation

• --- \KenoProject (source)
• --- \Bin (compiled executable)
• --- \Data (output file data) (Keno.xlsx)
• --- \Documentation (implementation documentation)
• --- \Obj (discardable binary intermediaries)

KenoProject Overview

1. Assignment CMPS 5243 Algorithm Analysis:

The casino game 'KENO' involves the selection of 20 balls from 80 balls numbered 1 ... 80. The player selects k numbers (1-20). The payoff depends on how many of the player's numbers that the casino machine selects. For example, if the player selects 9 numbers and 5 of them are generated by the machine, he/she wins $4.00; if 6 are generated, the player wins $43.00.

This program is to determine the probability of each possible situation and place these probabilites in a 20 x 21 array of real values. The entries in the [ith] row assume that the player has selected i numbers. The entry in the [jth] column is the probability that the player catches j spots out of i possible. Of course, if j > i, the probability is 0.0. In general, if i <= j, the probability is given by:

      P (catch j out of i numbers) = C ( i, j ) * P1 * P2 / P3, where
      C (i, j) = i! / ((i-j)! * j!)

      P1 ( factors ) = 20 * 19 * 18 ... factors, where factors = j
      P2 ( factors ) = 60 * 59 * 58 ... factors, where factors = i - j
      P3 ( factors ) = 80 * 79 * 78 ... factors, where factors = i

Together with this program specification there is a sheet of payoffs for between 1 & 9 spots marked. Calculate for each number of spots marked the "expected value" of a $1 bet.

Implementation

• The program used combinatorics to calculate the payout probabilities.

  • See https://en.wikipedia.org/wiki/Combination

• It further used COM Automation to create an MS Excel Spreadsheet (from within a Native C++ Console Application) as the final output file for the the calculated probability data.