Using RENO to Simulate a Roulette Bet

ReliaSoft > Software > RENO > Examples > Example C-2

	Visual Stochastic Event SimulatorSM Flowchart and solve the most complex probabilistic problems.
	EXAMPLES

Example C-2 - Roulette

Software Used:
RENO

Problem Statement:

The house edges on all possible bets for American roulette are described in the following table. It details expected gains and losses per 38 games for $1 bet. Each number has a probability of 1/38 of being a winner.

Bet	Bet on	Payoff	Odds	Wins	Losses	$ Won	$ Lost	Loss	House Edge
Straight up	one number	35 to 1	38 to 1	1	37	$35	$37	$2	$0.05
Split Bet	two numbers	17 to 1	38 to 2	2	36	$34	$36	$2	$0.05
Corner	four number	8 to 1	38 to 4	4	34	$32	$34	$2	$0.05
Five Numbers	five numbers	6 to 1	38 to 5	5	33	$30	$33	$3	$0.08
Line Bet	six numbers	5 to 1	38 to 6	6	32	$30	$32	$2	$0.05
Column	twelve numbers	2 to 1	38 to 12	12	26	$24	$26	$2	$0.05
Dozen	twelve numbers	2 to 1	38 to 12	12	26	$24	$26	$3	$0.08
Red or Black	eighteen numbers	1 to 1	38 to 18	18	20	$18	$20	$2	$0.05
Even or Odd	eighteen numbers	1 to 1	38 to 18	18	20	$18	$20	$2	$0.05
Low or High	eighteen numbers	1 to 1	38 to 18	18	20	$18	$20	$2	$0.05

You can use RENO to simulate different bets, including:

Only Straight Up Bet
Only Color Bet
Etc.

RENO Solution:

The analysis for a straight up bet is described here.

Define Random Variables to describe the probabilities for your pick and the roulette wheel outcome, as shown next for your pick.

MyPick Random Variable

Define two Constants to set the number of bets that you will place and the value of each bet.

NumberOfBets Constant and BetValue Constant

A Storage Variable will also be required to store the amount of money in your “Bank” during the simulation.

MyBank Storage Variable

Construct the flowchart as follows:

Main Flowchart to model the problem

The Flag Marker, Counter Block, Reset Block and Go To Flag constructs in the main flowchart are used to define a loop, which causes the simulation to continue placing bets up to the specified number of bets.

The Conditional Block in the main flowchart passes the roulette wheel outcome to the subchart.

Continue Conditional

The subchart is constructed as follows.

Subchart

In the subchart, another Conditional Block is used to determine whether the roulette wheel outcome matches your pick.

Win? Conditional

Two Blocks and a Summing Gate are then used to calculate and summarize your winnings or losses. The calculation for your winnings is shown next.

Standard Block to calculate winnings

The amount of your win or loss is then passed to the Result Storage construct in the main flowchart and the Go To Flag starts another loop to represent your next bet.

After performing 1,000 simulations, the results are displayed in the Simulation Results Explorer and in the flowchart, as shown next.

Main Flowchart with results displayed

A RENO project with the solution for this example (called "Roulette.rnp") is shipped with the software and stored in the Examples\Casino folder in the application directory (e.g. C:\Program Files\ReliaSoft\RENO\Examples\Casino\Roulette.rnp).

Questions?