Home Our Story Links Warranty Testimonials Site map Terms. PRODUCTS Overseas Slots Las Vegas Slots JVL Machines Pachinko Antique Slots Tokens & Extras Slot Stands Cherry Masters Currency Counters Casino Gifts Gum Machines Pedal Cars and Planes Specials Customer Photos. I am trying to write a simple slot machine program that will return three numbers as the slot icons using a loop. I can get the first part just fine (I think). But I am stuck at converting my icons to intergers or character that I can compare to see if it is a winner or not. Here so far: // slot.

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May 2016

Volume 31 Number 5

[Test Run]

By James McCaffrey | May 2016 | Get the Code: C# VB

Imagine you’re in Las Vegas, standing in front of three slot machines. You have 20 tokens to use, where you drop a token into any of the three machines, pull the handle and are paid a random amount. The machines pay out differently, but you initially have no knowledge of what kind of payout schedules the machines follow. What strategies can you use to try and maximize your gain?

This is an example of what’s called the multi-armed bandit problem, so named because a slot machine is informally called a one-armed bandit. The problem is not as whimsical as it might first seem. There are many important real-life problems, such as drug clinical trials, that are similar to the slot machine example.

It’s unlikely you’ll ever need to code an implementation of the multi-armed bandit problem in most enterprise development scenarios. But you might want to read this article for three reasons. First, several of the programming techniques used in this article can be used in other, more common programming scenarios. Second, a concrete code implementation of the multi-armed bandit problem can serve as a good introduction to an active area of economics and machine learning research. And third, you just might find the topic interesting for its own sake.

The best way to get a feel for where this article is headed is to take a look at the demo program shown in Figure 1. There are many different algorithms that can be used on multi-armed bandit problems. For example, a completely random approach would be to just select a machine at random for each pull, then hope for the best. The demo presented here uses a basic technique called the explore-exploit algorithm.

Figure 1 Using Explore-Exploit on a Multi-Armed Bandit Problem

The demo begins by creating three machines. Each machine pays a random amount on each pull, where the payout follows a Gaussian (bell-shaped) distribution with a specified mean (average) and standard deviation. The third machine is the best in one sense because it has the highest mean payout per pull of 0.1 arbitrary units. In a non-demo scenario, you wouldn’t know the characteristics of the machines.

The total number of pulls available is set to 20. In explore-exploit, you set aside a certain proportion of your allotted pulls and use them to try and find the best machine. Then you use your remaining pulls only on the best machine found during the preliminary explore phase. The key variable for the explore-exploit algorithm is the percentage of pulls you designate for the explore phase. The demo sets the explore-percentage to 0.40, therefore, there are 20 * 0.40 = 8 explore pulls followed by 20 - 8 = 12 exploit pulls. Increasing the percentage of explore pulls increases the probability of finding the best machine, at the expense of having fewer pulls left to take advantage of the best machine in the exploit phase.

During the eight-pull explore phase, the demo displays which machine was randomly selected and the associated payout. Behind the scenes, the demo saves the accumulated payouts of each machine. Machine 0 was selected three times and paid -0.09 + 0.12 + 0.29 = +0.32 units. Machine 1 was selected two times and paid -0.46 + -1.91 = -2.37 units. Machine 2 was selected three times and paid 0.19 + 0.14 + 0.70 = +1.03 units. In the case of the demo, the explore-exploit algorithm correctly identifies machine 2 as the best machine because it has the largest total payout. At this point the algorithm has a net gain (loss) of 0.32 + -2.37 + 1.03 = -1.02 units.

During the 12-pull exploit phase, the demo repeatedly plays only machine 2. The exploit phase payouts are 0.03 + 0.33 + . . + 0.45 = +2.32 units. Therefore, the total payout over all 20 pulls is -1.02 + 2.32 = +1.30 units and the average payout per pull is 1.30 / 20 = 0.065.

There are several different metrics that can be used to evaluate the effectiveness of a multi-armed bandit algorithm. One common measure is called regret. Regret is the difference between a theoretical baseline total payout and the actual total payout for an algorithm. The baseline theoretical payout is the expected payout if all allotted pulls were used on the best machine. In the case of the three machines in the demo, the best machine has an average payout of 0.10 units, so the expected payout if all 20 pulls were used on that machine is 20 * 0.10 = 2.00 units. Because the explore-exploit algorithm yielded a total payout of only 1.30 units the regret metric is 2.00 - 1.30 = 0.70 units. Algorithms with lower regret values are better than those with higher regret values.

This article assumes you have at least intermediate programming skills, but doesn’t assume you know anything about the multi-armed bandit problem. The complete demo program, with a few minor edits to save space, is presented in Figure 2, and it’s also available in the associated code download. The demo is coded using C#, but you shouldn’t have too much trouble refactoring the demo to another language, such as Python or Java. All normal error checking was removed from the demo in order to keep the main ideas of the multi-armed bandit problem as clear as possible.

Figure 2 Complete Multi-Armed Bandit Demo Code

using System;

namespace MultiBandit

{

class MultiBanditProgram

{

static void Main(string[] args)

{

Console.WriteLine('nBegin multi-armed bandit demo n');

Console.WriteLine('Creating 3 Gaussian machines');

Console.WriteLine('Machine 0 mean = 0.0, sd = 1.0');

Console.WriteLine('Machine 1 mean = -0.5, sd = 2.0');

Console.WriteLine('Machine 2 mean = 0.1, sd = 0.5');

Console.WriteLine('Best machine is [2] mean pay = 0.1');

int nMachines = 3;

Machine[] machines = new Machine[nMachines];

machines[0] = new Machine(0.0, 1.0, 0);

machines[1] = new Machine(-0.5, 2.0, 1);

machines[2] = new Machine(0.1, 0.5, 2);

int nPulls = 20;

double pctExplore = 0.40;

Console.WriteLine('Setting nPulls = ' + nPulls);

Console.WriteLine('nUsing pctExplore = ' +

pctExplore.ToString('F2'));

double avgPay = ExploreExploit(machines, pctExplore,

nPulls);

double totPay = avgPay * nPulls;

Console.WriteLine('nAverage pay per pull = ' +

avgPay.ToString('F2'));

Console.WriteLine('Total payout = ' +

totPay.ToString('F2'));

double avgBase = machines[2].mean;

double totBase = avgBase * nPulls;

Console.WriteLine('nBaseline average pay = ' +

avgBase.ToString('F2'));

Console.WriteLine('Total baseline pay = ' +

totBase.ToString('F2'));

double regret = totBase - totPay;

Console.WriteLine('nTotal regret = ' +

regret.ToString('F2'));

Console.WriteLine('nEnd bandit demo n');

Console.ReadLine();

} // Main

static double ExploreExploit(Machine[] machines,

double pctExplore, int nPulls)

{

// Use basic explore-exploit algorithm

// Return the average pay per pull

int nMachines = machines.Length;

Random r = new Random(2); // which machine

double[] explorePays = new double[nMachines];

double totPay = 0.0;

int nExplore = (int)(nPulls * pctExplore);

int nExploit = nPulls - nExplore;

Console.WriteLine('nStart explore phase');

for (int pull = 0; pull < nExplore; ++pull)

{

int m = r.Next(0, nMachines); // pick a machine

double pay = machines[m].Pay(); // play

Console.Write('[' + pull.ToString().PadLeft(3) + '] ');

Console.WriteLine('selected machine ' + m + '. pay = ' +

pay.ToString('F2').PadLeft(6));

explorePays[m] += pay; // update

totPay += pay;

} // Explore

int bestMach = BestIdx(explorePays);<

Slot Machine Code C#