running_of_the_bots_simulation.Rmd

---
title: "Running of the Bots"
author: "Girls Who Code at University of Michigan Department of Computational Medicine and Bioinformatics"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(ggplot2)
library(RColorBrewer)

```


# Simulate an Unfair Coin with Ozobot
```{r}

#set seed
set.seed=123

#sample size
n<-100

#simulate unfair coin
sim<-floor(runif(n,min=1,max=7))

#function to turn uniform distribution of values to directions
num_to_dir<-function(x){
  if (x==1){
    return("left")
  } else if (x==2){
    return("straight")
  } else if (x==3){
    return("right")
  } else if (x==4){
    return("right")
  } else if (x==5){
    return("right")
  } else if (x==6){
    return("right")
  }
}

dir<-unlist(lapply(sim,num_to_dir))
ddir<-data.frame(dir)
ddir$dir <- factor(ddir$dir, levels = c("left","straight","right"))

#barplot
ggplot(ddir,aes(x=dir,fill=dir)) + geom_bar() + theme_bw() + 
  labs(title="Unfair Coin Ozobot Simulation",x="Directional Choice",y="Count") +
  scale_fill_brewer(palette = "Set1")

#represent directions as numbers (1 is left, 2 is straight, 3 is right)
sim_fac<-factor(sim)
levels(sim_fac)<-c(1,2,3,3,3,3)
sim_num<-as.numeric(sim_fac)
ddir$num<-sim_num

#density
ggplot(ddir,aes(x=num)) + theme_bw() + stat_density() + labs(title="Unfair Coin Ozobot Simulation",x="Directional Choice",y="Density")

#probabilities
prob<-data.frame(table(ddir$dir)/n)
names(prob)<-c("direction","prob")

ggplot(prob,aes(x=direction,y=prob,fill=direction,label=prob)) + geom_bar(stat="identity") + theme_bw() +
  labs(title="Unfair Coin Ozobot Simulation",x="Directional Choice",y="Experimental Probability") +
  scale_fill_brewer(palette = "Set1") + geom_text(vjust=1.5,size=5)

```

# Simulate a Fair Coin with Ozobot

```{r}
sim_fair<-floor(runif(n,min=1,max=4))
sim_fair_fac<-as.factor(sim_fair)
levels(sim_fair_fac)<-c("left","straight","right")
ddir_fair<-data.frame(dir=sim_fair_fac,num=sim_fair)


#barplot
ggplot(ddir_fair,aes(x=dir,fill=dir)) + geom_bar() + theme_bw() + 
  labs(title="Fair Coin Ozobot Simulation",x="Directional Choice",y="Count") +
  scale_fill_brewer(palette = "Set1")


#density
ggplot(ddir_fair,aes(x=num)) + theme_bw() + stat_density() + labs(title="Unfair Coin Ozobot Simulation",x="Directional Choice",y="Density")

#probabilities
n<-100
prob_fair<-data.frame(table(ddir_fair$dir)/n)
names(prob_fair)<-c("direction","prob")

ggplot(prob_fair,aes(x=direction,y=prob,fill=direction,label=prob)) + geom_bar(stat="identity") + theme_bw() +
  labs(title="Fair Coin Ozobot Simulation",x="Directional Choice",y="Experimental Probability") +
  scale_fill_brewer(palette = "Set1") + geom_text(vjust=1.5,size=5)

```

# What sample size is needed for experimental probability to converge on theoretical probability?

```{r}
#function for simulation and plotting
fair_simulation<-function(n){
  sim_fair<-floor(runif(n,min=1,max=4))
  sim_fair_fac<-as.factor(sim_fair)
  levels(sim_fair_fac)<-c("left","straight","right")
  ddir_fair<-data.frame(dir=sim_fair_fac,num=sim_fair)
  prob_fair<-data.frame(table(ddir_fair$dir)/n)
  names(prob_fair)<-c("direction","prob")
  return(prob_fair)
}


#test sample sizes from 100 to 10000 incremented by 500
for (i in seq(100,10000,500)){
  prob_fair<-fair_simulation(i)
  title_text<-paste0("Fair Coin Ozobot Simulation N=",i)
  print(ggplot(prob_fair,aes(x=direction,y=prob,fill=direction,label=sprintf("%0.4f", round(prob, digits = 4)))) + geom_bar(stat="identity") +
          theme_bw() + geom_hline(yintercept=0.33333333,linetype="dashed") +
          labs(title=title_text,x="Directional Choice",y="Experimental Probability") +
          scale_fill_brewer(palette = "Set1") + geom_text(vjust=1.5,size=5))
  
}

```


# What is the theoretical probability of obtaining at least one run of length L if Ozobot traverses the track 100 times?

http://www.gregegan.net/QUARANTINE/Runs/Runs.html