##------BELOW ARE PARAMETERS WE CAN PLAY WITH ------#

minBetSize = 2
minBankSizeAtEndOfSim = 100
startingBalance = 100
edge = 0.1
confidenceInterval95 =  c(0,0.05,0.1,0.15,0.2,0.25,0.3,0.45,0.7)

numberOfSimulations = 700
numberOfBets = 1000
KellyFraction = 0.4



##--------------SIMULTATION CODE STARTS HERE------
#LOOP THROUGH THE ARRAY OF POSSIBLE CONFIDENCE INTERVALS PROVIDED		

goneBustArray = NULL;
for (confidenceCounter in 1:length(confidenceInterval95)){

										# WE WILL FIND THE PROB OF BUST FOR EACH CONFIDENCE INTERVAL
GoneBust = rep(0, length = numberOfSimulations)
FinalBalance = matrix(0, nrow = numberOfSimulations, ncol = numberOfBets)

for (i in 1:numberOfSimulations){		#LOOP THROUGH EACH SIMULATION

	currentBalance = startingBalance

	for (j in 2:numberOfBets){		#FOR THIS SIMULATION LOOP THROUGH THE NUMBER OF BETS TO MAKE
				
		believedProbability = runif(1)			#GET A PORBABILTY RANDOMLY FROM A UNIFORM DISTRIBUTION
		odds = (1+edge)/believedProbability				#FIND THE ODDS YOU WOULD USE FOR YOUR "PERCIEVED" EDGE
		stakeSize = ((believedProbability*odds - (1-believedProbability))/odds)*KellyFraction*currentBalance[j-1]	#GET YOUR STAKE SIZE OUT
		
	
		actualEdge = rnorm(1, mean = edge, sd = confidenceInterval95[confidenceCounter]/2) #FIND MY ACTUAL EDGE drawn from a norml dist.

		actualWinProbability = (actualEdge + 1)/odds	#DETERMINE MY ACTUAL PROB OF WINNING

		if (stakeSize < minBetSize){		# IF MY STAKE SIZE IS SMALLER THAN MY MIN THEN BET NOTHING
			stakeSize = 0
		}

		winProb = runif(1)

		if (winProb <= actualWinProbability){ 		#THEN WE HAVE ONE AND ADJUST BALANCE ACCORDINGLY
			currentBalance[j] = currentBalance[j-1] + (odds-1)*stakeSize
		}else{					#THEN WE HAVE LOST AND ADJUST BALANCE ACCORDINGLY
			currentBalance[j] = currentBalance[j-1] - stakeSize		
		}
		
		if (currentBalance[j-1] < minBetSize){	# YOUR BALANCE IS TO SMALL SO BUST
			GoneBust[i] = 1
			break
		}
		if (currentBalance[j] > 10000000){	# YOUR BALANCE IS MASSIVE STOP BETTING YOU WIN
			break
		}
	}

	if (currentBalance[j-1] < minBankSizeAtEndOfSim){	#IF BALANCE IS LESS THAN YOU STARTED WITH THEN YOU BUST
		GoneBust[i] = 1
	}
	currentBalance[j:numberOfBets] = currentBalance[j-1]		#FILLING IN SOME BLANKS IF WE LEFT THIS SIMULATION EARLY, IE. WENT BUST OR MADE LOTS 
	FinalBalance[i,] = currentBalance		#RECORD THIS SIMULATIONS PERFORMANCE SO WE CAN PLOT THE AVERAGE LATER
}

goneBustArray[confidenceCounter] = sum(GoneBust)/length(GoneBust)

plot(colSums(FinalBalance))		#PLOTTING THE AVERAGE OF ALL SIMS PERFORMANCE

}

plot(confidenceInterval95, goneBustArray, type = "o", xlab = "Confidence Interval", ylab = "Probability of Bust")


####------------END OF ONE SIMULATION TYPE -------------









########## SIMULATION TO PLOT A 3D SURFACE OF BUST PROB AS KELLY FRACTION AND CONFIDENCE INTERVAL VARY #####
#### THIS MAY TAKE HOURS TO RUN ##############
##------BELOW ARE PARAMETERS WE CAN PLAY WITH THIS CODE TAKES VERY LONG TIME TO RUN------#

minBetSize = 2
minBankSizeAtEndOfSim = 100
startingBalance = 100
edge = 0.1
confidenceInterval95 =  c(0,0.05,0.1,0.15,0.2,0.25,0.3,0.45,0.7)

numberOfSimulations = 1000
numberOfBets = 1000
KellyFraction = seq(from = 0.1, to = 1, by = 0.1)


##--------------SIMULTATION CODE STARTS HERE------
#LOOP THROUGH THE ARRAY OF POSSIBLE CONFIDENCE INTERVALS PROVIDED		

goneBustMatrix = matrix(0, nrow = length(KellyFraction), ncol = length(confidenceInterval95))

for (kellyCounter in 1:length(KellyFraction)){


goneBustArray = NULL;
for (confidenceCounter in 1:length(confidenceInterval95)){

										# WE WILL FIND THE PROB OF BUST FOR EACH CONFIDENCE INTERVAL
GoneBust = rep(0, length = numberOfSimulations)
FinalBalance = matrix(0, nrow = numberOfSimulations, ncol = numberOfBets)

for (i in 1:numberOfSimulations){		#LOOP THROUGH EACH SIMULATION

	currentBalance = startingBalance

	for (j in 2:numberOfBets){		#FOR THIS SIMULATION LOOP THROUGH THE NUMBER OF BETS TO MAKE
				
		believedProbability = runif(1)			#GET A PORBABILTY RANDOMLY FROM A UNIFORM DISTRIBUTION
		odds = (1+edge)/believedProbability				#FIND THE ODDS YOU WOULD USE FOR YOUR "PERCIEVED" EDGE
		stakeSize = ((believedProbability*odds - (1-believedProbability))/odds)*KellyFraction[kellyCounter]*currentBalance[j-1]	#GET YOUR STAKE SIZE OUT
	
		actualEdge = rnorm(1, mean = edge, sd = confidenceInterval95[confidenceCounter]/2) #FIND MY ACTUAL EDGE drawn from a norml dist.

		actualWinProbability = (actualEdge + 1)/odds	#DETERMINE MY ACTUAL PROB OF WINNING

		if (stakeSize < minBetSize){		# IF MY STAKE SIZE IS SMALLER THAN MY MIN THEN BET NOTHING
			stakeSize = 0
		}

		winProb = runif(1)

		if (winProb <= actualWinProbability){ 		#THEN WE HAVE ONE AND ADJUST BALANCE ACCORDINGLY
			currentBalance[j] = currentBalance[j-1] + (odds-1)*stakeSize
		}else{					#THEN WE HAVE LOST AND ADJUST BALANCE ACCORDINGLY
			currentBalance[j] = currentBalance[j-1] - stakeSize		
		}
		
		if (currentBalance[j-1] < minBetSize){	# YOUR BALANCE IS TO SMALL SO BUST
			GoneBust[i] = 1
			break
		}
		if (currentBalance[j] > 10000000){	# YOUR BALANCE IS MASSIVE STOP BETTING YOU WIN
			break
		}
	}

	if (currentBalance[j-1] < minBankSizeAtEndOfSim){	#IF BALANCE IS LESS THAN YOU STARTED WITH THEN YOU BUST
		GoneBust[i] = 1
	}
	currentBalance[j:numberOfBets] = currentBalance[j-1]		#FILLING IN SOME BLANKS IF WE LEFT THIS SIMULATION EARLY, IE. WENT BUST OR MADE LOTS 
	FinalBalance[i,] = currentBalance		#RECORD THIS SIMULATIONS PERFORMANCE SO WE CAN PLOT THE AVERAGE LATER
}

goneBustArray[confidenceCounter] = sum(GoneBust)/length(GoneBust)
plot(colSums(FinalBalance))

}

plot(confidenceInterval95, goneBustArray, type = "o", xlab = "Confidence Interval", ylab = "Probability of Bust")
goneBustMatrix[kellyCounter,] = goneBustArray

}

persp(x = KellyFraction, y = confidenceInterval95, z = goneBustMatrix,theta = -30, phi = 10, expand = 0.5, col = "lightblue",ltheta = 60, shade = 0.75, ticktype = "detailed",
xlab = "Kelly Fraction", ylab = "95% confidence", zlab = "Probability of ruin")