DOUBLE $1,000 INTO $2,000 Part 2

If Beginning new session Then
   bankroll = 1000 :
   autotake full odds = false
EndIf

If passline loses Then
   Bet last passline * 2 on passline
ElseIf comeout roll Then
   Bet $10 on passline
EndIf

If bankroll < 10 Or bankroll >= 2000 Then
   start new session
EndIf

##### suggest bankroll_target no lower than 20
# Gambler's Ruin - mean time in transient states 
# and probabilities to target goal and ruin
title <- 'pass 345x odds. over-shoot target possible'
bankroll_target <- 200 # Enter bankroll target (in units)
bankroll_start <- (bankroll_target/2)   
# Enter a different starting bankroll, default is 50% of target

##### do not change any below here
bankGainUnit <- (bankroll_target - bankroll_start)
startBr <- (bankroll_start)    # for avg # of trials sum (from Q returns Index #)
states <- (bankroll_target + 7)   # (target = 1st term))
#example target==20;(20+7)(over-shoot target states=7)

pass <- 244/495    # prob of win 1 unit flat bet (not enough for odds bet)
miss <- 251/495    # prob of loss 1 unit flat bet (not enough for odds bet)
SevenOut <- 196/495
Point <- 134/495 
ptFourLoss <- 1/9
ptFiveLoss <- 2/15
ptSixLoss <- 5/33
nat <- 2/9
craps <- 1/9

target <- bankroll_target # absorbing state target goal EXACT
state2state <- (target - 1) #last state index
absorb_states <- target # begin absorb states
row.col_Names <- c(1:(states - 1),0)

# enter transition probability matrix
P <- matrix(rep(0,states^2), nrow=states, ncol=states, 
dimnames = list(row.col_Names, row.col_Names))
# absorbing goal/ruin states = 1
	for (i in target:states) {P[i, i] <- 1 	} 
# to ruin from 1:6 bank trying to double-up
	for (i in 1:5) {P[i, states] <- miss } 
	P[6,states] <- ptSixLoss 
# to pass - 1 to 5 bank double-up success
	for (i in 1:5) {P[i, i * 2] <- pass } 
# Point diag starts at P[6,13]
	for (i in 6:state2state) {P[i,i + 7] <- Point }
# nat diag starts at P[6,7] 
	for (i in 6:state2state) {P[i,i + 1] <- nat } 
# craps diag starts at P[6,5] 
	for (i in 6:state2state) {P[i,i - 1] <- craps } 
# ptFourLoss diag starts at P[6,2] 
	for (i in 6:state2state) {P[i,i - 4] <- ptFourLoss } 	
# ptFiveLoss diag starts at P[6,1] 
	for (i in 6:state2state) {P[i,i - 5] <- ptFiveLoss  } 
# ptSixLoss diag starts at P[7,1] 
	for (i in 7:state2state) {P[i,i - 6] <- ptSixLoss } 					 
	
#P # uncomment to show matrix
#print(formatC(P),quote=FALSE)
P_sums <- as.matrix(rowSums(P))
colnames(P_sums) <- list("total")
#print(P_sums)

# take sub-matrix for transient states to states
P.s <- P[1:state2state, 1:state2state]
#P.s
# take sub-matrix for transient states to absorbing states
P.t <- P[1:state2state, absorb_states:states]
#P.t
# compute mean number of revisits matrix S
Q <- solve(diag(state2state)-P.s)
#Q

# sum entries in Xth row of Q
sum(Q[startBr,])
#bankroll_start
#startBr #Index number

Q_sums <- as.matrix(rowSums(Q))
colnames(Q_sums) <- list("avg trials")
#print(Q_sums)

QT <- Q %*% P.t
#QT

goalG <- QT[1:state2state, 1:7]
#goalG
success_target <- as.matrix(rowSums(goalG))
colnames(success_target) <- list("p(target)")
#print(success_target)

ruinR <- QT[1:state2state, 8]
#ruinR
ruinR <- as.matrix(ruinR)
colnames(ruinR) <- list("p(ruin) ")
#print(ruinR)

S2Srow_names <- as.matrix(seq(1, (bankroll_target - 1), by=1 ))
colnames(S2Srow_names) <- list("bank")
#print(S2Srow_names)

final <- cbind(S2Srow_names, success_target, ruinR, Q_sums)
rownames(final) <- c()
#print(final)
data <- as.matrix(final[startBr,  ])
colnames(data) <- list("data  ")
print(title)
print(formatC(data,digits=10),quote=FALSE)
bankroll_target
bankGainUnit