1r. Gambler's Ruin in R. Basic probabilities and average number of games to play for success or ruin.

This section uses a Markov chain method, creating a transition matrix and completing the math.

gambler.ruin2 <- function(p, bankroll_target, title, Printprint)

call with : gambler.ruin2(244/495, 20, "craps pass line. No odds", 0)

gambler.ruin2(prob of success, betting units, "title", print data table)

*****

The bankroll target is in units. For example, if you have $1,000 and flat betting $25 that gives you 1000/25= 40 betting units. That is exactly the same as $200 bankroll and betting $5 each bet or with a stake of $40 and betting $1 at each bet.

Printprint = 1 (0 does not print = default) is for printing a table of data up to the target from the lower Stakes.

Default data is to double the starting stake (bankroll)

One does not specifically enter a starting unit bankroll (stake) but can on line 5. example would be at Line 5; bankroll_start <- (bankroll_target/2) could be: bankroll_start <- 4#(bankroll_target/2) . Print = 1 is for all starting stakes in a data table.

2r. Gambler's Ruin formulas below in the R code produce

goal and ruin probabilities as well as

average games to either or to goal given goal is achieved and ruin, given ruin is attained.

Call example: gambler.ruin(10, 20, 18/37, "0 Roulette evens bet")

gambler.ruin(win goal (in units), stake - what one can lose(in units), probability of one trial success, "title")

Some Goal / Risk of Ruin tables in Google

These are built using Markov chains in R program and moved into Excel then into Google.

STILL Under Construction

Fair Coin toss (50/50) Goal / Risk of ruin

for 8 trials. more coming

link

Fair Coin toss T20 8 trials

link for above sheet

craps pass line with 345x odds

50 unit target and 50 wagers (N = 50, N = number of bets)

Pass 345x Odds 50T 50N

link for above sheet

craps pass line with 0x odds (No odds, just flat betting)

240 unit target and 30, 60 and 120 wagers (N = number of bets)

pass line 0x odds goal / ruin