Risk of Ruin in Blackjack

So you’re wondering about the odds to beat the house at Begado? Well, Blackjack is a game of many variables, complicated by a lack of standardization for House Rules not only from one casino to the next, but also from table to table. One question every player should be asking from time to time is “What is the likelihood that I will lose my entire bankroll if I play a particular game in a particular way for a certain number of hands?” The answer to this is found in complex mathematics indicating the “risk of ruin.”

Ascertaining Real Risk

“Risk of ruin” (ROR) is not nearly as ominously apocalyptic as it might sound. It is actually just the statistical probability of losing a given amount of money over a specific number of hands at the Blackjack table. Key variables are the player’s “win rate” in dollars per hour, the “standard deviation” in dollars per hour, the amount of the total “bankroll” in dollars and the “number of hands” to be played.

Suppose, for example, Curly, Larry and Moe sit down at a $5 table and begin flat betting the minimum, each with the expectation of winning $10 an hour on average. Their respective bankrolls are $20, $50 and $200. Past experience has shown that their hourly wins and losses fluctuate on the order of $25 an hour more or less than the $10 average.

As one might expect, Curly is playing “over his head” and has a much greater risk of ruin than his friends; his bankroll could be wiped out in just four bets. Larry’s cash will last him for at least ten wagers. Moe has the least risk of ruin of the three; he could lose 40 bets of $5 in a row without going bankrupt. In other words, the bigger the bankroll, the lower the risk of ruin.

Just exactly how great is the exposure of each player? The math is so complicated that computer modeling is used to come up with ROR figures. Calculations indicate that Curly can expect to go broke 52.7% of the times he plays. Larry will lose his bankroll 20.2% of the time and Moe has a risk of ruin of just 0.17%.

Using ROR Tables

A good substitute for ROR calculations is to refer to published ROR statistics. These are may appear as tables or graphs, and they are devised according to the specific rules of the version of the game being played. If you know the number of betting units (bankroll divided by average bet size) and the number of hands to be played, your risk of ruin can be easily determined by looking it up in the tables.

Conversely, if you know the number of hands to be played and the risk of ruin you are willing to accept, ROR stats can be used to determine the optimum number of betting units required and, hence, the size of the bankroll needed to wager at various levels of betting. For example, a player willing to accept a 1% ROR over the course of 500 hands will find the number 68 in middle of the table. That means 68 betting units or a bankroll of $680 at a $10 table or $1,700 at a $25 table. In other words, the bigger the bets are, the bigger the bankroll must be to keep the risk of ruin low.

Another use of ROR tables is to find out how long to play with a given bankroll and acceptable risk of ruin. Remember Moe, who has $100 and is making $5 bets? He has 40 betting units and his 0.17% ROR should apply as long has he doesn’t play many more than 100 hands. If he is okay with a 5% ROR, the tables indicate he can expect to play 300 hands. But if he loses track of time and remains at the table for 2,000 hands, his risk of ruin will shoot up to 50% and he’ll most likely be turning his pockets inside out like his friend Curly. In other words, the longer you play, the greater the risk of ruin.