Risk of Ruin for Basic Strategy Players

Blackjack Betting and Risk of Ruin for the Basic Strategy Player

By Brother William
(From Blackjack Forum Vol XV #3, September 1995)
© 1995 Blackjack Forum

[Editor’s note: Brother William’s article about fluctuations in your blackjack bankroll when flat betting and playing basic strategy have a new relevance for players who are taking advantage of online casino bonuses or loss rebate plays. If you are a basic strategy player for any reason, study the article and chart below to get a handle on the normal fluctuations you can expect in your blackjack bankroll. –Arnold Snyder]

In the June 1995 issue of Blackjack Forum, I suggested that it would be helpful to basic strategy blackjack players to print detailed risk charts indicating standard deviation (fluctuation) for flat betting when playing basic strategy. I think there is a danger for players who are milking comps and promotions in not understanding these risks.

In an attempt to remedy this problem, I have created an all-purpose risk chart for the basic strategy player. I hope basic strategy blackjack players will study this chart carefully.

How to Use the Blackjack Basic Strategy Betting Risk Chart

Assumptions:

1. House advantage over the basic strategy player is 0.54% (which would correspond precisely to a 6-deck shoe game with Strip rules, but works pretty well for most games available anywhere, as the house edge is usually set around ½% over the basic strategy player).

2. 60 hands per hour of play. (This is pretty close to what you’ll average with a full table.)

3. Flat betting 1 unit per hand.

Regardless of what your unit size is, you may use this chart simply by multiplying. If you were playing $1 per hand, then all of the chart entries in units can simply be read right from the chart in dollars and cents. Example: betting $1 per hand for 16 hours of play, as per the assumed game conditions, you would have an expected loss of $5.18. You will be within one standard deviation (SD) of this expectation 68% of the time, which translates to an actual result between a loss of $39.27 and a win of $28.90. You will be within three standard deviations 99.7% of the time, which translates to an actual result between a loss of $117.80 and a win of $86.69.

Using a $100 betting unit, if you intend to play a total of 16 hours of basic strategy in this game and you’re willing to accept a risk level of three SD’s, simply move the decimal point two places to the right. You would expect to lose $518.00, but your actual result 99.7% of the time would fall between a loss of $11,780.00 and a win of $8,669.00.

So, if you can stand the thought of losing somewhere around $12,000 every rare once in a while in 16 hours of play, you can afford to flat bet this game with black chips.

The charts are very easy to use with flat bets of $1, $10, $100 and $1000, because you simply have to move the decimal point. For flat bets of $5 or $25 or whatever, just use a pocket calculator.

Note that the entry in the “expected loss” column can be used to estimate what you are actually “paying” for any comps your action buys.

Again, I hope any basic strategy blackjack players out there will study this chart carefully. The bankroll you save my be your own. Good luck! ♠