HOW WE CALCULATED THE “RULE OF 33”
Method #1 to calculate the Rule-of-33
We took the well-known 3% rule — no bet should be larger than 3% of the bankroll — and reversed it to calculate the bankroll from the average bet — the required bankroll is always about 33 times the average bet (100 / 3).
Method #2 To calculate the “rule-of-33
We calculated the bankroll using the standard blackjack formula (see below) for maximum loss with a probability, assuming values consistent with an average player and a typical evening of blackjack, and got close to the same result.
Here’s a more detailed look at Method #2 using the formula for calculating the maximum loss in blackjack given a certain probability of error.
The Standard Formula for Maximum Loss
Maximum loss (with 95% confidence) =
[(Standard deviation x 2 {for 95%}) x
(Square root of the number of hands played) x
(Average bet)] -
[((Average bet) x (Number of hands played) x (House edge)) +
((Average bet) x (Number of hands played) x (Basic strategy handicap))]
The Same Formula with Typical Values
Maximum loss (with 95% confidence) =
[(1,17 x 2 {for 95%}) x
(12.8) x
(Average bet)] -
[((Average bet) x (165) x (0.005)) +
((Average bet) x (165) x (0.015))]
Which produces the result
Maximum Loss (95%…Prob.) = Average Bet x 33
Maximum Profit Target (with 98% probability) = Average Bet x 33
Which give us the “Rule of 33” with the following assumptions…
55 hands per hour (the rate of play);
3 hours (the length of play);
95% or 98% (the probability of the result being right);
0.5% (the house edge); and
1.5% = the player’s basic strategy handicap.