Money management for basic strategy is also not applicable for card counting, thus what we are about to discuss is only suited for players who employ basic strategy.
Money management in blackjack does not involve setting goals for profit or determining loss limits, neither does it circle around raising or reducing your bets (progression or regression betting). What money management in basic strategy does is to help you achieve the greatest return per dollar gambled.
Proper money management calls for a plan of action that involves the player’s bankroll, his risk of ruin (losing all of his money), and what results he strives to achieve. Good money management tells the player how much money he needs to have at disposal in order to avoid ruin at a sustainable level of risk over a number of hands.
In blackjack, progression betting simply does not work because it cannot take the house’s advantage away. Thus, progression systems, such as the Martingale progression (doubling down after each lost hand until you win a hand which offsets all the previous losses) are deemed useless. In blackjack, what matters is what cards have already been dealt and what cards are still in the deck, which directly affects the players’ win probability.
Progression betting is lucrative for games where the player has a positive win expectation but in blackjack, the player is always in disadvantage to the house. Thus, in the long term, he will always lose the amount of money he bets times the percentage of negative expectation. Progression betting will not turn that around.
However, keep in mind that blackjack is a game of probability (chance), which means that very often, even predominantly, you will fail to play to expectations, rather find your game somewhere in the range of the standard variation. You may earn better return than expected, or you can fall short of it, and the more you play, thus the larger the data sample becomes, the closer you will get to the expected results.
Calculations
Each casino game has a Standard Deviation number, for blackjack it is 1.14 per hand. To find the standard deviation for a particular game session, or a trip to a casino, you will need to do some very simple calculations:
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– Multiply the square root of total hands played by the SD number to find their standard deviation
– Multiply that SD by the average bet and receive one standard deviation for this game session
– Calculate the negative expectation for the game (average bet X hands played X house advantage)
– You then need to add the negative expectation to the SD to calculate the total loss and subtract from the SD for the total win (because expectation is negative, the total win will always be lower than the total loss).
– You will be within one SD in in 68.3% of the time, between two SDs in 95.4% of the time and between 3 SDs in 99.7% of cases.
– Calculating the total win/loss for two SDs is done by adding one standard deviation to the first total win/loss and a second one for three SDs.
Doing the math
Let us provide an example and go step by step.
Say you will play for 10 hours, 70 hands per hour, with an average bet of $100 and the house advantage is 0.3%.
The total hands played are 10 hours times 70 hands per hour, or 700 hands. The square root of 700 is 26.46. Multiply that by the SD for blackjack and we get 26.46 X 1.14 = 30.16.
This means that the standard deviation for the number of hands played is 30.16. Multiply that by the average bet of $100 and we reach to the conclusion that the Standard Deviation for our playing session is $3016.
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Now we need to dollar value of the negative expectation, so that we can calculate the maximum win/loss. The formula is: average bet ($100) X hands played (700) X house advantage (0.3%, or 0.003) = $210. This means that you expect, on average, to lose $210 for these 700 hands. As a basic strategy player aiming for comps, you should make sure the freebies you receive are at least near that sum.
Next, we add the negative expectation to the Standard Deviation for the session to receive the total loss, or $3016 + $210 = $3226, while the total win is $3016 – $210 = $2806. We said that your results will vary within the first SD in 68.3% of times. Thus, your play results will vary somewhere between +$2806 and – $3226 in 68.3% of cases.
Also, your results will fall within two SDs in 95.4% of the time. To calculate the win/loss totals, add one SD to the initial win/loss. Thus, in 95.4% of cases your session’s results will vary between a win of ($2806 + $3016) $5822 and a loss of ($3226 + $3016) $6242.
In 99.7% of time your results will range between three SDs, and following the same logic we will add two SDs to the initial total win and loss for the final values. Your performance will vary between a win of $8838 and a loss of $9258 in 99.7% of cases.
Thus, in order to avoid risk of ruin under those circumstances, you will need to carry at least $9258 with you. There is, of course, a 0.3% chance that you will get outside those boundaries, but it is highly unlikely.
However, players can determine a higher acceptable risk of ruin, depending on their risk appetite. There is computer software that can calculate what amount of money you will need in order to play a certain amount of time with a certain average bet and with an X% chance of ruin. And the best way to skew the numbers in your favor is to play slower games, with less hands per hour, which we’ve discussed in the article Slowing Down Blackjack Game.
