Blackjack Probability Fluctuation

When playing blackjack, your bankroll will fluctuate throughout the course of a session. Another word for this is risk and is expressed by a statistical term called standard deviation (SD). Standard deviation is variation from the “average” (mean, or expected value).

In blackjack the standard deviation is about 1.1418 when you do not vary your bet size (flat betting).

The following charts lists the expected range of results for a given number of hands played:

Blackjack Bankroll Fluctuation

You can interpret the standard deviation ranges as follows:

  • 1SD will occur 68.3% of the time. As a result 68.3% of the time your results will be between the low and high-end of the range given.
  • 2SD will occur 95.4% of the time.
  • 3SD will occur 99.7% of the time. So in 1 of every 333 playing sessions your results will be outside this range.

To interpret the above chart, if you are playing a blackjack game for $25/hand and play 1000 hands, your result will be between -77 units and 67 units 95.4% of the time.  So your bankroll could be down as much as $1,925 over those 1000 hands.  These ranges assume you are using basic strategy.

For the mathematically inclined here are the formulas:

  • EV (units) = EV (%) * Number of Hands
  • SD (units) = ( Square Root of the Number of Hands ) * 1.1418
  • 2SD Range Low = EV – ( 2 * SD (units) )

I hope that this post gives you some idea of the amount your bankroll will fluctuate over the course of a trip.  It is important to have enough money in your bankroll to get through these inevitable fluctuations.

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