The standard deviation in blackjack is simply calculating the probabilities you will win or lose and extracting your odds from that. That is, the standard deviation can tell you your odds of winning, losing or pushing when playing blackjack. Without getting too far into the numbers, at least one gambling math expert has figured there are over.
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For flat-betting with Basic Strategy, BJ has a Standard Deviation per hand of about 1.15. This means that if you play 'n' hands, your total SD will be 1.15.(n)^0.5. Approximately 95% of the time, your actual result will be within 2SD of your EV. Let's play with some numbers to illustrate. If you play 100 hands, your EV is -0.04.100 = -4 units.

The goal of every card counter is not playing to simply get complimentary services. Instead, he/she plays the game for hard cash and in order to accomplish such a goal, he/she needs a thorough knowledge of risk of ruin. He/she needs to identify his/her tolerance to risk and to devise an appropriate betting plan, with which to meet or overcome that risk.

Risk of ruin and bankroll size

A card counter will usually evaluate risk of ruin as a percentage. In simple words, it shows how often a player can expect to lose his/her entire bankroll in a certain number of hands. A risk of ruin of 10% means that the player has one chance in ten to vanquish his/her entire bankroll, if he/she does not introduce a change in his/her bet size.

When it comes to a total playing bankroll, every card counter needs to think about what could happen in a longer term. The counter needs to set a starting bankroll, exposed to a risk of ruin he/she feels comfortable with. Next, he/she needs to bolster that bankroll with earnings until a point is reached, where his/her risk tolerance and earning objectives are met.

What we should note is that there is a major issue when evaluating risk of ruin and it boils down to that no player will make the same play decisions in the same game all of the time. No one is immune to errors as well as no one will probably play one and the same type of game forever. Risk of ruin for one and the same bankroll is, to a great extent, dependent on the games one chooses to play. In addition, if one uses cover plays and cover bets, then the expected value of the game and the standard deviation figure will be changed, while they both are key elements to risk of ruin evaluation.

Different players will usually have different notions about the acceptable risk of ruin. In case a player uses a bankroll, which can be supplied with funds on a regular basis, he/she may be willing to expose it to a bit higher risk of ruin, compared to, for example, another player whose bankroll cannot be replenished that easily. Professionals, who make a living from blackjack, will usually prefer the smallest risk of ruin possible (such as 1% or even less).

If a non-professional player uses 5% risk of ruin as an acceptable risk level, in order to size his/her total bankroll and betting units, he/she needs to use the amount of his/her largest bet in the calculation. In case his/her largest bet is $100 and he/she uses a bet spread of 1-4 in the game, then his/her base betting unit may be $25. In another game, where the recommended bet spread is 1-10, the player will need to re-adjust his/her base betting unit to about 1/10 of his/her highest bet ($100), which will result in $10. By using this method, the player's risk of ruin will not be changed considerably.

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Standard deviation and how it affects one’s bankroll

For card counters who use a bet spread, the standard deviation figure will come in a number of variations. If the player increases the size of his/her bet spread, the standard deviation per hand will increase as well. In case the card counter uses a huge bet spread (1-12 units, for example) in a game, the standard deviation could exceed a value of 3. At the same time, when he/she employs back-counting (or Wonging, which is a play style we shall discuss later), the standard deviation could rise even above a value of 5. Such variations of the standard deviation could cause a counter to be either well above or well below the expected level of performance during any set period of time he/she spends playing. It should not be a surprise, according to experts, if a counter finds himself/herself below his/her best performance ever recorded, most of the time. At a later moment, he/she may reach a new all-time high and after that he/she may again find himself/herself below it. In case he/she uses a proper selection of games and employs sound play strategies, he/she will be able to bolster his/her bankroll, but the growth rate will probably be uneven. In other words, the counter may discover that he steps three times forward and two times backward all of the time.

Money Management for Card Counters
Risk of Ruin and Standard Deviation
Building up and Securing the Bankroll
Approaches Utilized by a Card Counter
Making a Proper Selection of a Game
Appropriate Games

Players who employ bet spreads will probably have a hard time evaluating the standard deviation per hand without the use of a computer program. The standard deviation per hand is influenced by an array of factors such as the rules of the game, the level of penetration, the number of decks, the bet spread and the betting ramp. The approximate standard deviation (SD) figures for the play-all style approach with ordinary bet spreads are as follows: 1. For a single-deck game with a bet spread of 1-4, the SD is 2.35; 2. For a double-deck game with a bet spread of 1-8 units, the SD is 3.00; 3. For a four-deck game with a bet spread of 1-8 units, the SD is 3.50; 4. For a six-deck game with a bet spread of 1-12 units, the SD is 3.75; 5. For an eight-deck game with a bet spread of 1-12 units, the SD is 3.50.

Card counting is meant to achieve two objectives – to help the player assess when to raise his/her bet based on the count and to help him/her assess when to use certain variations to the basic strategy, again taking into consideration the count. To employ variations to the basic strategy at the proper moment of time will usually benefit the player.

Blackjack Basic Strategy Standard Deviation