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. Jun 21, 2019 A hand of Blackjack has a Standard Deviation. It depends on the rules of the game but is usually around 1.1. But Blackjack can't be a Standard Deviation. Boolean logic refers specifically to how the words AND and OR are treated. The El Cortez is a casino AND it is located in Nevada. Therefore, if you lose $45 when playing 200 hands using basic strategy, it just wasn’t your day, because an outcome like that only happens 5% of the time. Tags: blackjack, blackjack odds, blackjack outcomes, blackjack probability, blackjack standard deviation, blackjack variance, online blackjack, standard deviation.
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.
Let us illustrate with an example. Imagine that you participate in a six-deck game with S17 and you hold 7-4, while the upcard of the dealer is an Ace. In case you conform to the basic strategy rules, you need to abstain from action in these conditions. At the same time, at your table there could be someone who decides to double down on that hand and has a success. Logically, you would blame yourself for not being decisive and courageous enough to double down on the same hand – you would have doubled your balance. However, professional blackjack players claim that your long-term win from hitting 7-4 represents 0.147 times the original bet you placed, while the long-term win from doubling down on the same hand represents 0.127 times that bet. Or, in case your original bet is $100, your average gain for that hand will be $14.7, while if you double down, you will gain $12.7 on average (13.61% less than what you would have scored as profit, in case you followed basic strategy guidelines).
If you happen to hold such a hand, you may double down, when your true count is +1 or higher! If you play this hand in such a manner, your expectation will move up to 0.148 from 0.147. Although the change may seem insignificant, you may play the hand in such a way by placing a larger bet. This is just one among the 18 basic strategy variations, which experts recommend. In case you play a six-deck game, all 18 variations could ensure you over 33% to the profit, which basic strategy alone grants you. These variations, which could add even more in a single-deck or a double-deck game, are famous for being the Illustrious 18. We shall dig deeper into them right after we discuss four variations to the basic strategy for games having the option to surrender. These four variations are known as the Fab Four.
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The Fab Four
While the Illustrious 18 are variations to the basic strategy for any blackjack game, the Fab Four are variations to help a player increase his/her profit in a game where the surrender option is offered. Don Schlesinger came up with the ”Fab Four” term, which refers to the top-four late-surrender plays based on the Hi-Lo system. You may play in such a manner, in case your true count is 0 or higher. Let us have a look at the Fab Four variations to the basic strategy, which are used in multi-deck games:
Running Count Keeping Hints
Learning to Keep a True Count
True Count Drills
Fab Four Basic Strategy Variation
The Illustrious 18
1. You need to surrender, if your hand is 15, the dealer's upcard is 9 and your true count is +3.
2. You need to surrender, if your hand is 15, the dealer's upcard is 10 and your true count is 0.
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3. You need to surrender, if your hand is 15, the dealer's upcard is an Ace and your true count is +2 (in S17) or -1 (in H17).
4. You need to surrender, if your hand is 14, the dealer's upcard is 10 and your true count is +4.
'According to gordonm888, your Expected Value per hand is -4%, or -0.04. This means that if you play 'n' hands, your total EV will be -0.04*(n).
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. Your SD is 1.15*100^0.5 = 1.15*10 = 11.5, so 2SD's is 23. This means that, with 95% certainty, your actual result will be between (-4-23) and (-4+23), so in the range of -27 to +19 units. If you are flat-betting $10 per hand, that's -$270 to +$190. Thus, you have a reasonable chance to be ahead after 100 hands.
If you play 10,000 hands, your EV is -0.04*10,000 = -400 units. Your SD is 1.15*10,000^0.5 = 1.15*100 = 115, so 2SD's is 230. This means that, with 95% certainty, your actual result will be between (-400-230) and (-400+230), so in the range of -630 to -170 units. If you are flat-betting $10 per hand, that's -$6,300 to -$1,700. Thus, you will almost certainly be losing after 10,000 hands.'
Blackjack Standard Strategy
RomesBasic Strategy Deviation Chart
EV(x hands) = (AvgBet*NumHands)*(HouseEdge)
SD(x hands) = Sqrt(x) * OriginalSD
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Example: $10 flat bet at .5% average blackjack game for 750 hands:
OriginalSD = 1.15*10 = 11.5
EV(750 hands) = (10*750)*(-.005) = -$37.50
SD(750 hands) = Sqrt(750) * 11.5 = ~$315 .. 2SD (95% confidence) = $630 ..3SD (99% confidence) = $945
So pending your level of comfort, if you want to do 2SD, with 95% confidence you will be down $37.50 +/- $630.. but again on 'average' in the long run you will be down $37.50, so that's what you can base your real value on if you're going to do this over and over and over.. that's the number that matters, if the comps are that worth it anyways.