Blackjack Math – The Mathematics Behind Advantage Play

This article will explain four of the most common blackjack mathematics terms used by card counters and advantage players, angstrom well as how they affect advantage play and card count. ( New to card counting ? Start with our comprehensive examination “ How to Count Cards ” page ! )

Variance

Variance a condition we all hear a bunch but may not in full understand what it is. In a gambler ’ mho world, if they hear this they will just say “ hey that ’ s merely a visualize word for luck ”. By definition it is simply the dispute in the expected advantage and the actual results produced. For exemplar, let ’ s say you are playing a becoming reckon plot and your hourly EV is $ 25 an hour. You play for a total of 100 hours and your expectation for those 100 hours is $ 2,500. You take a look at your logs and realized you are entirely $ 2000 ahead. This shows you are $ 500 below expectation which is the VARIANCE of what you would expect to win, on the flip side you could always be $ 500 ahead of your EV. *You were using a bet spread worth $ 25/hr, but after 4 hours, you were up or down $ 1500. You just experienced Variance, my ally. The good news program ( if you ’ re a winning player ) is that the more hours you play, the nearer you get to variance balancing out, and all you are left with is the “ long run ”. Advantage Play Math - variance

Standard Deviation (SD)

By Definition a standard deviation refers to how far or how much an consequence will deviate from the average. standard deviation and variance go hired hand in hand ( SD is actually the hearty settle of discrepancy ). At this point you are credibly asking yourself “ how do these things affect me as a player ? ” There is not one answer for this, but a multiple set of answers. Figuring what variance you have in a game and what the SD is for any particular crippled at any stakes can help you assess if you are playing a victorious game or how much bankroll you need to bring to a session. *Standard Deviation helps prepare you for what to expect, in terms of variation. If you are systematically experiencing results beyond 2 SD, you ’ re either one lucky/unlucky SOB, or something doesn ’ thyroxine add up !

N-Zero (N0)

Math behind advantage play and blackjack

N0 is something not looked at very often especially among new players. N Zero is the number of hands theoretically required before hitting a goal of being ahead by one standard deviation (4*N0 gives you the hours to overcome 2 SD). To get the most accurate evaluation of N0 one must play by the same set of rules and the same betting/playing strategies. Going back to our original example of $25 EV per hour, we would find our N0 by the following equation N0= Variance/EV^2. N0 is something not looked at very much particularly among newfangled players. N Zero is the act of hands theoretically required before hitting a goal of being ahead by one standard deviation ( 4*N0 gives you the hours to overcome 2 SD ). To get the most accurate evaluation of N0 one must play by the same fix of rules and the lapp betting/playing strategies. Going back to our original exercise of $ 25 EV per hour, we would find our N0 by the follow equation N0= Variance/EV^2. *Want to overcome division ( i.e. fortune ) and get to the “ long race ” agile ? Play games and use bet spreads that have a lower N0 .

Certainty Equivalence (CE)

This is besides known as risk-adjusted return. This is the product of taking the expected succeed rate and adjusting it based on the level of risk in proportion to the current bankroll and level of risk permissiveness. This will show you if the game is “ worth playing ” compared to your bank size. So you may have a $ 100 in EV but you CE may only indicate that the game is merely deserving $ 50 since your bankroll is then small. You can flush go then far as CE going into negative territory which indicates you are hard over betting your bankroll. The basic equation of figuring CE. EV- ( ( bet size*Standard Deviation ) ^2 ) / ( 2*Kelly factor*BR ) *Any easy way to think about the concept behind CE : “ I could pay you $ 100 cash, or you could take a 50/50 gamble at $ 200. Is it worth it ? What about a 50/50 chance at $ 101 ? 1/10 probability at $ 20,000 ? At some points, you will take the risk. At other times, the risk involved international relations and security network ’ thymine justified.

fortunately all areas of black flag mathematics are pretty much done for you in a program called CVCX by QFIT. All you have to do is plug in your stake size, bankroll and game conditions and it will spit out your EV, VAR, SD, N0, CE and even the optimum stake spread. .

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