Free Forum - Blackjack Math Formulas

weezrDASvegas

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Mar 27, 2018, 12:55:06 PM

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I cant fathom anyone here doubts the mathematical foundation of blackjack. So if its math its all about formulas.

Starting at the very beginning, there is a formula that calculates the odds of getting a natural (21 from A and T in the first two cards). Everybody agrees that the probability of a blackjack natural is 4.83% ( beginning of 1Deck). Odds change if adding players to the dealer. If I play headsup in 1D, some 5 rounds per shuffle, the odds of a natural go up to 22%. So from 1 in 21 (very first 2 cards) to better than 1 in 5 in 5 rounds.

Odds like those were verified and confirmed even in WoV forums. The most comprehensive calculations were published first here:
Blackjack Probability, Odds Formulas

My question is - are there similar math formulae for card counting? Logically there must be such formulas. In the natural 21 probability, the formulas are based on number of Aces and Tens in rapport to 2-card combinations of cards remaining in the deck. Cardcounting is also calculated on number of Aces and Tens in rapport to cards remaining in the deck.

I go with the systematic count system where only 8s are discarded. Thus this system covers most cards in the deck. I got 9, T, A in the plus/high zone of the equation. There must be at least one formula to calculate the odds of winning in plus/positive counts. No?

Think about it how valuable it would be. We know the odds of winning in the very next round (when the count is +). We then can easily calculate the probabilities in the next rounds. If we didnt win the previous + rounds we increase the best even higher in future + counts. Looks very logical to me.

For sure this will be for sure the first attempt to solve the mathematical mystery of bj card counting. I ghope good replies will ensue. Exception: Angry birds please dont reply. You know who (the one) ur. You better pour a strong one and watch march madness (and bet if you can)..

Gustav Shoes

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Mar 27, 2018, 11:25:20 PM

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Whether you win or lose a hand doesn't change the odds on the next hand. The odds on the next hand is based on the count just before that hand is dealt.

weezrDASvegas

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Mar 28, 2018, 4:51:47 PM

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Gustav Shoes:

You only consider one element in this complex fact of life: probability. No doubter if you take coin tossing, the probability of heads is always the same. New maths however considers three inseparable elements: probability, degree of certainty, number of trials.
We all heard the saying ‘The more tries the higher the chance [ie degree of certainty] that it’ll happen.’

We can handle a simple experiment. Get one deck of cards and a piece of paper. In the left column you mark a natural bj in your first 2 cards—just one try. In the right column you mark natural 21s after dealing the entire deck.

You deal the cards to a virtual dealer and a virtual player (you). We can assume a good average of 3 cards per hand. Thus an average of 8 rounds per deck. Draw also a horizontal line to separate the decks you dealing. Youll notice an average of 1 BJ every 3 decks, but none in your first 2 cards.

Here is more detailed maths. The opposite of getting [at least] one blackjack is, well, NOT getting a bj. By most accounts the probability of getting a blackjack in the first 2 cards (from a fresh deck) is 0.0483 or 4.83%. The complementary probability is 1 - 0.0483=0.9517.

Calculate first NOT getting a bj in the 8 rounds: 0.9517 ^ 8 = 0.673. Getting the BJ is the opposite: 1 - 0.673= 0.327 (very close to 1 in 3 or 33%). Enit clearer now that the more rounds you play to better chance you got at a blackjack?

I think the same is true about the + counts. You lost the first + count, bet a lil’ higher next + and so on. The more + counts you encounter the higher your chance to hit a big one. Otherwise you hear many BJ player complainin about variance. Always bad variance. That might be so because not every + count leads automatically to a win. Chances are you gonna lose more often than not.

Gronbog

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Mar 28, 2018, 5:11:35 PM

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You deal the cards to a virtual dealer and a virtual player (you). We can assume a good average of 3 cards per hand. Thus an average of 8 rounds per deck. Draw also a horizontal line to separate the decks you dealing. Youll notice an average of 1 BJ every 3 decks, but none in your first 2 cards.

Nonsense. You will get a blackjack in your first 2 cards about once every 21 new decks or shoes; the same rate at which you get them on a per-hand basis when playing continuously. If you were to only ever play the first hand of new decks or shoes, you will still get a blackjack about once every 21 hands played.

weezrDASvegas

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Mar 28, 2018, 5:43:24 PM

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You deal the cards to a virtual dealer and a virtual player (you). We can assume a good average of 3 cards per hand. Thus an average of 8 rounds per deck. Draw also a horizontal line to separate the decks you dealing. Youll notice an average of 1 BJ every 3 decks, but none in your first 2 cards.

Nonsense. You will get a blackjack in your first 2 cards about once every 21 new decks or shoes; the same rate at which you get them on a per-hand basis when playing continuously. If you were to only ever play the first hand of new decks or shoes, you will still get a blackjack about once every 21 hands played.

by: Gronbog

Exactly mate! You got it right… but you still wrong. The chance for a bj in one hand/round is pretty low… but it increases with the number of hands/rounds played (number of trials). If you played only one hand of blackjack, chances are you don’t know what a natural is. Of course you played many hands/rounds and you experienced several BJs by now… may you receive even more naturals!

Something simpler as to beat the nonsense (the ball is in your court mate): Coin tossing. You sez doesn’t matter how many times you toss the coin the probability heads is the same. Agree. But how about the chance [ie degree of certainty]? Toss it once? 1/2. Doit it twice. 1/2. Do it 7 times? 1/2. Do it 8 times? 1/2.

Look at it now the other way: the probability of NOT getting heads. 1/2 in the first try. 1/2 ^ 2 in the 2nd trial = 25%; winning is now 75%.1/2 ^ 7 in the 7th trial = 0.78%; winning is now 99.2%. 1/2 ^ 8 in the 8th trial = 0.4%; winning is now 99.6%. How clearer could it be? The chance [ie degree of certainty] grows with the number of trials. See how drastically the chance grows from 2 to 7 trials?

And they say ‘The more you try the better your chance.’ I don’t imply that the more you gamble the better your chance at winning. Ain’t so and as acard counter you know what bad variance does to you.

Gronbog

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Mar 28, 2018, 10:42:08 PM

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Sure, but that's not what you were saying. You said that the number of naturals received at the beginning of the deck would be zero. This is clearly nonsense.

barry

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Mar 29, 2018, 9:59:28 AM

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Perhaps many are theorizing too much and playing too little.
just go for it.

Gronbog

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Mar 29, 2018, 11:14:45 AM

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I just can't let blatant misinformation slide.

weezrDASvegas

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Mar 29, 2018, 11:49:31 AM

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@Gronbog
“I just can't let blatant misinformation slide.”

Exactly what I’m doing now. I never express something as idiotic as “number of naturals received at the beginning of the deck would be zero.” The probability can never be zero. The beginning of the deck means the first trial; that is, 1 trial. The probability of a natural in 1 trial is 4.83%. The degree of certainty to get a bj increases with the number of trials. Equivalently the degree of certainty to not get a bj decreases with an increase in the number of trials. That’s why it is not possible to lose forever OR win forever (as casinos would love to have gamblers believe). That’s not rocket science; it is basic maths.

The real truth behind all that kinduv “Norma Bates” maths: Gronbog is here for fighting. More precisely, Gronbog is here to fight me. He jumped at me beginning with my first poste here. Grona, Dona, Fran are Norma Bates’ envoys here.

To the Admin
Please look carefully at the posts by the three members I specified above, plus Norma. Their intent is to crush gambling forums. Norma did it before here, on WoV’s forums, the GamblingForums, ZenForums, etc.
They start here hostile posts against yours truly with the intent to crush my posts. That is, “incite” the admins to remove my posts and also remove the threads I participate in.

Gronbog

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Mar 29, 2018, 11:22:44 PM

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Youll notice an average of 1 BJ every 3 decks, but none in your first 2 cards.

Excuse me for paraphrasing. Your original statement is quoted above.

weezrDASvegas

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Mar 29, 2018, 11:42:33 PM

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Youll notice an average of 1 BJ every 3 decks, but none in your first 2 cards.

Excuse me for paraphrasing. Your original statement is quoted above.

by: Gronbog

@Gronbog

Excuse me for emphasizing average. I did a run of 10 decks today. The result: 4 bjs for me, 3 for “dealer”. 0 (zero, zilch, nada) naturals in the first 2 hands. I remember very, very well. My first hand when I started my first blackjack game did not result in a natural. If you honestly try to remember, probably the same thing happened to you (95% degree of certainty). So here is an average of 0 naturals in the very first hand. No doubt, after all these years, both you and I have received a plethora of blackjack naturals.

Switching gears, I think arguing should be done in a civilized manner, much like this latest exchange. Better late than never mate!

Gronbog

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Mar 30, 2018, 11:02:54 PM

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Since you expect to get a natural on the first hand once in about every 21 new decks/shoes, 10 trial decks is not nearly enough to draw any conclusions from.

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