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# Important Blackjack Odds, Probabilities

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### ions...@gmail.com

Jun 24, 2016, 7:24:26 PM6/24/16
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These are the latest and most accurate calculations for the most important blackjack parameters. The page presents easy-to-follow, easy-to-apply formulas and algorithms.

I. Probability, Odds for a Blackjack or Natural 21
II. House Edge on Insurance Bet at Blackjack
III. Calculate Double-Down Hands
IV. Calculate Blackjack Pairs: Strict or Mixed Ten-Cards
V. Free Blackjack Resources, Basic Strategy, Casino Gambling Systems
http://forums.saliu.com/blackjack-natural-odds-probability.html

Ion Saliu,
Doctor in Blackjackology
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### Ion Saliu

Nov 30, 2018, 5:45:54 PM11/30/18
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On Friday, June 24, 2016 at 7:24:26 PM UTC-4, Ion Saliu wrote:
>

These are the latest and most accurate calculations for the most important blackjack parameters. The page presents easy-to-follow, easy-to-apply formulas and algorithms.

“1. Probability, Odds for a Blackjack or Natural 21”
“2. House Edge on Insurance Bet at Blackjack”
“3. Calculate Double-Down Hands”
“4. Calculate Blackjack Pairs: Strict or Mixed Ten-Cards”
“5. Free Blackjack Resources, Basic Strategy, Casino Gambling Systems”

https://forums.saliu.com/blackjack-natural-odds-probability.html
• Calculate Blackjack Probability, Odds: Natural 21, Insurance, Double-Down Hands, Pairs.

https://forums.saliu.com/blackjack-insurance.html
• Blackjack Insurance Bet Favorable to All Players.

https://forums.saliu.com/card-counting-blackjack.html
• Card Counting Blackjack Systems: Reversed Counts, Total Count, All BJ Cards.

• Ion Saliu,
• Doctor in Blackjackology
• The Best Blackjack Player Ever!

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### Ion Saliu

Dec 30, 2020, 10:44:32 AM12/30/20
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On Saturday, June 25, 2016 at 2:24:26 AM UTC+3, Ion Saliu wrote:
>
• 1 – Probability, Odds for a Blackjack or Natural 21
• 2 – House Edge on Insurance Bet at Blackjack
• 3 – Calculate Double-Down Hands
• 4 – Calculate Blackjack Pairs: Strict or Mixed Ten-Cards
• 5 – Reversed Calculations: Probabilities, Odds to “Lose/Fail”
… and much more…

https://forums.saliu.com/blackjack-natural-odds-probability.html
• Calculate Blackjack Probability, Odds: Natural 21, Insurance, Double-Down Hands, Pairs.

The above resource has become the New Blackjack Bible! The search engines are “learning… mathematics”, namely calculating a wide variety of odds in blackjack. More and more students of ‘blackjack math’ are referred to the Web page created by the Blackjack Master Emeritus.

The eBook, however, is focused on blackjack. The good news is that there is more encompassing software –
The Best All-Purpose Software to Calculate Odds/Probability, Including for the Game of Blackjack.

The best apps are:

• SuperFormula.exe
• screenshot: https://saliu.com/ScreenImgs/super-formula-1.gif
• program presentation: https://forums.saliu.com/blackjack-natural-odds-probability.html

• Streaks.exe
• screenshot: https://saliu.com/ScreenImgs/blackjack-streaks.gif
• program presentation: https://saliu.com/gambling-lottery-lotto/blackjack-report.htm

Let’s work out a few case scenarios. Most accurate probability ‘to win’ for the blackjack player: 0.451; odds ‘to lose’: 0.549.

A. LOSE — p=0.549
-------------------------------
1) What is the probability to lose 13 consecutive blackjack hands – at the beginning of the game?
• Run SuperFormula, function ‘E = Exactly M Successes in N Trials’
• Answer for probability p=0. 549:’1 in 2430’ (once in 2430 bj games).

2) What is the probability to lose 13 consecutive blackjack hands – in the first100 blackjack hands?
• Run Streaks, function ‘1 = I Know p – Run Once’
• Answer: 0 (it takes 2430 hands to see one streak of 13 losing hands).

3) What is the probability to lose ‘exactly’ 13 blackjack hands in the first100?
• Run SuperFormula, function ‘E = Exactly M Successes in N Trials’
• Answer: ‘1 in 4 followed by 31 digits’ (virtually zer0).

4) What is the probability to lose ‘at least’ 13 blackjack hands in the first100?
• Run SuperFormula, function ‘L = At Least M Successes in N Trials’
• Answer: ‘~100%’ (virtually all the time, my computer sez).

5) What is the probability to lose ‘at most’ 13 blackjack hands in the first100?
• Run SuperFormula, function ‘M = At Most M Successes in N Trials’
• Answer: ‘1 in 3 followed by 31 digits’ (virtually “never happens”).

B. WIN — p=0. 451
------------------------------
6) What are the odds to win 13 consecutive blackjack hands – at the beginning of the game?
• Run SuperFormula, function ‘E = Exactly M Successes in N Trials’
• Answer for probability p=0.451:’1 in 31312’ (once in 31,312 bj games).

7) What are the odds to win 13 consecutive blackjack hands – in the first100 blackjack hands?
• Run Streaks, function ‘1 = I Know p –Run Once’
• Answer: 0 (it takes 31312 hands to see one streak of 13 losing hands).

8) What are the odds to win ‘exactly’ 13 blackjack hands in the first100?
• Run SuperFormula, function ‘E = Exactly M Successes in N Trials’
• Answer: ‘1 in 199989986867’ (virtually zer0).

9) What are the odds to win ‘at least’ 13 blackjack hands in the first100?
• Run SuperFormula, function ‘L = At Least M Successes in N Trials’

10) What are the odds to win ‘at most’ 13 blackjack hands in the first100?
• Run SuperFormula, function ‘M = At Most M Successes in N Trials’
• Answer: ‘1 in 164682221206’ (virtually “never happens”).

There is a huge discrepancy between losing and winning in blackjack. Despite what you’ve read, blackjack is far worse than hopes. Everybody can witness the hard truth every day of every year of grace in any casino of this once-blessed world.

At the end of this nightmarish year 2020, I wish you the best of luck, axiomatics!

Ion Saliu
The Best Blackjack Player Ever

“A good man is an axiomatic man; an axiomatic man is a happy man. Be axiomatic!”