• 6 Deck Blackjack Odds
• Blackjack Shoes 6 Deck
• 6 Deck Blackjack Rules

If the probability of a blackjack is p then the probability of not getting any blackjacks in 10 hands is 1- (1-p) 10. For example in a six deck game the answer would be 1- 0.952511 10 = 0.385251. What are the odds of getting 3 blackjacks in a row with 1 deck 4 players.

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Introduction

To use the basic strategy, look up your hand along the left vertical edge and the dealer's up card along the top. In both cases an A stands for ace. From top to bottom are the hard totals, soft totals, and splittable hands. There are two charts depending on whether the dealer hits or stands on soft 17.

Other basic strategy rules.

• Never take insurance or 'even money.'
• If there is no row for splitting (fives and tens), then look up your hand as a hard total (10 or 20).
• If you can't split because of a limit on re-splitting, then look up your hand as a hard total.

Ideally, the basic strategy shows the play which, on average, will result in the greatest win or the least loss per initial hand played. The way I usually go about this is to look at the initial 2-card hands only. Generally, this will result in the overall best play. However, soft 18 against a dealer ace when the dealer stands on soft 17 provides the only known exception that I am aware of for any number of decks. As my blackjack appendix 9 shows, a 2-card soft 18 vs A has an expected value of hitting of -0.100359, and of standing -0.100502. So with two cards it is very slightly better to hit. However, not all soft 18's are composed of two cards. The more the cards in the player's hand the more the odds favor standing. Simulations show that if forced to always hit or always stand, it is better to stand. I would like to thank Don Schlesinger for bringing this unusual play to my attention.

... which is very close with much less math.

Dieter, we're supposed to teach the kids that math is fun! =P

Dieter, we're supposed to teach the kids that math is fun! =P

It is! Math is great fun!
... but useful approximations are at least as fun, and quite useful, and often easier to remember.
Every schoolkid should know that (about) 1 hand in 21 should be a blackjack. If you play, that's just something you should

6 Deck Blackjack Odds

know. It should be obvious that 1 in 4 will be suited.
As for accuracy... 1.187% vs 1.190% is darn close. 3 one thousandths of one percent close. Surely good enough for government work.
It's right up there with 'pi seconds is about a nanocentury'. (Of course, it's actually closer to 'square root of 10 seconds', but that's less fun.)

I'm not sure what is meant by '5 deck shuffler', but if cards are discarded each hand, that will change your probability. That calculation would be rather cumbersome without programming.

Based on how the question is phrased, I'd assume that the game is being played out of a 5-deck CSM. If you're not acquainted with them, they're pretty common machines in the US where the cards are fed back into the machine and reshuffled every few hands. Based on what I've seen, I'd estimate that, on average, ten cards will be in the discard at a given time. (Obviously, highly dependent on casino policy, number of hands, etc.)
It's close enough to playing with a constantly fresh n-deck game that the math shouldn't be thrown off by much though.

It is! Math is great fun!
... but useful approximations are at least as fun, and quite useful, and often easier to remember.
Every schoolkid should know that (about) 1 hand in 21 should be a blackjack. If you play, that's just something you should know. It should be obvious that 1 in 4 will be suited.
As for accuracy... 1.187% vs 1.190% is darn close. 3 one thousandths of one percent close. Surely good enough for government work.
It's right up there with 'pi seconds is about a nanocentury'. (Of course, it's actually closer to 'square root of 10 seconds', but that's less fun.)

Am I missing pi ~ 22/7 in that image? How could Randall forget that, or is it too obvious?

Blackjack Shoes 6 Deck

Am I missing pi ~ 22/7 in that image? How could Randall forget that, or is it too obvious?

355/113 is closer. 7 digits of accuracy in only 6 digits.
Or, 4*atan(1) (in radians).

355/113 is closer. 7 digits of accuracy in only 6 digits.
Or, 4*atan(1) (in radians).

I agree 355/113 isbetter. 22/7 is just what we were told in some really basic math classes to use as an estimation.
4atan(1) = pi, not an approximation

6 Deck Blackjack Rules

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