Win / Lose probabilities.

[UK-21]

Mr Renzey's Blackjack Bluebook II hit my doormat yesterday. On page 79 there is a synopsis of 50 hands with the probabilities of winning or losing them (expressed as fractions).

Does anyone have a full list of hand combos (preferably expressed as decimals) to make available?

Thanks.

Newb99

 

[cardcounter0]

Blackjack Attack 3rd edition by Don Schlesinger has a complete set in the Appendix carried out to 6 decimal places and the frequency.

 

[callipygian]

C:\WINDOWS\system32\calc.exe

 

[UK-21]

Terrific. Problem is my version only has plus, minus, multiply and divide on it - not diamonds, hearts, spades and clubs. Do you think my version of windows might be a pirate ?

 

[Sonny]

Terrific. Problem is my version only has plus, minus, multiply and divide on it - not diamonds, hearts, spades and clubs.

Unless you're playing with special bonus rules the suits don't matter, only the numbers. But that calculator stuff is way outdated. CVData will give you those numbers much quicker and easier than that hand calculator.

-Sonny-

 

[cardcounter0]

http://www.bjmath.com/bjmath/ev/ev.htm (Archive copy)

 

[UK-21]

Thanks for the link.

That's the probability of the hand being dealt off of the top of a shoe, not the probability of winning it through?

 

[CowCantFly]

i dont understand the no that on the http://www.bjmath.com/bjmath/ev/ev.htm (Archive copy)

 

[KenSmith]

That's the probability of the hand being dealt off of the top of a shoe, not the probability of winning it through?

i dont understand the no that on the http://www.bjmath.com/bjmath/ev/ev.htm (Archive copy)

In answer to both of you...

At the top of the EV tables, notice that the final column is 'Probability' which is the probability that you will be dealt that specific hand against that specific dealer upcard.

How about an example. Let's look at 6-deck S17. The values are here:
http://www.bjmath.com/bjmath/ev/6ds17.htm (Archive copy)

Let's say we are interested in the strategies for playing a hand of 11 vs 9. Specifically, we'll look at the hand (7,4) vs a dealer 9.

Here's the data from the table:

Standing: -0.54421
Hitting: 0.156869
Doubling: 0.227194
Splitting: N/A
Probability: 0.000919

First, we see that we'll be dealt this specific hand only 0.000919 of the time, or about once in 1/0.000919 = 1088 hands.

The other numbers are the expected value in terms of the original bet amount. For a $10 bet, multiply $10 by the values.

If you choose to stand with your 11 (obviously a bad idea!), you'll still win sometimes and lose sometimes. But, if you play that hand many times, your average result per hand will be $10 X -0.54421 = A Loss of $5.4421 each time.

If you decide to hit (and continue to hit until you reach 17 or better) you'll win some money: $10 X 0.156869 = $1.56869 profit each time.

Doubling wins more still even though you'll actually have a lower overall win percentage than just hitting. Doubling your bet makes up for the lower win rate and you'll profit $10 X 0.227194 = $2.27194 profit each time.

(Note to purists: I'm ignoring the fact that the 'Hit' column number assumes computer perfect composition dependent play rather than basic strategy. The difference will be quite small.)

Now, back to newb99's initial question about getting win/loss percentages for various hands. It is true that the EV charts don't precisely answer that question. However, for most purposes the EV is quite a bit more meaningful than the raw win/loss/push percentages.

Even so, if you have interest in how often a particular double-down will win, lose or push, I have published a complete list of that data here:
http://www.blackjackinfo.com/bjtourn-doublechart.php

For non-doubling strategies, I am unaware of a similar list available online.