odds of dealer making hands in blackjack - Gambling and Probability

collegefund4 · 05-23-2012, 07:54 PM

was wondering if any1 could give me a link to the odds of dealers making certain hands in blackjack without taking into consideration up cards. For example should be something like (pulling #s out of my ass here) bust 25% 17 20% 18 15% 19 15% 20 30% 21 5% with the math behind it.

thx

NewOldGuy · 05-23-2012, 08:58 PM

Quote:

Originally Posted by collegefund4

was wondering if any1 could give me a link to the odds of dealers making certain hands in blackjack without taking into consideration up cards. For example should be something like (pulling #s out of my ass here) bust 25% 17 20% 18 15% 19 15% 20 30% 21 5% with the math behind it.

thx

http://wizardofodds.com/games/blackjack/appendix/2b/

Also see the links at the bottom of that page.

**BruceZ** · 05-23-2012, 09:03 PM

Quote:

Originally Posted by collegefund4

was wondering if any1 could give me a link to the odds of dealers making certain hands in blackjack without taking into consideration up cards. For example should be something like (pulling #s out of my ass here) bust 25% 17 20% 18 15% 19 15% 20 30% 21 5% with the math behind it.

http://wizardofodds.com/games/blackjack/appendix/2b/

See entry marked "all" to ignore the up card. I haven't checked these, and he doesn't say if these are simulated or computed exactly, but in Griffin's The Theory of Blackjack p. 158 there is a 28 line BASIC program to compute this exactly. It goes through every combination. I could try to run that, and it would also be easy to do a sim. How many decks do you want, and does the dealer hit or stand on soft 17? Also, why do you want to know this?

**BruceZ** · 05-24-2012, 01:22 PM

I confirmed the Wizard's numbers with an R simulation to within 0.01% with 50 million hands for 8 deck dealer stands on soft 17 (S17) and also for 1 deck S17. The 8 deck results are below, and the sim can generate the other results by changing num_decks and S17. Note that my entry for 21 includes BJs while the Wizard separates these, and my entry for 22 is for all busts 22-26. An exact calculation could be done with a recursive function.

Code:

sims = 50000000
num_decks = 8
S17 = TRUE

deck = c(rep(1:9,4*num_decks),rep(10,16*num_decks))
hit = ifelse(S17,6,7)
result = rep(0,26)

for (i in 1:sims) {
  cards = sample(deck, 14, F)
  j = 1
  total = 0
  ace = FALSE
  while (total < 17) {
    total = total + cards[j]
    if (cards[j] == 1) {ace = TRUE}
    if (ace && (total > hit) && (total < 12)) {total = total + 10}
    j = j + 1
  }
    result[total] = result[total] + 1
}

result[22] = sum(result[22:26])
result[1:22]/sims

Output:

>result[1:22]/sims
[1] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
[8] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
[15] 0.0000000 0.0000000 0.1452270 0.1393228 0.1336369 0.1796657 0.1203770
[22] 0.2817706

Wizard's results (17, 18, 19, 20, 21 non-BJ, BJ, Bust):
0.145215 0.139318 0.133629 0.179709 0.072838 0.0474513 0.281839

**BruceZ** · 05-24-2012, 10:40 PM

Note that in real life, it is less likely that the players will bust when the dealer upcard is 2-6 than 7-A if they are playing right. This will affect the dealer probabilities heads up, especially the dealer bust probability. The dealer's bust percentage will increase since he will be hitting upcards of 2-6, but he won't be hitting the upcards of 7-A when the player busts. The impact with 2 or more players won't be as significant.

zemlik · 05-26-2012, 11:37 AM

does the gaming board in the UK still put information on the table that the punter should stay at 16 whereas the better advice is I read to stay at 17 and take a card at 16.

NewOldGuy · 05-26-2012, 11:45 AM

Quote:

Originally Posted by zemlik

does the gaming board in the UK still put information on the table that the punter should stay at 16 whereas the better advice is I read to stay at 17 and take a card at 16.

If you want a rule that is independent of the dealer's upcard, then you are better off always hitting on 16 than you are always standing on 16.

Basic strategy would have you stand on hard 16 only if the dealer has 2 thru 6. With soft 16 you always hit (and double down if allowed when the dealer has 4 thru 6). With 8,8 you always split *. If surrender is allowed and the dealer is showing a Ten or Ace, you surrender on 16. If the game is S17 (dealer hits soft 17) the surrender would only be when dealer is showing an Ace.

* One exception to splitting 8,8 is in a S17 game when dealer is showing Ace, you surrender 8,8 if allowed.

jaakkang · 05-31-2012, 04:39 PM

Could somebody calculate what´s the probability of the dealer getting 8 cards.

To become eligible for the progressive, players may make a $1 side bet when they place their main wager. The Hit and Run® progressive bet is based solely on the dealer’s hand. Players win if the dealer hits blackjack or the dealer’s hand consists of five or more cards (including if the last card busts the dealer’s hand). With the dealer showing blackjack, a player will receive a $4 win. If the dealer’s hand consists of between five and eight cards, the winning ratio begins at $7 and pays as high as $100 or $200 depending on number of decks at that game, and if the dealer’s hand has eight or more cards, the progressive jackpot will be paid. When the progressive is hit, and multiple players placed the side bet, the pot is split amongst the players at the winning table. As of May 25, the progressive jackpot on Station Casinos Double Deck Hit and Run® games is now over $10,500 and the Shoe Hit and Run games are over $15,400.

http://www.stationcasinos.com/corp/n...012/052912.php

TY in advance!

Not good in math.

NewOldGuy · 05-31-2012, 04:48 PM

Quote:

Originally Posted by jaakkang

Could somebody calculate what´s the probability of the dealer getting 8 cards.

Possible Dealer Outcomes — Six Decks, Dealer Hits Soft 17

Bust with 4 cards 0.0893918
Bust with 5 cards 0.0204726
Bust with 6 cards 0.0026376
Bust with 7 cards 0.000214444
Bust with 8 cards 0.000011528
Bust with 9 cards 0.00000040805
Bust with 10 cards 0.00000000909509
Bust with 11 cards 0.00000000011986
Bust with 12 cards 0.000000000000824386
Bust with 13 cards 0.00000000000000222834

Note that these are not percentages, move the decimal 2 places if you want %.

From http://wizardofodds.com/games/blackjack/appendix/8/