Hit or stay on 16

  • Ace High

    Hit or stay on 16

    What is the mathematical statistic of hitting 16 against 7 through Ace?
    What percent will you win or push by hitting it?

    What percent will you win or push by not hitting it?

    Can anyone direct me to a site which publishes such stats?

  • iCountNTrack

     

    Quote: Ace High said:
    What is the mathematical statistic of hitting 16 against 7 through Ace?
    What percent will you win or push by hitting it?

    What percent will you win or push by not hitting it?

    Can anyone direct me to a site which publishes such stats?

    There ya go, i only posted the single deck values and S17, but you can get them for any number of cards

    http://code.google.com/p/blackjack-combinatorial-analyzer/downloads/list

    
    ///////1 deck, S17//////////
    ********************************************
    player's Hand  10,6
    dealer's upCard  7
     
    player's probabilities for standing
    p_-1 = 0.741662210131
    p_0 = 0
    p_+1= 0.258337789869
    p_+1.5 = 0
    EV for standing= -0.483324420261 ± 0.875441320009
     
    player's probabilities for doubling
    p_-2 = 0.657943433709
    p_0 = 0.060306641789
    p_+2= 0.281749924502
    EV for doubling= -0.752387018413 ± 1.78680922523
     
    player's probabilities for hitting
    p_-1 = 0.657943433709
    p_0 = 0.060306641789
    p_+1= 0.281749924502
    EV for hitting= -0.376193509207 ± 0.893404612615
    
    ************************************************
    
    player's Hand  10,6
    dealer's upCard  8
     
    player's probabilities for standing
    p_-1 = 0.76350326193
    p_0 = 0
    p_+1= 0.23649673807
    p_+1.5 = 0
    EV for standing= -0.527006523861 ± 0.849861237973
     
    player's probabilities for doubling
    p_-2 = 0.681168316615
    p_0 = 0.0624859167129
    p_+2= 0.256345766672
    EV for doubling= -0.849645099887 ± 1.74016077918
     
    player's probabilities for hitting
    p_-1 = 0.681168316615
    p_0 = 0.0624859167129
    p_+1= 0.256345766672
    EV for hitting= -0.424822549943 ± 0.870080389589
    
    **********************************************
    
    player's Hand  10,6
    dealer's upCard  9
     
    player's probabilities for standing
    p_-1 = 0.769615756767
    p_0 = 0
    p_+1= 0.230384243233
    p_+1.5 = 0
    EV for standing= -0.539231513534 ± 0.842157571249
     
    player's probabilities for doubling
    p_-2 = 0.708318244314
    p_0 = 0.0626698865513
    p_+2= 0.229011869135
    EV for doubling= -0.958612750359 ± 1.68237393247
     
    player's probabilities for hitting
    p_-1 = 0.708318244314
    p_0 = 0.0626698865513
    p_+1= 0.229011869135
    EV for hitting= -0.47930637518 ± 0.841186966233
    
    ************************************************
    
    player's Hand  10,6
    dealer's upCard  10
     
    player's probabilities for standing
    p_-1 = 0.790130953287
    p_0 = 0
    p_+1= 0.209869046713
    p_+1.5 = 0
    EV for standing= -0.580261906574 ± 0.814429935464
     
    player's probabilities for doubling
    p_-2 = 0.662971292784
    p_0 = 0.0579720249632
    p_+2= 0.197424029191
    EV for doubling= -1.01272718025 ± 1.58037894169
     
    player's probabilities for hitting
    p_-1 = 0.744603945845
    p_0 = 0.0579720249632
    p_+1= 0.197424029191
    EV for hitting= -0.547179916654 ± 0.801637146
    
    ***********************************************
    
    player's Hand  10,6
    dealer's upCard  1
     
    player's probabilities for standing
    p_-1 = 0.879580663876
    p_0 = 0
    p_+1= 0.120419336124
    p_+1.5 = 0
    EV for standing= -0.759161327752 ± 0.650902510708
     
    player's probabilities for doubling
    p_-2 = 0.501690908078
    p_0 = 0.0435060431592
    p_+2= 0.148680599783
    EV for doubling= -1.01214306557 ± 1.37228819686
     
    player's probabilities for hitting
    p_-1 = 0.807813357058
    p_0 = 0.0435060431592
    p_+1= 0.148680599783
    EV for hitting= -0.659132757275 ± 0.722521947852
    

    10,6 vs 10 is a very close call especially for mulitple decks for examples for 6D, S17

    
    
     
    player's Hand  10,6
    dealer's upCard  10
     
    player's probabilities for standing
    p_-1 = 0.788304231586
    p_0 = 0
    p_+1= 0.211695768414
    p_+1.5 = 0
    EV for standing= -0.576608463173 ± 0.817020611856
     
    player's probabilities for doubling
    p_-2 = 0.680144821752
    p_0 = 0.0551878170108
    p_+2= 0.186997458325
    EV for doubling= -1.06396462977 ± 1.55377549531
     
    player's probabilities for hitting
    p_-1 = 0.757814724664
    p_0 = 0.0551878170108
    p_+1= 0.186997458325
    EV for hitting= -0.57081726634 ± 0.786752713016
     
    
  • tthree

     

    Quote: Ace High said:
    What is the mathematical statistic of hitting 16 against 7 through Ace?
    What percent will you win or push by hitting it?

    What percent will you win or push by not hitting it?

    Can anyone direct me to a site which publishes such stats?

    You push 0% by not hitting. I hope that helps.

  • zengrifter

     

    Quote: Ace High said:
    What is the mathematical statistic of hitting 16 against 7 through Ace?
    What percent will you win or push by hitting it?

    What percent will you win or push by not hitting it?

    Can anyone direct me to a site which publishes such stats?

    Its not even close. Just trust correct basic strategy, which we are guessing you do not know. zg

  • Coach R

     

    Quote: Ace High said:
    What is the mathematical statistic of hitting 16 against 7 through Ace?
    What percent will you win or push by hitting it?

    What percent will you win or push by not hitting it?

    Can anyone direct me to a site which publishes such stats?

    Just follow the basic strategy charts. What makes the difference what the odds are of the dealer busting? it’s all calculated in basic strat. If you stand on a 16, you’re not betting that’s enough to beat the dealer, you’re betting the dealer will bust. Your odds of winning by standing on a 16 vs. a dealers 7, are the exact same odds of winning by standing on an 11 (5-6). You can’t win unless the dealer bust.
    Pushing is impossible by standing on 16

  • BJLFS

     

    Quote: Coach R said:
    Just follow the basic strategy charts. What makes the difference what the odds are of the dealer busting? it’s all calculated in basic strat. If you stand on a 16, you’re not betting that’s enough to beat the dealer, you’re betting the dealer will bust. Your odds of winning by standing on a 16 vs. a dealers 7, are the exact same odds of winning by standing on an 11 (5-6). You can’t win unless the dealer bust.
    Pushing is impossible by standing on 16

    Also the reason you sometimes would hit on a 16 vs dealer 10 is so you will lose less, not to win.

  • iCountNTrack

     

    Quote: Coach R said:
    Just follow the basic strategy charts. What makes the difference what the odds are of the dealer busting? it’s all calculated in basic strat. If you stand on a 16, you’re not betting that’s enough to beat the dealer, you’re betting the dealer will bust. Your odds of winning by standing on a 16 vs. a dealers 7, are the exact same odds of winning by standing on an 11 (5-6). You can’t win unless the dealer bust.
    Pushing is impossible by standing on 16

    I am sorry but this is not true, the odds are different

    16 vs 6
    player’s probabilities for standing
    p_-1 = 0.589511449401
    p_0 = 0
    p_+1 = 0.410488550599
    p_+1.5 = 0
    EV for standing= -0.179022898802 ± 0.983844907343

    ***********************************************
    11 vs 5
    player’s probabilities for standing
    p_-1 = 0.566326835062
    p_0 = 0
    p_+1= 0.433673164938
    p_+1.5 = 0
    EV for standing= -0.132653670123 ± 0.991162450763

    Basic strategy takes into account all possible combinations of playerHand/dealerHand , bust rate of the dealer is mythical figure used by scam system promoters

  • tthree

     

    Quote: iCountNTrack said:
    I am sorry but this is not true, the odds are different

    16 vs 6
    player’s probabilities for standing
    p_-1 = 0.589511449401
    p_0 = 0
    p_+1 = 0.410488550599
    p_+1.5 = 0
    EV for standing= -0.179022898802 ± 0.983844907343

    ***********************************************
    11 vs 5
    player’s probabilities for standing
    p_-1 = 0.566326835062
    p_0 = 0
    p_+1= 0.433673164938
    p_+1.5 = 0
    EV for standing= -0.132653670123 ± 0.991162450763

    Basic strategy takes into account all possible combinations of playerHand/dealerHand , bust rate of the dealer is mythical figure used by scam system promoters

    I hope you realize that you did 11 and 16 v 5 and 6 respectively, not 7 as was the situation in question. Why didn’t you site 11 and 16 against the same upcard?

  • Coach R

     

    Quote: tthree said:
    I hope you realize that you did 11 and 16 v 5 and 6 respectively, not 7 as was the situation in question. Why didn’t you site 11 and 16 against the same upcard?

    I noticed that too, I think some people look way too deep for some kind of a quotion, or mathmatic formula to make something easy look complex. The dealer is either going to bust or not, that’s why counters count, and understand the best times to do certain things. It doesn’t matter if you have 4,7,9,12,or 16, you can’t win if the dealer doesn’t bust. There is a very long and complicated equation that explains why, and how gravity affects objects of all sizes, shapes, and weight. The bottom line is, if you throw a ball in the sky, it is going to drop.

  • iCountNTrack

     

    Quote: tthree said:
    I hope you realize that you did 11 and 16 v 5 and 6 respectively, not 7 as was the situation in question. Why didn’t you site 11 and 16 against the same upcard?

    It doesnt make a difference it is still diferrent see below:

    11 vs 6
    player’s probabilities for standing
    p_-1 = 0.574852433669
    p_0 = 0
    p_+1= 0.425147566331
    p_+1.5 = 0
    EV for standing= -0.149704867338 ± 0.988730728103
    *****************************
    16 vs 7
    player’s probabilities for standing
    p_-1 = 0.741662210131
    p_0 = 0
    p_+1= 0.258337789869
    p_+1.5 = 0
    EV for standing= -0.483324420261 ± 0.875441320009

    the odds will always be diferrent because they depend on BOTH the players’s hand and the dealer’s upCard

  • 21gunsalute

     

    Quote: tthree said:
    You push 0% by not hitting. I hope that helps.

    Not always true. Depends on how alert the dealer is.

  • tthree

     

    Quote: iCountNTrack said:
    It doesnt make a difference it is still diferrent see below:

    11 vs 6
    player’s probabilities for standing
    p_-1 = 0.574852433669
    p_0 = 0
    p_+1= 0.425147566331
    p_+1.5 = 0
    EV for standing= -0.149704867338 ± 0.988730728103
    *****************************
    16 vs 7
    player’s probabilities for standing
    p_-1 = 0.741662210131
    p_0 = 0
    p_+1= 0.258337789869
    p_+1.5 = 0
    EV for standing= -0.483324420261 ± 0.875441320009

    the odds will always be diferrent because they depend on BOTH the players’s hand and the dealer’s upCard

    You did it again, you used different dealer upcards for the 2 situations. You are comparing apples to oranges.

  • Cardcounter

     

    Quote: Ace High said:
    What is the mathematical statistic of hitting 16 against 7 through Ace?
    What percent will you win or push by hitting it?

    What percent will you win or push by not hitting it?

    Can anyone direct me to a site which publishes such stats?

    Hitting a 16 vs a 7 is significantly better than staying. Hitting a 16 vs a 10 is only marginally better.

    With 16 you are going to lose most of your hands no matter how you play it you are going to bust the hand 62% if you hit it. But the 38% of the time that you draw a hand you will be much better off especially if drawing against a 7.

    If you don’t hit 16 against a 7-A ace the dealer will make a hand 75% of the time on average with those hands and beat you 80% with an ace. You will win 20%-25% of the time if you don’t hit. There will be a zero percent chance of a push because the dealer must draw to 17 or higher.

  • iCountNTrack

     

    Quote: tthree said:
    You did it again, you used different dealer upcards for the 2 situations. You are comparing apples to oranges.

    Ah, I misunderstood the poster’s point i thought he meant 11 vs 5 or 6, he meant 11 composed of a 5 and 6. Nevertheless, the odds will still be different because as i have mentioned they depend on BOTH the dealer upCard and the player hand.

    11 vs 7
    player’s probabilities for standing
    p_-1 = 0.744468761037
    p_0 = 0
    p_+1= 0.255531238963
    p_+1.5 = 0
    EV for standing= -0.488937522075 ± 0.872318806118
    *********************************************************
    16 vs 7
    player’s probabilities for standing
    p_-1 = 0.741662210131
    p_0 = 0
    p_+1= 0.258337789869
    p_+1.5 = 0
    EV for standing= -0.483324420261 ± 0.875441320009

    There is no systematic way to “explain” optimum decisions. Some playing decisions will sometime look weird, that is because most of the time we are overlooking some cases. A combinatorial analysis takes care of that by enumerating all possible outcomes.

  • tthree

     

    Quote: iCountNTrack said:
    Ah, I misunderstood the poster’s point i thought he meant 11 vs 5 or 6, he meant 11 composed of a 5 and 6. Nevertheless, the odds will still be different because as i have mentioned they depend on BOTH the dealer upCard and the player hand.

    11 vs 7
    player’s probabilities for standing
    p_-1 = 0.744468761037
    p_0 = 0
    p_+1= 0.255531238963
    p_+1.5 = 0
    EV for standing= -0.488937522075 ± 0.872318806118
    *********************************************************
    16 vs 7
    player’s probabilities for standing
    p_-1 = 0.741662210131
    p_0 = 0
    p_+1= 0.258337789869
    p_+1.5 = 0
    EV for standing= -0.483324420261 ± 0.875441320009

    There is no systematic way to “explain” optimum decisions. Some playing decisions will sometime look weird, that is because most of the time we are overlooking some cases. A combinatorial analysis takes care of that by enumerating all possible outcomes.

    Thanks. I knew there would be some difference but also knew it would be fairly insignificant. Your numbers confirm this.

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