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 Code: ///////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 Code: 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

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

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.

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.

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.

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.