Hit or stay on 16

[iCountNTrack]

Originally Posted by tthree

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]

Originally Posted by tthree

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

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

[tthree]

Originally Posted by iCountNTrack

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]

Originally Posted by Ace High

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]

Originally Posted by tthree

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]

Originally Posted by iCountNTrack

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.