H17

Both Cac and I have had our software for many years now. We have used them for lots of calculations. If there were a bug, we would have noticed it earlier. They are independent programs, we use different algorithms. So the odds of our both having done it wrong are quite small.

It occurs to me that maybe you are not quite familiar with H17 and how it is played here. In this case, if the dealer has a 2 in the hole, he would then pull an Ace, he would continue drawing. Similarly, if we had Ace in hole, and then 2. Or if he had 4-A-A-A, he would draw again.

If the dealer hits Soft 17, if he gets a 16 or less, he continues to draw. But if he draws a 4 or less, he stops.

Your standing numbers differ only by .1%. between S17 and H17. This is simply too small a number. We can estimate the size of this number by doing some pencil and paper calculations, without a computer. Let us call this number D, for difference.

When you stand on 12, your EV is 2p-1, where p is the probability that the dealer busts. To calculate D, we compute p for the two different rules sets, take the difference, and then double it. Let me call that difference DP, for differnce in probabilities.

Now DP can computed as follows. Note that this is the probability that dealer busts with H17, but does not bust with S17. It is simply the probability of a dealer drawing sequence that gets to Soft-17, and then subsequently busts.

You can get to Soft-17 by drawing 2-A or A-2 plus A-A-A. I compute the probability of this to be greater than 1.2%. Now once the dealer has a Soft 17, there are 5 denominations that will produce a stiff. Probability of that, in this situation, is 40%.

So more than .48% of the time, and H17 dealer will get a Soft 17, and then get a stiff. How many of these stiffs break? At least 50%. That would means that DP is at least .24%, which means the D is at least .48%. You see this is much bigger than the difference in your standing values, but slightly less than the difference in ours.

PS: For those of you who may be wonging into this thread late, this is all in the above context. 12 v 4, played against a complete 52-card remainder.