Basic Strategy
I'm trying to verify the mathematics around basic strategy. After several hours of programming I have a way to calculate the average gain you will have depending on your final score and the card of the dealer. This will allow me to calculate the average gain of the highest counts (21,20) to be able to decide for the lower counts (12,13,14,15,16) whether it is worth to hit or not.
The problem is I am not sure of my data, I have found for example that your average gain if you have 21 and the dealer has 7 is 1.90 but when he has a 2 it is 1.88. This means that you have a higher chance of winning if he has a higher card which I find weird.
So do you guys know where I could find this kind of data to verify my own ?
Thanks for the help :)
Julian
Quote: JulianHey guys,
I'm trying to verify the mathematics around basic strategy. After several hours of programming I have a way to calculate the average gain you will have depending on your final score and the card of the dealer. This will allow me to calculate the average gain of the highest counts (21,20) to be able to decide for the lower counts (12,13,14,15,16) whether it is worth to hit or not.
The problem is I am not sure of my data, I have found for example that your average gain if you have 21 and the dealer has 7 is 1.90 but when he has a 2 it is 1.88. This means that you have a higher chance of winning if he has a higher card which I find weird.
So do you guys know where I could find this kind of data to verify my own ?
Thanks for the help :)
Julian
Well, isolating your example, 21 the worst you can do is push. Not sure how you're weighting pushes, if at all.
But besides that, the dealer will stand and lose on 5 cards and hit on 8, when he has a seven. He will always hit a 2. So he has more opportunities to make 21 and push with a 2 than he does with a 7, so with a higher card he's more likely to lose to you, as you said.
Look in the Wizard of Odds blackjack appendices. There's one that breaks down the relative values of every starting player hand vs. every dealer hand by EV of splitting, doubling, hitting, or standing to 6 decimal places (huge chart: not for the phone lookup). Might be helpful .
Thank you for the information, I didn't know the rule about the 5 cards rule, I will have to add that to my program.
I looked up the appendix you talked about and it was exactly what I was looking for thanks :D
Have a good day !
Julian
Quote: JulianHey beachbumbabs,
Thank you for the information, I didn't know the rule about the 5 cards rule, I will have to add that to my program.
I looked up the appendix you talked about and it was exactly what I was looking for thanks :D
Have a good day !
Julian
Don't misunderstand me. If the dealer has a 7, and their hole card is a ten, jack, queen, king, or ace, they will have to stand. Since you already have a 21, however you got there, you will win. So the dealer has that many more opportunities to improve their hand on a 2, because there is no hole card that will make them stand with only 2 cards.
Quote: beachbumbabsDon't misunderstand me. If the dealer has a 7, and their hole card is a ten, jack, queen, king, or ace, they will have to stand. Since you already have a 21, however you got there, you will win. So the dealer has that many more opportunities to improve their hand on a 2, because there is no hole card that will make them stand with only 2 cards.
Don't worry I got that. But the thing that was tilting me was the fact that when you have a 21 your Expected Return decreases when the dealer has a lower card from 9 to 2. But I looked up the appendix you talked about (/games/blackjack/appendix/1/) and it seems it is this way. Still, what you said must be a big factor of this but it was a bit counter intuitive.
By the way, all the expected return I found from 9 to 2 where the exact same as the appendix I'm pretty happy :D
