charliepatrick
Joined: Jun 17, 2011
• Posts: 2321
October 30th, 2018 at 1:02:55 AM permalink
Quote: tomchina123

consider to stay at 17 when coding rather than to stay at 16

As you probably know the technically correct method is to work out what to do with all ways of getting to 17's, then 16's etc. In this case the only 16's to worry about are 772 and 7711 but they need to know about your chances with 772x and 7711x. Similarly the only 15 is 771 and this needs 771x (including 7711).
tomchina123
Joined: Aug 26, 2015
• Posts: 282
October 30th, 2018 at 7:44:29 PM permalink
Hand EV Stand EV Hit
772 yours -0.515 857 -0.526 637
mine: dealer's 10 not considered.
-0.515857161 -0.534281989
mine: dealer's 10 considered.
-0.514246374 -0.521199017

7711 yours -0.504 830 -0.522 302
mine: dealer's 10 not considered.
-0.50482967 -0.529991852
mine: dealer's 10 considered.
-0.503658146 -0.516650066

77111 yours -0.421 725
mine: dealer's 10 not considered.
-0.421725263
mine: dealer's 10 considered.
-0.41775807

7721 yours -0.430 736
mine: dealer's 10 not considered.
-0.430736135
mine: dealer's 10 considered.
-0.426209636

the reslut is the same, standing 16 is better.but for the numbers, when standing, it seems yours is the same with me when not considering 10.
JoeMacmilan
Joined: Oct 31, 2018
• Posts: 2
October 31st, 2018 at 4:15:38 AM permalink
omg how many statistics)
tomchina123
Joined: Aug 26, 2015
• Posts: 282
November 2nd, 2018 at 12:58:35 AM permalink
it is by full combinations. so full theorictical statistics. or 14,658,134,400 hands.

i am also not sure of the calcluation, as you can see, it is a question mark.

let's be so.

i am doing sth on poker. it seems there is a need by different aspects. i finished basic things. i will check how excel performs vs coding.
gordonm888
Joined: Feb 18, 2015
• Posts: 2802
November 2nd, 2018 at 5:57:37 AM permalink
for 77 vs 10 in single deck, removing the 10 and both sevens from the deck, I calculate the dealer probabilities (via Excel spreadsheet) to be:

17 0.0872
18 0.1298
19 0.1282
20 0.3706
21 0.0390
Bust 0.2451

Stand= -0.5097
Hit = -0.5148

When calculating the Hit EV, I do include that the card or cards that are drawn to 7-7 are therefore unavailable to the dealer, thus changing the above dealer probabilities. For instance, when HIT and drawing a 5 to make a 19, I factor in that that 5 is now unavailable to the dealer (to make a 15, for example.)

The EV calculation for HIT also takes into account that we know that the dealer's facedown card is not an Ace, thereby elevating the chances of the player drawing an Ace slightly and reducing the probabilities of drawing all other ranks.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
charliepatrick
Joined: Jun 17, 2011
• Posts: 2321
November 2nd, 2018 at 7:05:49 AM permalink
Quote: gordonm888

...The EV calculation for HIT also takes into account that we know that the dealer's facedown card is not an Ace, thereby elevating the chances of the player drawing an Ace slightly and reducing the probabilities of drawing all other ranks.

I think I initially used the same method, working out the stand chances on a variety of card holdings for the player and then working out the chances of each dealer hand given the cards that were missing.

The part I haven't yet worked out properly is (say) starting with 77 then your chances when hitting are Pr(A)*f(771)+Pr(2)*f(772)...Pr(7)*f(777)+Pr(8)*Bust..Pr(10)*Bust. I've only looked at what's left in a fresh deck with 77X missing, but appreciate that one has to take into account you know the dealer hasn't an Ace. It's probably only a small factor so guess that's why my hit numbers are just slightly different from those on the wizard tool.

One method maybe that you just consider all the different starting two-card hands for the dealer, so against an K2 your 77 options etc.
tomchina123
Joined: Aug 26, 2015
• Posts: 282
November 3rd, 2018 at 8:13:21 AM permalink

17 0.0872
18 0.1298
19 0.1282
20 0.3706
21 0.0390
Bust 0.2451

are u sure it is 10-removed? because it is the same with my 10-not-reomoved.
also you may check this link, http://www.bjstrat.net/cgi-bin/cdca.cgi ( this website is recommended by WIZARD here doing EOR,,https://wizardofodds.com/games/blackjack/appendix/7/, which i may read most of the time in the world.)
you may see, you numbers are the same with 10 not removed.

for stand, Stand= -0.5097, it is the same with my 10-not removed.

for Hit = -0.5148, i cannot see this number in my caculation. do you set it to stand at 15 or 16 or 17 after hitting?

quote:''When calculating the Hit EV, I do include that the card or cards that are drawn to 7-7 are therefore unavailable to the dealer, thus changing the above dealer probabilities. For instance, when HIT and drawing a 5 to make a 19, I factor in that that 5 is now unavailable to the dealer (to make a 15, for example.)''.

by first thinking, i though i had mistake because of this point, the "5". but i found i didn't.

77 is surely 'yes'. but if to removed possible future instanced card 5, we don't really need to remove it. because after getting 5, the stragey to be faced is 14+5 VS 10, only in this hand, 5 is removed. (so) we consider all possible cards but have no need to remove it. don't u think so?

quote: "The EV calculation for HIT also takes into account that we know that the dealer's facedown card is not an Ace, thereby elevating the chances of the player drawing an Ace slightly and reducing the probabilities of drawing all other ranks.''

well noted, i am doing it like this.
LitheInvestor
Joined: Nov 12, 2018
• Posts: 1
November 12th, 2018 at 11:38:26 PM permalink
While 7,7 against a 10 is a stand due to half the key cards to reach a 21 for a player being removed there is a small strategy error on wiz of odds basic strategy and that's a player 9,9 against a dealer Ace to split with hit on soft 17 in single deck. It's slightly better to stand according to the hand calculator on site (which is very helpful thank you!)
Last edited by: LitheInvestor on Nov 13, 2018
tomchina123
Joined: Aug 26, 2015