DaUmega
Joined: Oct 6, 2020
• Posts: 4
October 6th, 2020 at 8:08:27 PM permalink
Hi,

In the wizard of odds excel sheet for calculating house edge for blackjack, dealer blackjacks were calculated separately because it was assumed that dealer would peek for both 10's and Aces. I'm trying to figure out how to calculate the odds if the dealers aren't allowed to peek, or only peeks aces.

In a lot of the calculations the probability was multiplied by 12/13 for 10's and 9/13 for Aces, because it was assumed that they have been peeked and no BJ. I tried removing these 12/13's and 9/13's to see what the house edge would be if no peeking rule is applied (and removed the dealer blackjack modification at the end). I ended up with a positive house edge! That can't be right, since no peeking should remove more house edge is my understanding.

What am I missing here? Besides removing all the 12/13 and 9/13, removing the dealer BJ modifier. How can I calculate the proper house edge for no peeking or only peek aces?

Thanks,
ChesterDog
Joined: Jul 26, 2010
• Posts: 997
October 6th, 2020 at 9:19:34 PM permalink
Quote: DaUmega

Hi,

In the wizard of odds excel sheet for calculating house edge for blackjack, dealer blackjacks were calculated separately because it was assumed that dealer would peek for both 10's and Aces. I'm trying to figure out how to calculate the odds if the dealers aren't allowed to peek, or only peeks aces.

In a lot of the calculations the probability was multiplied by 12/13 for 10's and 9/13 for Aces, because it was assumed that they have been peeked and no BJ. I tried removing these 12/13's and 9/13's to see what the house edge would be if no peeking rule is applied (and removed the dealer blackjack modification at the end). I ended up with a positive house edge! That can't be right, since no peeking should remove more house edge is my understanding.

What am I missing here? Besides removing all the 12/13 and 9/13, removing the dealer BJ modifier. How can I calculate the proper house edge for no peeking or only peek aces?

Thanks,

I used to make my infinite-deck spreadsheets as you want to do (not using 12/13 for 10's and 9/13 for Aces.)

The first major change in the Wizard's spreadsheet after taking out the 12/13 and 9/13 is to account for the player's non-blackjack 21's losing to the dealer's blackjack.

For example, the Wizard's EV of a player's 21 vs A is 0.90426 for H17 and 0.92219 for S17 . But for a non-peek spreadsheet the corresponding EV would be 0.31833 for H17 and 0.33075 for S17.

And the second change (assuming your spreadsheet is for "original bets only" blackjack,) the formulas for the EV of a double-down or a split must be modified to add in an extra term, which is P(BJ)*(1). So, the extra term vs Ace would be 4/13 and vs 10 would be 1/13.
DaUmega
Joined: Oct 6, 2020
• Posts: 4
October 7th, 2020 at 8:38:25 AM permalink
Thank you for the pointers, it was very helpful. I was able to adjust the stand table, H21(S21 identical) easily and matched your values given. But I'm still struggling with the double down and split tables. My understanding is that the probability of winning would be reduced overall to 12/13 for dealer Ace and 9/13 for dealer 10's.

So for the double down and split tables, I tried multiplying the column with dealer 10's by 12/13 and dealer ace's by 9/13. The overall house edge is better but still shows higher edge for no peek rules. Should it be a subtraction instead? What are your EV's after modifying them?

Thanks,
ChesterDog
Joined: Jul 26, 2010
• Posts: 997
October 7th, 2020 at 9:42:05 AM permalink
Quote: DaUmega

Thank you for the pointers, it was very helpful. I was able to adjust the stand table, H21(S21 identical) easily and matched your values given. But I'm still struggling with the double down and split tables. My understanding is that the probability of winning would be reduced overall to 12/13 for dealer Ace and 9/13 for dealer 10's.

So for the double down and split tables, I tried multiplying the column with dealer 10's by 12/13 and dealer ace's by 9/13. The overall house edge is better but still shows higher edge for no peek rules. Should it be a subtraction instead? What are your EV's after modifying them?

Thanks,

Perhaps this example for doubling 11 vs 10 will explain better.

Below are the EV's for standing for various totals vs dealer's 10:
TotalEV(stand)
210.81165
200.43496
19-0.01866
18-0.24151
17-0.46436
16-0.57578
15-0.57578
14-0.57578
13-0.57578
12-0.57578

To calculate the EV of doubling 11 vs 10, use the following formula:
EV(double 11 vs 10) = 2 * [ p(Ace)*EV(stand 12) + p(2)*EV(stand 13) + p(3)*EV(stand 14) + p(4)*EV(stand 15) + p(5)*EV(stand 16) + p(6)*EV(stand 17) + p(7)*EV(stand18) + p(8)*EV(stand 19) + P(9)*EV(stand 20) + P(10)*stand(21) ] + p(dealer has blackjack)*(1)

We can understand the last term, p(dealer has blackjack)*(1), as the dealer's giving us back one bet when he has blackjack.

The formula becomes:
EV(double 11 vs 10) = (2/13) * [ EV(12) + EV(13) + EV(14) + EV(15) + EV(16) + EV(17) + EV(18) + EV(19) + EV(20) + 4*EV(21) ] + 1/13 = 0.08894

(By the way, later you can calculate the EV of just hitting 11 vs 10 as 0.03337 for infinite decks.)
DaUmega
Joined: Oct 6, 2020
• Posts: 4
October 7th, 2020 at 11:10:54 AM permalink
Thanks again! I got these results for house edge currently:

Dealer stands on S17, DAS, SUR, peeks for both A and 10: -0.485% (makes sense)
Dealer stands on S17, DAS, no surrender, peeks both A and 10: -0.57% (makes sense)
Dealer stands on S17, DAS, no surrender, no peeks and lose all bets (not just original): -0.36% (should be lower than -0.57% instead of higher correct?)

Without the original bets rule, I assume I would just leave doubles and splits as is. If I modify it to only losing original bets, the house edge is expected to go higher up. Is there something else I forgot to compensate for?
ChesterDog
Joined: Jul 26, 2010
• Posts: 997
October 7th, 2020 at 8:04:20 PM permalink
Quote: DaUmega

Thanks again! I got these results for house edge currently:

Dealer stands on S17, DAS, SUR, peeks for both A and 10: -0.485% (makes sense)
Dealer stands on S17, DAS, no surrender, peeks both A and 10: -0.57% (makes sense)
Dealer stands on S17, DAS, no surrender, no peeks and lose all bets (not just original): -0.36% (should be lower than -0.57% instead of higher correct?)

Without the original bets rule, I assume I would just leave doubles and splits as is. If I modify it to only losing original bets, the house edge is expected to go higher up. Is there something else I forgot to compensate for?

I get your first two EV's (-0.485% and -0.57%) using both types of spreadsheets.

For S17, DAS, no surrender, and player loses all bets (not just original), I get -0.682%, which is worse then -0.57% as it should be.

And for S17, DAS, SUR, and player loses all bets (not just original), I get -0.589%, which is worse than -0.485%, also as it should be.

I can't think of what caused your third EV to be higher, but I remember two additional adjustments we have to make when using a "no-peek" spreadsheet: the EV of late surrender vs Ace or 10 is not -0.5--it's -17/26 vs Ace and -7/13 vs 10.

And of course, the EV of blackjack is not 1.5 vs Ace or 10--its 27/26 vs Ace and 18/13 vs 10.
DaUmega
Joined: Oct 6, 2020
• Posts: 4
October 7th, 2020 at 10:18:24 PM permalink
I feel like I'm so close. I made these 2 adjustments and now:
Case 1: S17, DAS, no SUR, no peek all bets lost is -0.692% (typo?)
Case 2: S17, DAS, SUR, no peek and all bets lost -0.606%

I also assume players can only split their hands once, not sure if that is what caused our minor differences.
I think there's something off with my Ace peek calculations still, for Case 1, I added peeking Ace only and I got -0.73%, which should've been an increase. Peeking 10's seem to work properly now.

So far my modifications since this post, Stand on Soft 21 row modified, Surrender table all 10's and Aces (changed from -0.5 to the values given), EV for Soft 21 against 10 and A (multiplying not just 1.5).
Some other random house edges for comparison if you want, I'm pretty sure it's only the A and 10 peeks that are still a bit bugged:
S17, DAS, SUR, peek A only: -0.644%
S17, no DAS, SUR, peek A and 10: -0.605%
H17, DAS, SUR, peek A and 10: -0.688%