TaylorHound
TaylorHound
Joined: Feb 20, 2022
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February 20th, 2022 at 11:22:10 AM permalink
I recently got back from a trip to Biloxi Mississippi, I really liked the city, and table conditions were... fine I guess lol. My favorite casino we went to was Treasure bay, the limits were low (even during the super bowl) and the rules seemed fine enough. However, while I was there they had what is probably the worst blackjack game or variation I have ever seen in my entire life. It's called 3 card blackjack but it seems like it has different rules than the version listed on this site.


Essentially it's a 6 deck game, you can only hit to get one additional card, Dealer also can only hit once. you can only split aces no other splits are allowed, no double downs are allowed, Blackjack pays even money, dealer stands on 16

I actually thought my girlfriend was joking when she was reading out the rules from the website. The minimum at this game was $5 and the table seemed always packed, even when there was a traditional blackjack game with a $10 limit right next to it. Does anyone know what the house edge on this game would be? It's gotta be rough.
mcallister3200
mcallister3200
Joined: Dec 29, 2013
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February 20th, 2022 at 11:58:20 AM permalink
WoO shows 3.4%. However Wizís calculations are based on a single deck; Iíve seen this game twice, both from six deck shoes.

Any blackjack game on the main floor at Golden Nugget LV is worse when played at table minimum, almost all are 6/5 and all REQUIRE a high house edge side bet. Which of course makes it not really a side bet since itís not optional.

If playing table minimum on the main game those games are in the 5% range. You can argue if playing more than minimum or lowers the house edge, but similar to an odds bet in craps it more dilutes the house edge and doesnít in any way lower the EV cost on a $ basis (in this case would increase it.)
charliepatrick
charliepatrick
Joined: Jun 17, 2011
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February 20th, 2022 at 1:59:09 PM permalink
I think there might be different games here.

The wizard's game, if I understand it correctly, is an Ante/Raise/DNQ based game where you see one of the Dealer's cards and all three of yours; there's no drawing you get to see all three of yours (and presumably so will the dealer, there's no peeking). You can use the best two or all three to make a hand, so with A5K you can ignore the 5 and make a BJ. The dealer only qualifies with 17 or more. There's a strategy and the House Edge is 3.4%
https://wizardofodds.com/games/three-card-blackjack/

I think the game being described here is different. It starts out like regular BJ but as a player you can either split Aces, stand on two cards, or draw a third (and no more). The dealer will either stand on two cards or draw a third. (I assume they hit soft 16 but not soft 17 and stand on hard 16 or more.) Interestingly the best dealer's card for the player is a "2", since they could land up stranded on a low total. Given you have to stand on three cards it seems reasonable to stand on lower soft totals than normal. Also, because the dealer may have to stand on 3-cards or 16, the chances of their busting is lower (e.g. vs 2 only if it's 2TT).
ChesterDog
ChesterDog 
Joined: Jul 26, 2010
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February 20th, 2022 at 5:14:58 PM permalink
Quote: TaylorHound

I recently got back from a trip to Biloxi Mississippi, I really liked the city, and table conditions were... fine I guess lol. My favorite casino we went to was Treasure bay, the limits were low (even during the super bowl) and the rules seemed fine enough. However, while I was there they had what is probably the worst blackjack game or variation I have ever seen in my entire life. It's called 3 card blackjack but it seems like it has different rules than the version listed on this site.


Essentially it's a 6 deck game, you can only hit to get one additional card, Dealer also can only hit once. you can only split aces no other splits are allowed, no double downs are allowed, Blackjack pays even money, dealer stands on 16

I actually thought my girlfriend was joking when she was reading out the rules from the website. The minimum at this game was $5 and the table seemed always packed, even when there was a traditional blackjack game with a $10 limit right next to it. Does anyone know what the house edge on this game would be? It's gotta be rough.
link to original post



Here's a link to the rules on the website: 3 Card

Here is picture of the splitting rules. See if you can find a funny mistake they made here.



I find that the game is actually not bad with an infinite-deck house edge of 0.628%. I assumed the dealer stands on soft 16 as well as hard 16; player's blackjack pushes the dealer's blackjack; and only the player's original bet is lost when the player splits against blackjack. Also, I assumed the player cannot hit split aces, despite the rule hinted at in the above picture.

I find the player should stand on all soft 18s. And the player should stand on soft 17 vs 2-7 and ace.

Here are my hard standing totals: 14 vs 2, 15 vs 3-5, 17 vs 7-10, and 16 vs 6 or ace.

And the player should always split aces.
charliepatrick
charliepatrick
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Thanks for this post from:
ChesterDog
February 21st, 2022 at 12:49:25 AM permalink
Quote: ChesterDog

...I find that the game is actually not bad with an infinite-deck house edge of 0.628%. I assumed the dealer stands on soft 16...

I originally assumed the that dealer hits Soft 16 and got a HE of 0.803%, but agree with 0.6279% and the strategy for s16.

The problem I'm having is that my simulations are coming up with 1.1% for no peek and 1.0% for peeking. But it's close enough to say it's a reasonable game.
ChesterDog
ChesterDog 
Joined: Jul 26, 2010
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February 21st, 2022 at 5:27:04 AM permalink
Quote: charliepatrick

Quote: ChesterDog

...I find that the game is actually not bad with an infinite-deck house edge of 0.628%. I assumed the dealer stands on soft 16...

I originally assumed the that dealer hits Soft 16 and got a HE of 0.803%, but agree with 0.6279% and the strategy for s16.

The problem I'm having is that my simulations are coming up with 1.1% for no peek and 1.0% for peeking. But it's close enough to say it's a reasonable game.
link to original post



In your simulations, is it possible you have the player's blackjack losing to the dealer's blackjack? (That would increase the house edge in an infinite-deck game by 0.224%.)
charliepatrick
charliepatrick
Joined: Jun 17, 2011
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February 21st, 2022 at 6:08:38 AM permalink
Quote: ChesterDog

...In your simulations, is it possible you have the player's blackjack losing to the dealer's blackjack? (That would increase the house edge in an infinite-deck game by 0.224%.)
link to original post

Thanks for the idea. I did cobble it together fairly quickly based on my UK (re-split) based code just to get a rough idea; so I've now had to add peeking, stop the player and dealer taking a fourth card, etc. Historically my sims tend to be within 0.02% of the expected result so suspect there's a small code bug somewhere.

Edit I have just noticed that the "How To Play" flyer you posted mentions that "A Player Blackjack ... will be paid Even Money", that would suggest the Player gets paid even if the Dealer has one (otherwise the wording could be "winning Blackjack"). However, for mathematical purposes, I'll continue assuming it's standard BJ rules so is a standoff.
charliepatrick
charliepatrick
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ChesterDog
February 23rd, 2022 at 4:41:40 PM permalink
I created a program, assuming the infinite deck strategy remained correct, to look into the combination of all the possible hands and whether they won, lost or tied assuming peeking and dealer stood on all 16s. The House Edge goes down with fewer decks. This is for six decks:
UpCardHandsWinLoseEV
1
20687229023852160
6343882542634752
12704829026137344
-0.307481803
2
20687229023852160
12425383895945472
6909791829490944
0.266618215
3
20687229023852160
12089531356436736
7286506886389248
0.232173408
4
20687229023852160
11809062601899264
7545873332104704
0.206078314
5
20687229023852160
11798225610665472
7589489122262016
0.203446120
6
20687229023852160
11318906650249728
7682924053294848
0.175759769
7
20687229023852160
10446969154169088
8560467570624768
0.091191603
8
20687229023852160
9516986892221184
9473810603626368
0.002087099
9
20687229023852160
8511202977304320
10407030800216832
-0.091642424
10
82748916095408640
28625031637069824
46368804150226940
-0.214429063
Total
268933977310078080
122885183318595840
124529527374374020
-0.006114304
charliepatrick
charliepatrick
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Thanks for this post from:
ChesterDog
February 24th, 2022 at 8:15:48 AM permalink
Finally found the bug - it was when the player couldn't draw to a soft total with 3-cards (e.g. A22); my logic to add 10 only took effect when the player had stood and it was a soft hand with a total less than 12. Normally it doesn't matter as a 5 is the same as 15, but in this game sometimes 15's can win whereas 5's can't. This quick sim (66% penetration, six decks) is only 0.01% more than the calculation, so this seem to indicate the value is correct.
UpCardHandsWinLoseBJEV
1
3,195,694
879,570
1,961,871
101,212
-.307003
2
3,197,783
1,767,314
1,069,115
152,382
.265991
3
3,198,291
1,715,072
1,127,085
153,472
.231830
4
3,200,418
1,673,920
1,167,637
152,273
.205772
5
3,194,682
1,669,048
1,172,376
152,201
.203110
6
3,196,620
1,596,344
1,186,404
152,805
.176044
7
3,194,243
1,458,455
1,322,419
152,754
.090410
8
3,193,939
1,316,915
1,462,506
152,176
.002062
9
3,191,302
1,161,105
1,605,593
152,619
-.091458
10
12,780,486
3,860,521
7,163,128
558,648
-.214699
Total
41,543,458
17,098,264
19,238,134
1,880,542
-.006242
priyank
priyank
Joined: Apr 1, 2022
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April 1st, 2022 at 2:22:08 AM permalink
Quote: ChesterDog

Quote: charliepatrick

Quote: ChesterDog

...I find that the game is actually not bad with an infinite-deck house edge of 0.628%. I assumed the dealer stands on soft 16...

I originally assumed the that dealer hits Soft 16 and got a HE of 0.803%, but agree with 0.6279% and the strategy for s16.

The problem I'm having is that my simulations are coming up with 1.1% for no peek and 1.0% for peeking. But it's close enough to say it's a reasonable game.
link to original post



In your simulations, is it possible you have the player's blackjack losing to the dealer's blackjack? (That would increase the house edge in an infinite-deck game by 0.224%.)
link to original post

Last edited by: unnamed administrator on Apr 1, 2022

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