Mirage
• Posts: 3
Joined: Sep 4, 2022
September 4th, 2022 at 6:34:56 PM permalink
There's a bunch of RNG games online - I know, I know - with OK rules. But sometimes, you see a particular combination:

- Single deck
- Multiple hands (at least 3)
- Min bet 1
- Max bet 500+

The claimed RTP of these games are usually in the mid-high 99's. My question is this:

Let's say I place a max bet on the leftmost hand and the minimum bet on all other hands. I then apply the following strategy:
- If I can split, split
- Otherwise, hit, even if I have a 21

Now, by my calculations, this should give me a view of the top 10 or so cards, sometimes more and sometimes less. Assuming that I use a bot to count cards perfectly and I play perfect combination-dependent strategy, what will my EV be? Losing the two small bets shouldn't factor in (I suppose I could stand on 18 and above without losing too much), and getting to see like 20% of the deck should have some non-trivial value to inform my betting.

How many hands would I have to be allowed to play simultaneously before the RTP became positive?

EDIT: Apparently, this is known as depth-charging, but I can't find any exact numbers.
gordonm888
• Posts: 5119
Joined: Feb 18, 2015
September 4th, 2022 at 8:19:02 PM permalink
I can tell you that if this were a 6-8 deck shoe that a penetration of three hands cannot be exploited by computer perfect compositional play. However, it's an interesting question with a single deck - I just don't know. A lot of times you will only be seeing 4 or 5 cards in hands #1 and #2.

Any decision to "depth charge" on the first two hands would have to be guided by the dealer's up card. For example, vs a dealer Ace there are very few hands you could be dealt in the 3rd hand that could possibly benefit from seeing more cards, only an A-8 in hand 3 and maybe an 11 (double vs hit) in hand 3.

Many of your best opportunities to change decisions due to composition changes occur vs dealer 2 - 6. Your more optimal depth-charging strategies vs 2-6 would include hitting on 12 or 13 (or higher) and not doubling on some soft 17's and 9s and some 10s. Opportunities to split are somewhat less frequent in single deck.

I don't know, I can't do this one in my head. A spread in your wagers such as 500 units on hand 3 and 1 unit on hands 1 and 2, is very extreme and outside of my experience. And combined with the use of a single deck, which is so sensitive to variations in card composition? It would require a lot of computations to form an opinion.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
ksdjdj
• Posts: 1707
Joined: Oct 20, 2013
September 4th, 2022 at 10:05:48 PM permalink
I haven't read it myself, but the book "Blackbelt-Blackjack-Playing-Martial-Art" may be helpful?
OnceDear
• Posts: 7481
Joined: Jun 1, 2014
September 5th, 2022 at 2:31:52 AM permalink
Quote: Mirage

There's a bunch of RNG games online - I know, I know - with OK rules. But sometimes, you see a particular combination:

- Single deck
- Multiple hands (at least 3)
- Min bet 1
- Max bet 500+

The claimed RTP of these games are usually in the mid-high 99's. My question is this:

I can't help with the maths, but I suspect this would be marginal at best. Remember that even if you get a half percent advantage, you need the massive bankroll to keep your risk of ruin down.

I've never seen single deck RNG. Can you point one out for me/us? I;m guessing they shuffle after each round?
Psalm 25:16 Turn to me and be gracious to me, for I am lonely and afflicted. Proverbs 18:2 A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
Dieter
• Posts: 5608
Joined: Jul 23, 2014
September 5th, 2022 at 6:03:22 AM permalink
Quote: Mirage

Let's say I place a max bet on the leftmost hand and the minimum bet on all other hands.

They let you bet asymmetrically?
Fascinating.

Suppose you plan on losing the first two hands every round, to buy information.
Is the information you buy worth 0.4%?
May the cards fall in your favor.
OnceDear
• Posts: 7481
Joined: Jun 1, 2014
September 5th, 2022 at 6:24:20 AM permalink
Quote: Dieter

Quote: Mirage

Let's say I place a max bet on the leftmost hand and the minimum bet on all other hands.

They let you bet asymmetrically?
Fascinating.

good point. Never seen that on any rng bj
Psalm 25:16 Turn to me and be gracious to me, for I am lonely and afflicted. Proverbs 18:2 A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
SOOPOO
• Posts: 11083
Joined: Aug 8, 2010
Thanked by
September 5th, 2022 at 7:28:11 AM permalink
Quote: Dieter

Quote: Mirage

Let's say I place a max bet on the leftmost hand and the minimum bet on all other hands.

They let you bet asymmetrically?
Fascinating.

Suppose you plan on losing the first two hands every round, to buy information.
Is the information you buy worth 0.4%?

LOL. That is the question the OP is asking !

We would need to know the exact ratio of the ‘big’ bet to the two ‘little’ bets. If you could bet \$.01 on the little bets and \$1000 on the big bet it’s likely worth it. If the ratio is \$500 on the big bet and \$1 on the little bets maybe not.

As little as I know about online casinos, I would think if you won using this technique I wouldn’t be confident when I tried to withdraw….
Dieter
• Posts: 5608
Joined: Jul 23, 2014
September 5th, 2022 at 8:58:40 AM permalink
Deliberately busting a 21 on a 1/500 spread would seem to cost 0.2%, so that may not be a "good strategy".

That assumes you're even allowed further action on a 21.

If you're allowed surrender, I can almost see it working.
May the cards fall in your favor.
gordonm888
• Posts: 5119
Joined: Feb 18, 2015
September 5th, 2022 at 9:34:59 AM permalink
Quote: Dieter

Deliberately busting a 21 on a 1/500 spread would seem to cost 0.2%, so that may not be a "good strategy".

That assumes you're even allowed further action on a 21.

If you're allowed surrender, I can almost see it working.

OP gave some examples of the strategies that might be used on the first two hands:
- always split a pair (maybe including TT?)
- perhaps hit until hard 18
- never double

OP didn't suggest going 'full monty' and hitting a hard 19- 21 (I'm pretty sure that no BJ game allows you to hit a soft/hard 21.)

IMO, surrender has nothing to do with this. Indeed, one of the hands that is most important to optimize on the 3rd hand is 16 vs 10, but surrender removes the possibility of exploiting 16vs10. So, surrender would be a major disadvantage towards what OP is proposing.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
gordonm888
• Posts: 5119
Joined: Feb 18, 2015
September 5th, 2022 at 9:37:33 AM permalink
Quote: OnceDear

Quote: Mirage

There's a bunch of RNG games online - I know, I know - with OK rules. But sometimes, you see a particular combination:

- Single deck
- Multiple hands (at least 3)
- Min bet 1
- Max bet 500+

The claimed RTP of these games are usually in the mid-high 99's. My question is this:

I can't help with the maths, but I suspect this would be marginal at best. Remember that even if you get a half percent advantage, you need the massive bankroll to keep your risk of ruin down.

I've never seen single deck RNG. Can you point one out for me/us? I;m guessing they shuffle after each round?

Yes they always shuffle after one round, which is the point of the discussion: is it possible to attack a 3-hand single deck game?
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
Dieter
• Posts: 5608
Joined: Jul 23, 2014
September 5th, 2022 at 11:59:55 AM permalink
Quote: gordonm888

So, surrender would be a major disadvantage towards what OP is proposing.

Surrender would appear valuable on the money hand.
I agree it makes little sense on the small potatoes hands.
May the cards fall in your favor.
gordonm888
• Posts: 5119
Joined: Feb 18, 2015
September 6th, 2022 at 3:36:56 PM permalink
I've been taking a look at the strategy of always splitting in order to reveal more cards prior to the third hand. I've been looking at the following rules: SD, S17, DA2, NO DAS, No Resplitting

Here's a strategy chart for how one would normally play pairs in such a single deck game. (Green = split, Red = hit, Yellow = Stand and Blue = Double). I've also added the EV penalty on every paired hand that is normally not split; this EV impact of splitting is shown as percentage points.

So, for example, if you split a TT pair versus a dealer 2, your EV for that hand will be reduced by 31.1 percentage points.

Altogether, this "Always Split a Pair" tactic would have you departing from basic strategy 11.3 percent of the time, and would decrease the players cumulative EV by about 4.1%. That is, the penalty for Always Split a Pair is that the overall House Edge of the game will be increased by 4.1 percentage points.

As you can see, about 80% of the additional split pairs come from splitting TT. Splitting 55 pair, instead of doubling it, will certainly reveal more cards from the deck but the ΔEV penalty when you do this ranges from -0.62 to -0.77 on those specific 55 hands.

There is very little penalty to EV for splitting these hands:
66 vs 7
77 vs 8
33 vs 2, 3, 8
22 vs 2,8
99 vs 7, A
44 vs 5

but these low penalty splits only occur with a frequency of about 1%.
Last edited by: gordonm888 on Sep 7, 2022
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.