Single-Hand Sims vs. Two-Hand Play: Does Splitting Bets Impact EV, RoR, or Count Freq

[REKO_Champion]

I’ve simulated my blackjack system for a single hand, but I switch to two hands (e.g., 2x150 instead of 1x300 recommended by my sim) when the count reaches a threshold, if a spot is available. If not, I stick to one hand.

1. Does playing two hands (same total bet) reduce my actual EV compared to the sim?
2. Does it lower my Risk of Ruin (RoR)?
3. Does splitting bets this way alter the frequency of advantageous counts?
4. What if I play three hands (same total bet)?

I’m unsure how covariance between hands or seat availability impacts these factors. Insights appreciated!

[JohnGalt007]

I’ve simulated my blackjack system for a single hand, but I switch to two hands (e.g., 2x150 instead of 1x300 recommended by my sim) when the count reaches a threshold, if a spot is available. If not, I stick to one hand.

1. Does playing two hands (same total bet) reduce my actual EV compared to the sim?
2. Does it lower my Risk of Ruin (RoR)?
3. Does splitting bets this way alter the frequency of advantageous counts?
4. What if I play three hands (same total bet)?

I’m unsure how covariance between hands or seat availability impacts these factors. Insights appreciated!

What sim program do you use? If I have it then I'll look into it more deeply; I'm fascinated now. Also, I'm sure Don wrote an article or two in BJA about these very issues already, since they ring several bells, but it's late for me and I can't confirm that at the moment.

[Archvaldor]

I’ve simulated my blackjack system for a single hand, but I switch to two hands (e.g., 2x150 instead of 1x300 recommended by my sim) when the count reaches a threshold, if a spot is available. If not, I stick to one hand.

1. Does playing two hands (same total bet) reduce my actual EV compared to the sim?
2. Does it lower my Risk of Ruin (RoR)?
3. Does splitting bets this way alter the frequency of advantageous counts?
4. What if I play three hands (same total bet)?

I’m unsure how covariance between hands or seat availability impacts these factors. Insights appreciated!

TLDR Yes it lowers variance. There is a card-eating effect which is largely cancelled out by the reduced variance. Three hands is usually overkill.

EDIT: I misread: I thought you were spreading to a higher dollar amount and you aren't. See Freightman and Gman comments below.

If these questions are important to you then you need BJA where this type of thing is discussed in detail.

This assumes that you play your hands independently of each other, it gets more complicated if you consider the co-variance between specific hands and adjust playing decisions accordingly.

[Freightman]

When you’re in a positive count with $300 at risk, then splitting to 2x150 - not good. Same amount of money at risk and chewing up more good cards getting to the cut card faster. You’re getting less money out resulting in less EV. The magic number for covariance purposes is 75% of $300 or $225.00 for each 2 hands. This of course assumes a non heads up situation.

When heads up and you’re not butting up to table max, stick with 1 hand. So, on your formula

1. yes
2. you’re not betting optimally, that’s for sure. Not sure, I would think you’re increasing ROR as you’re reducing the number of positive hands available to overcome your waiting bets.
3. you wouldn’t alter the frequency of positive counts, but you are abusing that frequency
4. even uglier

[G Man]

For 2. You're not betting optimally, so you don't get the full EV you're entitle to by betting 73% (or rounded to 75%) more, however you reduce you're risk.

[REKO_Champion]

@Freightman, Is the opposite also true? Meaning that if my sim tells me my min bet is 100 hypothetically, if I bet 2x50 instead of 1x100 during neutral and negative counts, does that "increase" my EV somehow even though I'm playing the same amount because I'm "eating up" the bad cards faster? That would be mind boggling to me.

[DSchles]

So, it was fun reading all the above: different takes on various aspects of your questions. To resume--and possibly add a thing or two:

1. Betting the same amount of money per round, but spreading over two (or more) hands, will, of necessity, lower your hourly EV, because you're betting the same amount per round, but will receive fewer rounds per hour.
2. Yes, it lowers your risk of ruin, because, per round, your EV is the same, but the variance is reduced. As ROR is a function of the two, if you keep the EV the same but decrease the variance, the ROR decreases.
3. No, the frequencies of the counts are the same, but you're getting fewer good counts per hour. Obviously, you're also getting fewer bad counts per hour, but you're betting more on the good counts.
4. As Freightman points out: all of the above, but worse!

Don

[Freightman]

@Freightman, Is the opposite also true? Meaning that if my sim tells me my min bet is 100 hypothetically, if I bet 2x50 instead of 1x100 during neutral and negative counts, does that "increase" my EV somehow even though I'm playing the same amount because I'm "eating up" the bad cards faster? That would be mind boggling to me.

Eating up high cards faster at no additional outlay has merit, provided your simmed minimum equals table minimum. Clearly, since you can also bet $50 and if that is also table minimum. why not reduce to 1 square of $50. In negative counts, you would only be risking 1x50 vs. 2x50 or 1x100. Remember, you got up to 1x300 before you dropped to 2x150. Unless there is something I’m missing, your approach is flawed.

Question - if $50 is table minimum for 1 square, then, is table minimum for 2 squares 2x50 or 2x100. Consider your bankroll size when consudering other sims. If the former, then think about playing 2 squares all the time or 1 square starting at $100, ramping upwards in higher counts. Goatlife, who used to post here, played this way at high stakes.

I have various approaches. Consider a heads up $25 min table. I may start off at $25 or I may start off at $50. If I start at $25, then a gradually ramped betting approach will produce a SCORE of x. If I start off at $50, I will ramp upwards on that $50 as count increases. If count drops to let’s say to, -2, then I will drop to $25. This produces a SCORE of x - some dollars depending on my ramp and to my way of thinking a highly effective strategy despite the drop in SCORE.

In summary, your approach is flawed and I would experiment with CVCX.

[DSchles]

@Freightman, Is the opposite also true? Meaning that if my sim tells me my min bet is 100 hypothetically, if I bet 2x50 instead of 1x100 during neutral and negative counts, does that "increase" my EV somehow even though I'm playing the same amount because I'm "eating up" the bad cards faster? That would be mind boggling to me.

Sometimes, in math, doing what we call a reductio ad absurdum argument--reducing to the absurd--helps to grasp a concept more quickly. Suppose you're playing an eight-deck game and have a very bad count with about two decks of the shoe already dealt out. So, you decide to bet your 100 dollars by spreading to 100 hands of $1 each (absurd, but humor me). You have only $100 at risk, and, by the time you're done playing all of the hands, the stop card appears and the shoe is over! Do you suppose that's better than playing one spot for $100 a hand until the shoe expires?!

I don't know why this would be mind boggling to you, but it obviously would be the way to go, no?

Don

P.S. I answered while Freightman was posting, so missed the above. His advice is solid, but I simply answered the exact question you asked without offering further recommendations.

[Freightman]

Or I would wong out if the count drops to say, -2 and then table hop. It is just me with my wong in and wong out style. @REKO_Champion but find the optimal wong in and wong out point for the count systems you are using.

A couple of comments
1. You need other tables to go to. If not available, then you should rely on your knowledge of negative indices.
2. I play negative counts all the time - no big deal. What does annoy me are the table crashing graduates of the Colin Jones School of Robotics playing their silly games.

[REKO_Champion]

Sometimes, in math, doing what we call a reductio ad absurdum argument--reducing to the absurd--helps to grasp a concept more quickly. Suppose you're playing an eight-deck game and have a very bad count with about two decks of the shoe already dealt out. So, you decide to bet your 100 dollars by spreading to 100 hands of $1 each (absurd, but humor me). You have only $100 at risk, and, by the time you're done playing all of the hands, the stop card appears and the shoe is over! Do you suppose that's better than playing one spot for $100 a hand until the shoe expires?!

That's a good example. Yes, I believe playing 100x$1 would be better than playing 1x$100 in a really bad shoe. Thanks for the explanation. Please forgive me, I'm still new to theory in my beginning career for asking obvious questions.

So if you're playing heads up, ideally the best way to play is play 2 hands during -EV hands, and play one hand in +EV hands. Is that correct?

[Freightman]

That's a good example. Yes, I believe playing 100x$1 would be better than playing 1x$100 in a really bad shoe. Thanks for the explanation. Please forgive me, I'm still new to theory in my beginning career for asking obvious questions.

So if you're playing heads up, ideally the best way to play is play 2 hands during -EV hands, and play one hand in +EV hands. Is that correct?

Your roll is likely weak. Answer - no. Just play 1 square for now.

[peterlee]

Suppose that n cards are used per hand, for both the player and the dealer.

-EV hands, where you dislike the cards, you'll need to buy them out.
With one hand, you're dealing with 2n cards, split one for you and one for the dealer. The dealer pays out the same as you.
With two hands, it's 3n cards: two for you, one for the dealer. You're paying twice what the dealer pays out. So, this is a bad deal.

+EV hands, you want to get the most profit from each card. That means using the fewest cards possible in a round.
(Or even use "less card strategy" (is there such a strategy in the market?), surrender/double down/stay/not split when you have to calculate the TC and not easy to make decision.

Two hands requires 50% more cards, but it also allows for a 50% increase in the wager, resulting in a relatively small difference.

But with one hand, the count can shift after each round, letting you bet based on the new count. This makes one hand seem better.
Some exceptions:
You can bet more then the table maximum.
Or you know that it is the last round before shuffle.
Or it is not a heads-up.