OBO different from Peek

[NotEnoughHeat]

I think I brought up something similar when I first joined the forum but never quite received a satisfactory response.

From what I understand, OBO should be equivalent to hole card games since the important issue is whether you lose your original bet against dealer blackjack (which from what I understand is the case in almost all hole card games regardless of peeking).

However, in CVCX the sim results do not seem to agree.

I ran six sims: hole card, no peek; hole card, peek ace; hole card, peek aces & 10s; 2x OBO; 2x dealer takes all (DTA).

Each sim was 4 billion rounds which the exact same setting. 1-2x20 spread.

The following are the SCOREs:

HC: 43.89
HC-PA10: 43.78
HC-PA: 43.50
OBO2: 38.94
OBO1: 38.83
DTA2: 32.99
DTA1: 32.88

As expected OBO beats DTA. I simmed DTA because I had a suspicion that OBO was still being counted as DTA.
The disparity in results looks large enough to rule out variance between sims.

What's going on here?

[Three]

One thing that happens is you eat cards on rounds that the dealer has BJ on no hold card with any rules. That amounts to fewer rounds per shoe. I am tempted to say reduced pen but you do see the extra cards when the dealer has BJ. Having never played no hole card OBO it is hard to comment on procedures but I did play no peek OBO which amounted to the same thing. The dealer should get BJ about 1 out of every 20 rounds. If you simmed heads-up there's about 8 cards used per round if you went to 1 hand at all those rounds used 5.4 cards/round. Assuming you simmed 6 deck/1.5 decks cut off there are 234 cards before the cut card. That's only about 30 rounds per shoe. So extra cards are eaten on 1 or maybe 2 dealer BJ rounds per shoe. It might cost you a round of play on average per shoe. That doesn't seem like enough to explain the difference since if all assumptions hold true your difference in EV per round should be less than $0.5/round assuming you left the 100 rounds per hour assumption most use.

[davethebuilder]

NHC OBO means that the dealer takes Original Bets Only so the player can safely split and double without fear of losing more than their original bet. For calculations, it is the same as the dealer peeking for BJ.

[Phoebe]

What he said.
From template, try to change both "Dealer peeks" to NHC/OBO. Look at results.

[NotEnoughHeat]

Dave. While I appreciate you taking the time to respond, that didn't add anything. You might want to look at the problem in the OP again.

Philippe. The results are as posted above.

[Phoebe]

Philippe. The results are as posted above.

Yes, I know. It was a sample protocol for Dave.
And anyone who will want check the issue.

[davethebuilder]

I was just trying to clarify the playing procedure of NHC OBO for T3 as he stated he has never played under those rules. As for the OP's issue, assuming the sims were set up correctly, I do not understand why the results differ so much so I suggest you talk to Norm.

[NotEnoughHeat]

I was just trying to clarify the playing procedure of NHC OBO for T3 as he stated he has never played under those rules. As for the OP's issue, assuming the sims were set up correctly, I do not understand why the results differ so much so I suggest you talk to Norm.

Fair enough. Occasionally even I would clear things up that everyone in the thread already understood but could come off as cryptic to newcomers.

[Three]

I ran six sims: hole card, no peek; hole card, peek ace; hole card, peek aces & 10s; 2x OBO; 2x dealer takes all (DTA).

Each sim was 4 billion rounds which the exact same setting. 1-2x20 spread.

The following are the SCOREs:

HC: 43.89
HC-PA10: 43.78
HC-PA: 43.50
OBO2: 38.94
OBO1: 38.83
DTA2: 32.99
DTA1: 32.88

Okay, realizing you were talking SCORE and not EV I decided to see if I could choose something that has the same EV for peek and then cut off 8 more cards to simulate a lost round from playing a round each shoe when the dealer has BJ so it wouldn't eat 8 cards. Now this is not exactly the same because you get to see that extra cards eaten so they are not like cards behind the cut card but you will get 1 round less some of the time.

Using Hiopt2/ASC with H17,DAS rules, 6 deck/69 cut off. The c-SCORE for 2x1 unit to 2x20 units is 43.53. To get the c-SCORE to of 39.84 you need to have 4 more cards cut off, cut off 73 cards. This would all make sense if you didn't see 4 extra cards used in a round the dealer had BJ and didn't check for BJ for whatever reason but you do see those cards. The effect is like losing a round without affecting penetration I think that is a slightly different matter. The thing to consider is you lose the last round of the shoe which will have much higher average EV than the average EV per round. Factoring that in it would come close to explaining things.

[NotEnoughHeat]

Factoring that in it would come close to explaining things.

Thanks for the post. I had considered the card eating but perhaps didn't give it as much weight as I should have. I'm still surprised that there is such a difference here, but considering the spread it could make sense that differences are more noticeable.

[Skyler62]

If someone spent their entire life playing Blackjack, do you know the maximum number of hands they could expect to play? The following is just a rough calculation and should be much greater than the actual result:

Suppose someone starts playing casino BJ when they are 21 and plays every day until they die at age 100. Furthermore, suppose they play 18 hours per day and they find a game in which there are very few players so they can play one hand every minute. How many hands will they play over a lifetime? The answer is ...

60 hands every hour x 18 hours per day x 365 days per year x 79 years = 31,141,800

Why is this important? And what is the relevance to playing billions of simulations? There are several excellent discussions of the "Law of Large Numbers" in several books that show why this is important.

In my copy of The World's Greatest Blackjack book, there is a discussion on page 199 regarding the Law of Large Numbers. It is very brief although there are several other more detailed discussions in other books that are more concerned with the theory of gambling. These include:

. Blackjack Strategy Ebook
. Math of Gambling
. Science of Casino Blackjack
. Blackjack Secrets

In any case, the following is an extract from TWGBJB on page 199:

Law of Large Numbers

While a statistical percentage will converge on the theoretical, the absolute difference is likely to get larger.

It is perfectly possible, and very likely, that your losses could keep increasing in an even game. This in no way violates the statistical theory, but it does show the fallacy in waiting for a trend to reverse. The next table shows how your net losses could be getting larger and larger even though you are getting closer to the expected theoretical percentages in an even fifty-fifty game.

LAW OF LARGE NUMBERS IN EVEN GAME

Hands...Hands..Hands....%.....Net
Played...Won....Lost....Won...Loss

...10.......4.......6..........40.....2
..100......43......57........43....14
.1000.....460.....540......46....80
10000....4900....5100....49...200

I added all the "dots" into the above table in an attempt to make the colums "line up". It was difficult to do that with the forum software. So I will just try to specify all the rows and colums again using text.

In the above table there are four rows.

The 1st column is "Hands" (meaning "Hands Played"). The four rows correspond to: 10 100 1,000 10,000.
The 2nd column is "Hands Won". The four rows correspond to: 4 43 460 4900.
The 3rd column is "Hands Lost". The four rows correspond to: 6 57 540 5100.
The 4th column is "% Won". The four rows correspond to: 40 43 46 49.
The 5th column is "Net Loss". The four rows correspond to: 2 14 80 200.

Even more startling are the calculations that are shown in the following table. In an even game, you would think that each side should be ahead for about half the time (which is consistent with the idea that "things even up"). Surprisingly, this is the least likely result.

The point I'm trying to make is that we have to be very careful when assuming that running large numbers of simulations (in the billions and trillions) mean the results carry more authority. It seems like a very powerful conclusion. But the truth (according to the Law of Large Numbers) is something very different.

The example I calculated showing that someone who devoted their entire life to playing Blackjack could expect to play a maximum of about 30 million hands (the actual result figures to be seriously lower - maybe just a few million hands) and so it's dangerous to draw any conclusiong and place your money at risk by running billions of simulations because in a lifetime of playing Blackjack, the max number of hands one can expect to play is not really related to the maximum number of simulations one can run and you will likely just be left with huge errors and the results will be unreliable.

I don't know what the answer is. It is much easier to find flaws with existing ideas than it is to correct them. All I'm trying to say is, "Be careful with your money."

[Norm]

The example I calculated showing that someone who devoted their entire life to playing Blackjack could expect to play a maximum of about 30 million hands (the actual result figures to be seriously lower - maybe just a few million hands) and so it's dangerous to draw any conclusiong and place your money at risk by running billions of simulations because in a lifetime of playing Blackjack, the max number of hands one can expect to play is not really related to the maximum number of simulations one can run and you will likely just be left with huge errors and the results will be unreliable.

This is not why we run billions of hands. When we run a billion hands, we are really running 50,000 hands 20,000 times to get a more accurate result of what happens in 50,000 hands. Or, 1,000 hands one million times. The more hands we sim, the lower the standard error. But, you don't have to play anything like a million hands, much less a billion, to have a high probability of being on the right side of the curve.

[Three]

I don't know what the answer is. It is much easier to find flaws with existing ideas than it is to correct them. All I'm trying to say is, "Be careful with your money."

With the law of large numbers the results seem to converge on the expected because the denominator in the fraction makes the likely distance from expectation insignificant not that it ever reduces it. Like you get 50 straight heads to start a series of coin flips. That puts an initial bias in the sample of 50 heads. After 100 total flips that is half the flips, 50%. After 1000 the bias is reduced to 1/20th or 5%. After 10000 the bias is 1/200th or .5%. After 1,000,000 flips the bias is .005%. This is because expectation increases linearly as trials continue to accumulate while the SD increases by the square root of number of trials.