Percentage In Favor Of Dealer

BobG

New Member
Hi Folks,

I'm new to this site so before asking my beginner's question, I'd like to say hello to everyone.

Now for my question:

I have studied and memorized the correct responses to all hands and I understand that the percentage advantage to the dealer is .44% For the sake of this discussion, let's round it off to .5%

As I see it, if I play \$100 per hand, after 1000 hands I would have bet \$100,000 and I should have lost only .5% of this amount or only \$500.

In practice at this site, it doesn't seem to be working this way. I am definitely losing much more than the amount that I calculated.

Please tell me what is wrong with my logic, if anything.

BTW. The above numbers are for illustrative purpose only. I am a low roller!

Bob Guercio

Cass

Well-Known Member
BobG said:
Hi Folks,

I'm new to this site so before asking my beginner's question, I'd like to say hello to everyone.

Now for my question:

I have studied and memorized the correct responses to all hands and I understand that the percentage advantage to the dealer is .44% For the sake of this discussion, let's round it off to .5%

As I see it, if I play \$100 per hand, after 1000 hands I would have bet \$100,000 and I should have lost only .5% of this amount or only \$500.

In practice at this site, it doesn't seem to be working this way. I am definitely losing much more than the amount that I calculated.

Please tell me what is wrong with my logic, if anything.

BTW. The above numbers are for illustrative purpose only. I am a low roller!

Bob Guercio
It's called standard deviation, unless you have played 1million hands or more your short term results probably wont reflect your Expected valuation. Sometimes card counters can play months without winning money even though they have more than a 1% advantage. If you play long enough you will get to the long term EV.

ScottH

Well-Known Member
There is a way to calculate the number of hands that will take to have a good chance of being at your expected value. The mathematical term for it is N0. There was a site I went to where you can enter in your rules and bankroll and it gave you the number, but I cant remember it. It was on zengrifters list of free blackjack resources, so check that out. If anyone knows what I'm talking about, point him in the right direction.

Sonny

Well-Known Member
ScottH said:
There was a site I went to where you can enter in your rules and bankroll and it gave you the number, but I cant remember it...If anyone knows what I'm talking about, point him in the right direction.
Here you go:

http://www.bjmath.com/bjmath/refer/N0.htm (Archive copy)

There are a lot of great articles at that site so be sure to look around:

http://www.bjmath.com/bjmath/toc.htm (Archive copy)

http://www.blackjackforumonline.com/content/longrun.htm

-Sonny-

BobG

New Member
Hi Folks,

I'm back because this issue is deeply troubling to me. I strongly have my doubts that the dealer has only a .44% advantage when making all the correct calls.

In order to try to make my point again, let me give you another example and, again, allow me to round the dealer's advantage to .5%

If one wagers ten dollars per hand, with a dealer advantage of .5%, he expects to lose, on average, \$0.05 per hands. This means that, again on average, it would take 2000 hands to bust if one starts out with \$100.00.

Now I've played enough blackjack, both at this site and in casinos, to know that this is just not possible.

So what gives?

Thanks,

Bob Guercio

Sonny

Well-Known Member
BobG said:
If one wagers ten dollars per hand, with a dealer advantage of .5%, he expects to lose, on average, \$0.05 per hands. This means that, again on average, it would take 2000 hands to bust if one starts out with \$100.00.

Now I've played enough blackjack, both at this site and in casinos, to know that this is just not possible.

So what gives?
The key phrase there is "on average." Again, this is just a factor of variance. That player might only play for 100 hands before losing his \$100, or he may actually win money after playing 2000 hands! Check out the link I gave above about about fluctuations, and check this one as well:

Good and bad "luck" will come and go, but in the long run you will start to see your "average" results emerging.

-Sonny-

Canceler

Well-Known Member
Looking at it another way...

As the others have mentioned, the key words are "on average" and "variance".

Suppose you bet \$10, and your expectation is that you will lose a nickel. Disregarding the possibility of splitting or doubling down, here's what really happens:

You get a blackjack: +\$15
You win: +\$10
You push: \$0
You lose: -\$10

Notice that only one of these outcomes (pushing) is even close to your expectation. That's variance.

The number of hands you need to play to make your actual results equal your expected results is not measured in the thousands. More like millions.

Eliot Jacobson

Member
A twist of language

>The number of hands you need to play to make your actual results equal your expected results is not measured in the thousands

Your actual and expected results are not destined to be equal.

If you flip a coin, the law of large numbers does NOT say that at some future point 1/2 of the tosses will be heads. The law says that the ratio (heads)/(tosses) --> 1/2 as the the number of tosses goes to infinity (that's a calculus limit).

For example, suppose you toss a coin 100, 1000, 10000, 100000, ... times and after each of these the number of heads you got was 51, 502, 5003, 50004, and so on. Then you can see that the actual number of heads wlll get further and further from 1/2 of the tosses, while the ratio is getting closer to 1/2 (use a calculator).

The same applies to blackjack, your expected and average results can diverge, but the ratio will approach 1 as the number of hands goes to infinity.

I corrected this same error in a book I reviewed by an author on blackjack before it went to print. It is a common misconception about the law of large numbers.

Automatic Monkey

Banned
BobG said:
I'm back because this issue is deeply troubling to me. I strongly have my doubts that the dealer has only a .44% advantage when making all the correct calls.
This is something you are going to have to accept if you want to play BJ profitably. The concept of house edge with Basic Strategy is real. At an online casino one time I started with a \$100 deposit, got a \$100 bonus, and ended up cashing out \$900 using Basic Strategy play. Many other times I've lost all my money, and you always feel ripped off when that happens, as an AP approaches a game expecting to win.

There is always the possibility of a crooked game, and all bets are off if you are playing one of those. There aren't many crooked or user-corruptible software packages out there but they exist. The online gaming experts in the other sections should be able to help you with this.

Canceler

Well-Known Member
Eliot-

It's possible that I understood your post! Now let's see if I can ask an intelligent question. Is your point that whether we are playing our 100th hand, or our 100 millionth hand, we're still subject to variance?

BobG

New Member
Hi Folks,

I would like to thank everybody for their comments, recommendations and information.

I am going to keep data with respect to the blackjack computer games that I am playing and sometime in the future I will post my results so that we have something more tangible with which to discuss this most interesting subject.

Again, thanks,

Bob Guercio

Sonny

Well-Known Member
Eliot Jacobson said:
Then you can see that the actual number of heads wlll get further and further from 1/2 of the tosses, while the ratio is getting closer to 1/2 (use a calculator).
Well put. Lance Humble also mentions this in The Worlds Greatest Blackjack Book. Even though the overall ratio is approaching the expected result, the absolute difference is becoming larger.

Canceler said:
Is your point that whether we are playing our 100th hand, or our 100 millionth hand, we're still subject to variance?
That's right. Every hand you play is subject to variance. That is why short term results are often so drastic. The phrase “random walk with an upward trend” is a good description of Advantage Play. I’ve always loved Peter Griffin’s “drunkard trying to get home“ analogy. His path will be very erratic but he will always be heading towards his goal. :laugh:

-Sonny-

BobG

New Member
Hi Folks,

I have played a tremendous amount of free blackjack at this site, all in accordance with the basic strategy, and I now am going to post my data.

Allow me to first explain what I think should have happened.

The house has a .44% advantage which I will round out to .5%. Now, at each session, I've started with \$1000 and played each hand for \$100. Now, on average, one would expect to lose \$.50 on each hand (\$100 times .005) so on average, each session that starts with \$1000 should last for 2000 hands.

My data is quite different. Here is a posting of all the sessions that I have had and the number of hands I played until broke. In several cases, I did not play until broke and left with some money.

403, 143, 260,74, 67, 48, 46, 12, 79, 45, 1010 and left with \$3300, 1045 and left with \$2600, 27, 241, 509, 867, 361, 1000 and left with \$5200, 27, 38, 53, 355 and left with \$1300, 27, 277, 72, 320, 68, 196, 187, 224, 1260, 66, 458, 1003 and left with \$4300, 18, 46, 1003 and left with \$2550, 52, 1203, 69, 1547, 42, 33, and 59.

Now I never went over 2000 hands which should be the average by my logic. This is roughly equivalent to flipping 50 heads in a row with a simple coin.

What is wrong with this logic.

Thank you,

Bob Guercio

gobbledygeek

Well-Known Member
I'm not too good at math but here's my guess: you can't "guess" the length of your session (in hands) given 0.5% disadvantage playing \$100 hands out of \$1000 session bankroll; rather, you can only "guess" that after playing 2000 hands you'll on average have lost \$1000 (and that's a guess at best given this is such a small sample). For example, by your reasoning you would also say that your average game length should last 200 hands if you were placing \$1000 bets with your \$1000 session bankroll, but that is highly unlikely given that you'll bust your session bankroll 50% of the time on your first hand. Um, don't think I 'plained that too good.

I noticed your shortest games were 12 and 18 hands, lucky you! In the past couple of weeks using the same session bankroll limit (I bet \$5 a hand playing with \$50) I've had sessions of 12 (9 losses, 1 surrender, 2 pushes), 11 (9 losses, 1 surrender, 1 push), 11 (10 losses with 1 double down loss, 1 win) and 8 (8 losses with 2 double down losses). A warning for any of those thinking of using a Martingale betting progression!

Sonny

Well-Known Member
So you played 14,939 hands and lost \$24,750 for an EV of -1.66%. That may seem high, but it is certainly within the expected variance of the game. Let’s take a look at what “should” have happened.

Your EV was -0.5%, your SD was about 1.33 per hand and your bet was \$100 per hand. That gives us the following information:

EV = \$100 * -0.005 = \$0.50 (exactly as you had calculated )
SD = Sqrt(1.33) = 1.15 units

So after 14,939 hands we expect:

EV = \$100 * 14,939 * -0.005 = -\$7,469.50
SD = Sqrt(1.33 * 14,939) = 141 units = \$14,100

So after 14,939 hands you will be between -\$21,569.50 and \$6,630.50 about 68% of the time. You can also expect to be between -\$35,669.50 and \$20,730.50 about 95% of the time and between -\$49,769.50 and \$34,830.50 about 99.7% of the time. As you can see, your results are slightly beyond one standard deviation from your expectation. In reality, your results were exactly what “should” have happened.

I think you are confused because you weren’t expecting to go broke as often as you did. The reason you lost so often is because you were grossly overbetting your bankroll, which is guaranteed to make you broke even if you are playing with an advantage. The reason is that you did not have enough money to come back from a losing session. That is what Don Schlesinger calls the “premature bumping into the barrier syndrome.” I think of it more as a “crash and burn” effect. When you are having a losing streak your plane is tumbling toward the ground. If you only have 100 units in your bankroll then you will not have much time before your plane hits the ground because you are flying so close to the earth. When you are "flying high" with a large bankroll (say 1,000 units) then you have much more time to “pull up” before you hit the ground. A larger bankroll will give you more of a chance to win your money back before going broke.

Even a card counter who plays with an advantage will go broke if they are overbetting their bankroll. Here are a few examples to show you what I mean:

EV = 1.5 units per hour
SD = 26 units per hour

Bankroll Size
100 units = 64% ROR (well over a 1-in-2 chance of going broke)
250 units = 33% ROR (about 1-in-3)
500 units = 11% ROR (about 1-in-9)
1000 units = 1.18% ROR (about 1-in-85)

As you can see, proper bet sizing should be a huge concern for all blackjack players even if they are just playing for fun. If you do not bet appropriately you may end up going broke much sooner than you anticipated. That is why you were losing so many sessions even though your results were typical.

-Sonny-

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Canceler

Well-Known Member
Well, that explains it!

Sonny, your explanations are the best! I really like the plane analogy.
Sonny said:
100 units = 64% ROR (well over a 1-in-2 chance of going broke)
In BobG's experiment he was using only a 10 unit BR. That plane's definitely going to crash. Which it did, over and over.

Now I know why my plane keeps crashing whenever I play a certain \$25 table. 40-60 units isn't enough to keep me flying very long.

BUT, if I'm playing at an advantage, I'll still end up winning eventually, right? It will just be at the expense of being sent home broke a lot, correct?

ScottH

Well-Known Member
Canceler said:
Sonny, your explanations are the best! I really like the plane analogy.

In BobG's experiment he was using only a 10 unit BR. That plane's definitely going to crash. Which it did, over and over.

Now I know why my plane keeps crashing whenever I play a certain \$25 table. 40-60 units isn't enough to keep me flying very long.

BUT, if I'm playing at an advantage, I'll still end up winning eventually, right? It will just be at the expense of being sent home broke a lot, correct?
Even if you have a really high ROR, if you're playing with the advantage, in the long run you'll come out ahead.

sagefr0g

Well-Known Member
Canceler said:
Sonny, your explanations are the best! I really like the plane analogy.

In BobG's experiment he was using only a 10 unit BR. That plane's definitely going to crash. Which it did, over and over.

Now I know why my plane keeps crashing whenever I play a certain \$25 table. 40-60 units isn't enough to keep me flying very long.

BUT, if I'm playing at an advantage, I'll still end up winning eventually, right? It will just be at the expense of being sent home broke a lot, correct?
what are the rules at the \$25 table? assumming it is a 6 deck game s17 das nra with good penetration 60 units should be sufficient most of the time if you are wonging out and betting optimally. you should be going home ahead more often than going home broke.

best regards,
mr fr0g

Sonny

Well-Known Member
Canceler said:
BUT, if I'm playing at an advantage, I'll still end up winning eventually, right? It will just be at the expense of being sent home broke a lot, correct?
Yes. Your trip ROR might be high, but because you are replenishing your bankroll after each trip (when necessary) your lifetime ROR will be more reasonable and you will have more chances to return from a negative swing.

The only problem is that going broke during a trip can cause you to lose precious playing time. Instead of being at the tables earning EV you will be sitting in your room (or car) broke. Also, betting your last few chips may cause you to miss out on certain plays that require additional money, such as insurance, splits and doubles. If you miss too many of those plays then your EV will drop due to your lack of proper BS.

Other than that, there is nothing wrong with using individual trip ROR instead of an overall lifetime ROR if you have a replenishable BR.

-Sonny-