Anomaly?

[toolman1]

Voodo math or misplaced logic

what this means is that with a sequence of ten or more hands - you can play tbj and use the expected probabilities you are used to seeing in live bj - there will be more variance - but you are just as likely to drift towards favoring the player as the dealer - and vice versa - in short sequences - this is not the case -

for eight hand or fewer sequences - in somewhat more than 1/2 the sequences - the probability skewing favors the players - and the players will have a positive ev for the sequence - in somewhat less than 1/2 the sequences - the probabiliities skew towards favoring the dealer - and the players will face a negative ev worse than expected -

thus in eight hand sequences - you will get - more often than not - results favoring the players - the dealer dumps chips - and aggressive betting will be rewarded - and in the minority of sequences - the dealer will take down the players hard - exactly what you see in ebj -

Let me start off by making one thing perfectly clear (sounds like Nixon), I am not a math guru so I can't dispute your calculations because I don't have the math background to do so. That being said, I'm having difficulty justifying your conclusions when applying the fact that 1) the house has 0.5% advantage (unless you count cards) at all times and 2) the probability outcome for any given hand is: 44% player wins, 8% pushes, 48% house wins.

First paragraph quoted above:
Since the house has a mathematical advantage, seem to me that the "drift" favors the house. I guess what I'm saying is that since the house will win more hands, over the long term, I can't see how the "drift" can be equal between the player and the house.

Second and Third paragraphs quoted above:
You say the player has a positive EV in 8 hand sequences. Sorry, but this makes no sense to me. Let's say I play 800 hands in a trip to my local casino but divide that into 100 separate sittings so I play 8 hands per sitting. Since you are saying I have a positive EV for the first 8 hand sequence then I should win, the majority of times, over the course of playing 100 separate sittings by simply flat betting. If I do this over a whole year then I should have enough to retire (oops, I'm already retired) but we both know that will not happen.

Now I know you have repeated this same theory/logic in several other threads. However, until you or another math guru can prove, in math and/or logic that the average person can understand, how the house loses it's advantage in a short sequence, then I am of the opinion that your math and/or logic is faulty.

 

[Angel]

the problem is not in the cards - they are behaving exactly as the probabilities project - the problem is in your expectation of what those probabilities are - the players on this site are pretty experienced and know what bj probs are - for the live game - and in tbj - which is a long sequence - at least 15 hands for a typical tbj table - in ebj - you have short sequence probabilities - as only 7 or 8 hands separate the elimination hands - so experienced players are playing the wrong probabilities - and the inexperienced ploppies with their aggressive betting are playing it right - they are taking advantage of the fact that at the majority of ebj tables - the first sequence of hands - leading to the first elimination hand - favor the player -

yea

 

[Monkeysystem]

the probability functions for bj are discrete distributions - that means only whole numbers, integers - while the expected frequency of stiffs in an eight hand sequence may be 3.4 stiffs - you can't have 3.4 stiffs - you can have 3 - or you can have 4 - but there is no such thing as .4 stiffs

Getting a stiff isn't the only way for you to lose. Nor is it a guarantee that you'll lose. Rounding down the expected number of stiffs in an eight hand sequence should not imply you've got a better chance of improving your bankroll in an eight hand sequence than you do in a longer sequence.

However, your arguement does have some validity for other reasons.

If you're flat betting and playing BS your chance of improving your bankroll in an eight hand sequence is much better than in, say, an 8,000 hand sequence. This is because of variance.

An aggressive bettor is counting on this variance to grab a lead, then use correlation betting to defend it. This is a common strategy, and a particularly tempting one after a series of losses in which dealers dumped and your catch up bets failed.

But you're not trying to win a series of independent eight hand sequences. You're trying to win an entire tournament. You will have to place a bet in each and every one of dozens of hands of blackjack. Your starting bankroll is a max bet (in EBJ) and your bankroll is reset to a max bet several times at roughly even intervals through the tournament. This is all occurring in a game where the mathematical expectation is for the dealer to take your bet more often than paying you your bet.

You have to get lucky to win a tournament. If you're conservative this means not having a dealer dump. If you're aggressive this means not having a dealer get hot. In a game where the dealer wins more than the players this means the conservatives have a better chance of getting "lucky" than the aggressives.

 

[London Colin]

RKuczek,

I wish you would have responded to the points Ken raised when you first put forward these ideas - https://www.blackjacktournaments.com/posts/21640, rather than go silent and then just reassert the same ideas here, as if they had never been questioned.

First paragraph quoted above:
Since the house has a mathematical advantage, seem to me that the "drift" favors the house. I guess what I'm saying is that since the house will win more hands, over the long term, I can't see how the "drift" can be equal between the player and the house.

Second and Third paragraphs quoted above:
You say the player has a positive EV in 8 hand sequences. Sorry, but this makes no sense to me. Let's say I play 800 hands in a trip to my local casino but divide that into 100 separate sittings so I play 8 hands per sitting. Since you are saying I have a positive EV for the first 8 hand sequence then I should win, the majority of times, over the course of playing 100 separate sittings by simply flat betting. If I do this over a whole year then I should have enough to retire (oops, I'm already retired) but we both know that will not happen.

Now I know you have repeated this same theory/logic in several other threads. However, until you or another math guru can prove, in math and/or logic that the average person can understand, how the house loses it's advantage in a short sequence, then I am of the opinion that your math and/or logic is faulty.

While I am firmly in the unconvinced camp, and certainly far from guru status, I think I might have grasped the points being proposed. If I understand correctly, then -

1st Para: means that for ten hands or more the probabilities are 'normal'. On such a short sequence you can get a wide divergence from the expected results (like Tex was recently whining about ), but the dealer and player are equally likely to benefit from such fluctuations. The 'drift' in this context is a drift away from the norm, and the norm is indeed the usual house edge.

2nd/3rd Para: means that for eight hands the actual results favour the player more often than not (because you get three stiffs more often than you get five). However, that wouldn't affect the overall EV, even if you consider your BJ career as a series of 8-hand sequences, because on average when you lose a sequence you lose more heavily than when you win one. A good analogy might be with the martingale which is useless in the long run, but gives a high probability of a short-term profit.

I think part of the problem may be that EV is perhaps the wrong terminology for the effect that is being described. In a three-step progression you have an 86% chance of success, but your EV is no different to what it is at any other time; similarly your EV going into a sequence of eight hands must surely be the same as at any other time, but (according to the theory) just as with the martingale that EV is composed of a high probability of a small win balanced against a low probability of a big loss.

(Apologies RKuczek, if I've misinterpreted your words.)

It's the assumption that less stiff hands (for player and dealer alike) means more winning hands for the player that looks to be suspect, as Ken and Monkeysystem have pointed out.

 

[toolman1]

I see what I missed

It's the assumption that less stiff hands (for player and dealer alike) means more winning hands for the player that looks to be suspect, as Ken and Monkeysystem have pointed out.

After studying and rereading over and over I have to concur with London Colin's response.

 

[RKuczek]

London interpreted my post right

I don't have my home computer with me - am up in Laughlin area on a business trip - so don't have all my stuff I used to analyze probs -

but - hypothetical example - purely for illustration - when the probabilities skew for short sequences - it does not change the long term odds - if you track results over many eight hand sequences - the cummulative result will reflect the expected probabilities - but what happens is: example - in 55% of eight hand sequences - the player will have an ev of +1.5% - in 45% of eight hand sequences - they player will have an ev of -2.9% - those numbers may actually be fairly close to correct - and all the probabilities will skew off - not just the prob of getting a stiff - as I remember - not having the spreadsheets and data with me - as I plotted out the functions - the skewing seemed to generally favor the player - consistently - in short sequences - the result - is more extreme results - more often - but they average out - over the long run - and the long run would include a 30 hand table - the issue is that if the first eight hand sequence in ebj favors the player more than 1/2 the time - aggressive betting early will benefit you more often than not - and you need to adjust your play to deal with this - as the wild cat betters will tend to pile up chips - too aggressive betting will hurt you badly - when you get an extra negative sequence - these are tendencies - but occur with enough frequency that experienced players have noted them -

my approach is to bet more aggressively - but to use a risk adverse playing strategy - fewer doubles - double for less when I do - very few splits - and surrender many more hands -

problem is - even when I bet aggressively - I still can't go with the wildcatters who are putting out half their bankroll on the first bet - that's just too nuts even for me -

I think there is a general problem in tbj/ebj - of people trying to apply live bj probs to tbj/ebj - fine for single hands - like final hand probs - but the goal is not to max ev - it is to win the table - which is entirely different - we need probs for TABLES and HAND SEQUENCES - not individual hands - or infinite sequences of hands - to develop effective strategies

 

[toolman1]

Theory still defies logic

RKuczek,

OK. We have the correct interpretation of what you said so let's get to the meat. In the interest of easy reference I quoted only the relevant parts of your last post. I don't believe this resulted in any change of your intended meaning:

example - in 55% of eight hand sequences - the player will have an ev of +1.5% - in 45% of eight hand sequences - they player will have an ev of -2.9% - those numbers may actually be fairly close to correct - and all the probabilities will skew off - not just the prob of getting a stiff ... ... the skewing seemed to generally favor the player - consistently - in short sequences...

This is where I have a real problem. Assuming no card counting, the moment before the cards are dealt, the player outcome probabilities for the hand are: WIN=44% , PUSH=8%, LOSS=48%. These probabilities hold true whether it is the 1st hand out of a shoe, the last hand out of a shoe, or anywhere in between. In other words, the dealer has the advantage on every hand. Since the dealer has the advantage on every hand, it is illogical for the player to have an advantage on any sequence of hands be it 2, 5, 8 or whatever. Or to restate:

Given: Before the cards are dealt, the dealer has the advantage on every hand.
Therefore: Before the cards are dealt, the player never has the advantage.

Now I'll restate what I said in an earlier post:
Let's say I play 800 hands in a trip to my local casino but divide that into 100 separate sittings so I play 8 hands per sitting. Since you are saying that the skewing effect results in me having the advantage for the first 8 hand sequence then I should win, the majority of times, over the course of playing 100 separate sittings at 8 hands per sitting by simply flat betting. If I do this over a whole year then I should have enough to retire. Now you can't seriously think that this will happen, do you? If so, then you have just made the most gigantic discovery in blackjack history. Everyone, including ploppies, can now win at blackjack, that is until the casinos remove the game completely from the floor.

In summary: I can't believe that what you are saying can possibly be true - it is, as Spak would say "illogical".

 

[RKuczek]

toolman1

this is the critical distinction - you are looking at the odds for each individual hand - I am looking at the odds for a sequence of hands - we are dealing with different worlds of probability here - the odds on each hand don't change - but the odds for a sequence depends on the number of hands in that sequence - for sequences of 10 hands or more - you can play with normal probabilities - for eight or less - you need to take into account the effect of the probability mass function being asymetrical -

I know that is math talk - but it is the essence of the difference between tbj and live bj and ebj - you can't - or shouldn't - play ebj/tbj using your expectations from live bj - because probabilites for short sequences differ from the probabilities for long sequences - if you are trying to win the final hand - go with the probabilities that you are familiar with from basic strategy - if you are trying to gain the best possible advantage in the early and mid hands - so you go into the final hands in a good BR position - you need to work with sequence probabilities -

the bottom line I think - is that the 'anomalous' results in the first eight hands of an ebj table that people have seen - over and over again - is real - and that reflects the short sequence probability skewing - so is 'normal' for these short sequences - so we need to adjust our play to use these skewed results to our advantage - because they happen

 

[toolman1]

Theory still slaps logic in the face

Still not convinced. If your theory is correct then you should be able to apply that theory to live BJ and win all the money you will ever need. I'll repeat what I said before:

Let's say I play 800 hands in a trip to my local casino but divide that into 100 separate sittings so I play 8 hands per sitting. Since you are saying that the skewing effect results in me having the advantage for the first 8 hand sequence then I should win, the majority of times, over the course of playing 100 separate sittings at 8 hands per sitting by simply flat betting. If I do this over a whole year then I should have enough to retire. Now you can't seriously think that this will happen, do you? If so, then you have just made the most gigantic discovery in blackjack history. Everyone, including ploppies, can now win at blackjack, that is until the casinos remove the game completely from the floor.
​

And you answer to that is...???

Why not post your calculations so the math gurus on this site can analyze them?

 

[Reachy]

Yeah but...

How can I apply it to my TSS?

Cheers

Reachy

 

[KenSmith]

Question for RKuczek:
Let's say we play 8 hands, starting with $1000 bankroll.
Who will have the larger average bankroll afterwards? A $5 flat-bettor, or a $100 flat-bettor? Play the hands using any strategy you like, as long as they both play the same way.

 

[London Colin]

Let's say I play 800 hands in a trip to my local casino but divide that into 100 separate sittings so I play 8 hands per sitting. Since you are saying that the skewing effect results in me having the advantage for the first 8 hand sequence...

Overall, I'm unconvinced too, but the above is not what I understand RKuczek to be saying. His assertion is that a sequence of eight hands is more likely to be a winning one than a losing one, but you lose more in the losing sequences than you win in the winning ones.

example - in 55% of eight hand sequences - the player will have an ev of +1.5% - in 45% of eight hand sequences - they player will have an ev of -2.9%

As I said, I think EV really isn't the right term here and is causing some confusion all round. You don't know in advance whether the next sequence of eight hands will be one of the 55% or one of the 45%; the expected value is the same for one hand, eight hands or any other number of hands.

What I assume you are saying is that there is a 55% probaility of a +1.5% return over the next eight hands and a 45% chance of a -2.9% return, giving an EV of around -0.5%.

I'm doubtful, though the mathematics is somewhat beyond my abilities. I would suggest that a simulation is probably the only way to resolve the question. Any amount of convincing theorising could miss some subtle effect, but gather a few million actual results and the answer should be incontravertable.

 

[toolman1]

London Colin,

You are reading more into my comment than I intended or thought about. We are both of the opinion that the theory is flawed unless proved otherwise. So let's leave it at that. The ball is in RKuczek's court to produce some proof of his theory. It's interesting that you suggested a simulation. Just before I logged in here I was thinking the same thing. I have a very good and versatile simulator, CVData (same people that make Casino Verite Blackjack). I'm going to run a simulation tonight (after I pack up the garbage for tomorrow's pick up) and will post the results then.

Reachy,

This is beyond TSS, sorry. It's even Beyond Wong.

In the meantime I am interested in RKuczek's response to my last post and Ken's inquire. Not sure exactly what he has in mind but I want to find out.

 

[S. Yama]

Anomally

There are situation when a player of blackjack game may possess additional information about composition of cards from which the next hand or hands will be dealt, and/or information about changed chances of upcoming, either his or dealer’s cards, differentiating from the statistical norm. This can be obtained through various legal techniques like counting, shuffle tracking, card steering, getting a glimpse at cards due to a sloppy dealer, etc, and various forms of illegal acts, which we as a community - condemn. Even simple fact of knowing outcomes of prior hands, without seeing the specific cards can help assess minimally changing expected values of the following hands – but this is beyond the scope of this thread.
Here we are talking about changed EV for blackjack hands in a short series of consecutive hands (eight or so), and to a smaller degree its usefulness in blackjack tournament of EBT type.

Before I try to present more technical analysis I would like to express my compliments to RKuczek for bringing in and applying his mathematical knowledge. All the mathematical elements (in my somewhat limited expertise opinion) used here are correct and supply the necessary “thruthiness”. Our differences come in individually drawn conclusions.
So, let’s move into more meaty parts.

As many contributors to this thread noted, the final conclusion that because of “random walk” playing short series of hands can obtain positive expectation in a game where statistical hand has a negative expectation seems unreal.
It could be simply rebuked by an axiom that series of bets each of which has negative expectation, must result in expected loss, no matter how they are chosen, partitioned or combined.

As to the specifics, RKuczek noted correctly that we are dealing with discrete distribution, and should use binomial distribution, as we can only win, push, or lose a bet (and deal with the bet whole integer multiplier, plus some half bets for surrender and blackjacks). The fact that a stiff hand occurs (I am using cited statistics) 42.7% of the times, means that it should happen 3.418 times per series of eight hands. Since in real life we can’t have fractional number of stiff hands we will have zero, one, two, and so on, up to eight stiffs in a series. Most frequently we will have three stiffs – that’s correct. There are important mathematical aspect of it but we could trivialize it that this is due to rounding to whole numbers. But it does not mean that in any particular series we will get three stiffs or less. Statistically (and that’s the important part) we will get stiffs 3.418 times and the EV is not changed. The fact that occurrence of only three stiffs, which is less than the average, is dominant does not change the EV, as it is balanced out by occurrences of four and more stiffs per series, together with even more beneficial occurrences of two or less stiffs.

Perhaps it may be helpful to look at corresponding but somewhat simpler example using black and white balls.
We will be drawing from the box containing infinite number balls in which for every three white balls there is one black ball.
In blackjack game we consider stiff hand as a negative expectation – that will be picking a black ball. Hands other than stiffs, for our purpose, we consider as positive expectation – that will be white balls. We talked about series of eight hands, for ball drawing game let’s have series of just two picks.
Each drawing is a bet of $100, by drawing a black ball we lose, but picking a white ball wins net of $32.
[-100+3x32]/4=-1 The Expected Value for each drawing is minus one dollar – Disadvantage of 1%, like in a bad rules blackjack game, or a ploppy’s game.

Does anyone can think that this game can be turned into a winning series?

The chance of picking up black ball is 25% for each drawing. When we look at binomial distribution for two trials we have for black ball: exactly zero = 56.25%, one time = 37.5%, and exactly two times = 6.25%
Picking zero black balls in a series of two drawings is the dominant occurrence.
If we calculate value for two drawings .5625 x $64 + .375 x -$68 + .0625 x -$200 = -$2
This confirms EV of -$1 per drawing.

Comparison:
..........................................Series...average....in series....dominant...offered conclusion
A stiff hand (negative value)..... 8 ........ 0.427 ........ 3.4 ....... 3 ......... less disadvantageous occurrences?
Black ball (negative value) ....... 2 ......... 0.25 ......... 0.5 ....... 0 ......... less disadvantageous occurrences?
Answer: No change in advantage.

The same remains true for games with much bigger disadvantage. We could use in our example that picking black ball cost us $100 and picking white ball wins just one cent. Still the most common occurrence in series of two drawings would be zero black balls but it would be wrong to conclude that game of e.g. almost 100% disadvantage can be look up as a positive game.

There are aspects where in spite of negative EV, increasing of betting can be turn into overall positive/increased expectations; One is in tournament situations and the other is by using progression betting, but both require a special set of coexisting circumstances.

More later,
S. Yama

 

[toolman1]

A simulation to consider

S. Yama, nice to see you posting again. Your insights on this matter are, as usual, above and beyond.

I have been busy this evening running simulations to support my position on this subject and I'd like to present them here for information/discussion. I ran simulations to find out if the first 8 hands dealt out of a shoe produced a player advantage as RKuczek believes it does.

The parameters I set for the simulation are:
Cut card was placed to cut off 146 cards (out of a 6 deck shoe). The simulator will not allow a re-shuffle after 8 hands are dealt so I had to do some innovating. I figured the theoretical number of shoes dealt (8 hands per shoe) should be 31,250,000 (250,000,0000 / 8). Then I experimented with the cut card until I came close to the 31,250,000 shoes. In reality, the computer dealt out 31,101,159 shoes. In my efforts to tweak the cut card to as near theoretical as possible, I found the house advantage stayed within a narrow range so I concluded the cut card placement contributed no significant part in altering the house advantage.
Number of decks: 6
Total number of players: 7
My seat number: 1
Number of hands to be dealt: 250 million
Burn cards: 1
Split up to 4 hands for card values 2 through King
Split up to 2 hands for card value of Ace
If Aces split, only receive 1 card on each Ace – no Double Down permitted
Any 2 “Ten Value” cards can be split i.e. a Jack and a King can be split
Double Down permitted after split except split Aces
Double Down permitted on any 2 card hard or soft total
No surrender
Never take insurance
Dealer stands on soft 17
Blackjack pays 3:2
Flat Bet $1
Shuffle type: Random (as opposed to casino shuffle)

Now the results:
Simulation gave the house advantage as 0.425%
Wizard of Odds says that with the parameters I detailed above, the house advantage is 0.403115%
I cannot account for the difference between my simulation and the Wizard of Odds. For our purposes, the difference is insignificant.

My Conclusion:
In the long term, playing only the first 8 hands out of a shoe produced no significant change in the house edge. Any “skewing” apparently works both ways and they cancel each other out over the long term. Therefore, making larger bets on the first eight hands will result in the same losses that will occur if the same bets were placed on any other series of hands over the long term.

RKuczek, your comments please.

PS: I’ll be glad to rerun the simulation with changed parameters but it won’t produce any significant change in the house edge.

 

[RKuczek]

toolman

you're still not seeing it - while you will have the ev in your favor in more sequences than you expect - from the base single hand probabilities - when the ev is negative - it is enough negative that the ultimate result is a negative ev -

here are the probabilities of receiving stiffs (defined as 12-17) in a seven hand sequence - that I posted before on another thread - I used a seven hand sequence because there are seven hands before the first elimination hand - and it is very important to go into the first elimination hand with a good BR position -

# of stiffs Probability

0 0.02799
1 0.13064
2 0.26127
3 0.29030
4 0.19354
5 0.07740
6 0.01720
7 0.00164

71% of seven hand sequences will vary significantly from the expectation - and when they vary - they are 1.449 times as likely to vary in favor of the player - the player receiving fewer stiffs than expected -

in the 41.99% of hands where the player receives significantly fewer stiffs - the player will get 1.555 stiffs, on average - while in the 28.98% of sequences where the player receives significantly more stiffs - the player will receive 4.40 stiffs, on average -

The most common result - three stiffs - is slightly more negative than the calculated expectation - but close enough that the difference would not be extreme - the problem is that extreme variance is more common than not

the probabiliities are that the hands in a seven hand sequence will skew significantly either towards the player or against, 71% of the time - and when they skew - they skew in favor of the player much more often - since stiffs have such a heavy negative ev - reducing the number of stiffs by 1 1/2 in a seven card sequence - or increasing by that number of stiffs - will produce a major swing in the ev of the sequence -

and when it favors the player - it will produce a significant positive ev for the player - simply from the variance in the proportion of hands received which are stiffs -

I don't have the numbers for eight hand sequences available to me right now - but since the expectation for stiffs in an eight hand sequence would be a little above 3 stiffs per sequence - the skewing over eight hand sequences would be more extreme - so including the elimination hand just makes the variance more extreme and more favorable to the player -

this is not some change in the expected probabilities for each hand dealt - just the opposite - it is the result of those probabilities when they are realized in a short hand sequence - in a long sequence of hands - such as a 30 hand table - or an evening of live bj - you'll see the over all probabilities you expect - over time - but if you tracked seven or eight hand sequences within that longer sequence - you'll see the results in the table above

conclusion - you are better off more of the time with aggressive betting before and through the first elimination hand than with conservative betting -

 

[KenSmith]

It's late, so I'm going to make 2 brief comments/questions...

1) I recommend replacing your "number of stiffs" metric with the only metric that really matters: the net gain or loss in units after 7 flat-bet hands. This table would contain all cumulative result values from -56 units to +56 units. (To win 56 units, you'd need to split and make 4 double-down hands every time for 7 consecutive hands.) Let's see the associated probabilities of each of those outcomes, and we can ascertain the real probabilities of interest.

2) The concept I'll dub "preservation of EV" means that if we were to have an increased probability of favorable outcomes, then that increase must be offset by the magnitude of the negative outcomes, since we know the weighted sum must still equal the house edge.

If I haven't been clear in these, let me know and I'll elaborate tomorrow.

 

[London Colin]

Thanks to S. Yama and Ken for adding some extra elumination to this murky subject

Toolman,

If the software allows it, what you could try is to partition your record of 250 million dealt hands into groups of 8. (The hands don't necessarily have to have been played sequentially, any unique group of 8 will do.)

For each group of 8, you can then apply a test to see if it gave a better or worse return than one would expect overall. You could use Ken's idea of recording how many groups yield each possible number of units, or maybe you could calculate the apparent EV* for each group and record whether it is above or below the known EV for the game (and then, having thus partitioned the groups into two sets - the overs and the unders - calculate the apparent EV for each of these two sets.)

If RKuczek is right, you will discover an asymmetry - more overs than unders (and moreover, the apparent EV of the overs will in fact be positive.)

There would then be the separate question of whether the phenomenon is significant enough to warrant aggressive betting in EBJ (or I suppose whenever you are faced with <=8 remaining rounds?).


[* I've used the term 'apparent EV', to try to get away from the confusion. 'Actual Value' might also be a good term to use?]

N.B. I just noticed that we've shifted to talking about groups of 7 hands, rather than 8. The above calculations could be carried out with groups of various sizes to see if an effect can be found.

 

[London Colin]

Theory

The most common result - three stiffs - is slightly more negative than the calculated expectation - but close enough that the difference would not be extreme - the problem is that extreme variance is more common than not

the probabiliities are that the hands in a seven hand sequence will skew significantly either towards the player or against, 71% of the time - and when they skew - they skew in favor of the player much more often - since stiffs have such a heavy negative ev - reducing the number of stiffs by 1 1/2 in a seven card sequence - or increasing by that number of stiffs - will produce a major swing in the ev of the sequence -

As has already been said, I think a simulation of actual hand win/lose outcomes is the only way to get to the bottom of this.

However, regarding the theory aspects, Ken pointed out that the dealer will be just as affected as the player by any skew in the probability of receiving stiffs. It occurs to me also that the dealer is hurt more by receiving a stiff than the player is, since the player can stand but the dealer cannot.

So wouldn't a reduction in the proportion of stiffs received benefit the dealer more than the player?

 

[toolman1]

London Colin,
Unfortunately, simulation software does not provide for the type of analysis you suggested. The best I could do is what I did - do a shuffle after each 8 hands to simulate beginning playing at a new table every 8 hands.

RKuczek,
Much of what you are saying is beyond my math background to comment on with any intelligence. So I'll leave such comments to others such as Ken Smith, S. Yama, and others that may want to join in. But there is one thing I'd like to say.

You keep talking about the "skewing" effect of stiff hands. That seems to me to be unimportant. The important thing is if you win or lose not what you get as your first 2 cards. My simulation proved that the first 8 hands produce no more wins than normal. The house edge is virtually unchanged.

So what if I get more or less stiff hands to start with. I'm not winning any more hands than normal so increasing my bets just because it's the first 8 hands will not benefit me.