Anomaly?

Skew is no predictor

RKuczek,

Had another thought while painting my bedroom walls. You are applying the skew factor to the first 7 or 8 hands and concluding that a player should bet more in those early hands because of that skew factor. So let's take this one step further:

Since the skew factor applies to any group of 7 or 8 hands, why not bet more during the 5th through 12th or the 10th through 17th hand or the 12th through 19th hand, etc.? If you claim you have an advantage because of the skew factor, then it can be used in any group of hands not just the first 7 or 8 hands.​

The obvious answer to this is no, it won't work. And why won't it work? Because the imbalance created when only looking at a narrow range of hands tend to get balanced out as more and more hands are played. The problem is that you just don't now when this imbalance will favor the player and therefore is invalid for betting purposes. In card counting, you know when a player friendly imbalance occurs and one would the bet accordingly. But you just don't know when the "skew factor" is in your favor.

When one starts a tournament he will always have an imbalance in the first 8 hands - but that imbalance can favor him or be against him. When he starts another tournament, another imbalance will occur. After he plays several thousand tournaments the net of these imbalances will even out and tend to go to the norm.

Now, since you don't know if the imbalance will favor you or be against you when you start your first hand you are at the mercy of randomness. You just don't know because you don't have a crystal ball. The house edge is still there irregardless of the hand. To put it another way, the skew factor may help one to understand the randomness of the cards but it is not a predictor of things to come and, due to randomness, one gains no mathematical edge by having this knowledge (that knowledge being the "skew factor").

 

responses

London is right - you need to simulate eight card sequences - and track how many of the sequences have positive and negative results - and toolman is right - that the existing simulaiton software won't allow you to do that -

actually - all the posts are right - pretty much - the odds on each hand don't change - it is still dumb to go all-in on the first hand - etc. - and over the long term - you'll get the expected results if you add up all the individual hands - and my arguement does apply to all eight card sequences - but

this is tbj/ebj - not live bj - and we don't care about long sequences - we want to win tables - not long sequences of hands - and in ebj - we want to go into the first elimination hand with a good BR position -

I am argueing that it doesn't matter if the long term results over many eight hand sequences are negative ev - and it doesn't matter if when you have a negative ev eight card sequence that you get smashed and ploppy out - if - when you take advantage of the skewing - you improve your chances of surviving the first elimination hand and winning the table - more than 1/2 the time -

the goal is to win/advance tables - not to max ev - maxing ev is simply not relevant in tbj/ebj - winning/advancing tables is - winning/advancing tables is the goal in tbj/ebj - so give me an edge that improves my chances of winning/advancing at more than 1/2 of the tables I play - and I don't care if I ploppy the other tables - I'll use an all-in bet or two step progression to try and regain position - and take my chances at those losing tables - and play to establish myself in good position to win at the majority of tables I play -

in regular tbj - I tend to play conservtively - though not minimum bets - I try to 'under bet' - I like to have - say - the fifth highest bet out on most hands - staying in range if the cards favor the players - and gaining position if they go against the players -

in ebj - I am starting to bet more aggressively in the first sequence of hands - and then switch to more conservative play after the first elimination hand -

but with the real wild betting that occurs - my concept of agressive betting sometimes gets washed away when the all-in guys go at it - I am incapable of betting 1/2 of my BR on the first hand -

I think we are getting at something here that really needs to be explored - the inherent differences between live bj, tbj, and ebj - all the simulation software and even the discussions on this site - look at the probabilities for single hands - based on long sequences - when what we really want is to explore the probabilities and opportunities for TABLES - or short sequences of hands - and find ways to win TABLES - not simply individual hands - that is the difference between developing tactics and real strategies -

someone please develop simulation software that lets you track results by SEQUENCES of hands - if you win or lose the sequence - not simply accumulate results over all hands played - then please put that software in the public domain -

 

A series of related points

1. There is a real clear way to produce the results that RKuczek is talking about, and that's a progression. Start by betting $2,000, double until win, then bet $500 through hand 7. That has a far better than 50% chance if you ending up with a winning result, with a small chance of going broke instead. Most variations of this will also produce this result, though possibly to lesser degrees.

2. It's also true that average stack size increases going into hand 8, as there is a risk that people will be eliminated, and their stack size is ignored pragmatically and mentally. If you included the zero stacks, the overall EV would necessarily be negative.

3. RKuczek argues that, for example, that 54% of the time, you will end up with an EV of +2 and 46% of the time have an EV of -4. That is all well and good, but unless there is some meaning to what the 54% and the 46% represent that you can take advantage of, the overall stat is meaningless. For example, if I said "61% of the time, the dealer's hole card for the first hand will be a 2-9, and the EV for that hand followed by the next 7 is +.2 units. 39% of the time, the dealer's hole card for the first hand will be a T-A, and the EV for that hand followed by the next 7 is -.4 units." Overall, there is a negative EV, but I carved out a situation that has a +EV a majority of the time. But the stat can't possibly be useful. There's no way to know before hand 1 whether the 8-card run will fall into category 1 or 2, and by the time you know, the information is useless. The carveout didn't add value, so it doesn't help.


4. Finally, I know someone could do a simulation of 10,000 simulations of an 8-hand series, assuming BS and count how many times the result is +8, +7, +1, 0, -1.5, etc. But logic dictates that the result will be losses in excess of a coin flipping distribution. This is because the player can raise his bets in winning simulations and lower his bets in losing situations.

Take the example of a coin flipping game where heads comes up 49.75% of the time (EV=-.005) and you are forced to bet $1 on heads. Results are:
-8: 0.4%
-6: 3.2%
-4: 11.2%
-2: 22.1%
+0: 27.3%
+2: 21.7%
+4: 10.7%
+6: 3.0%
+8: 0.4%
Note that in this case, 37% of the time you lose and 36% of the time you win.

Now, imagine playing 8 hands of BJ flat-betting. The probability of going +6 or greater due to a good run of BJ, splitting and doubling hands is likely greater than 3.4%. And the odds of a -6 or worse are probably smaller than 3.6%, since you can surrender the bad hands and losing is less likely in hands where you double and split according to BS. But since the overall EV has to be equal, and that the average magnitude of wins is likely to be greater than the average magnitude of losses, that the frequency of losses will be greater than the frequency of wins experienced in the flipping game.

 

Anomaly

I was hoping that by using example for other than blackjack situation it would become more apparent that the main reason for this discussion -the effect of “random walk” or “skewness of results for short sequences”, or whatever it can be called -has zero effect for adjusting blackjack tournament strategy.

The mathematical elements brought forth were all right but the conclusion incorrect. What we dealt with was just a typical/natural/existing distribution of particularly chosen elements of the event – interesting, but nothing more. There is no practical use of the observation as this observation does not identifies nor suggest existence of anything unusual or different from what we knew before. It is just a look at a “slice of distribution of elements building the event” which does not change any statistics, values, occurrences.
If this skew could produce other than expected results one could pick plenty of elements that could be used to promote opposite conclusions and even ones that are mutually exclusive. If something could help a player it could help dealer, which in turn hurts the player. If less frequent occurrence of stiffs in short sequences would help the player than by the same token, and the same theory, occurrence of, for example, first two-card twenties would lower it. There is an infinite number of slices that could be used for and against if they would have any effect on the event but they don’t.
Also, the series could be used one after another, they could be “tiled”, consisting of series of miniseries, etc. Doesn’t matter - it does not apply.
No need for sims in this case.

Now about the other aspect - the practical use of a real gained edge in a particular hand(s) playing blackjack tournament. I may sound like a broken record but there are very few “golden rules” -if at all. The optimal plays are “fluid” at different rates.
Different bets should be considered for players with different skill level, depending on who are their opponents, rules, positions, hand number, etc.
Generally, the edge would have to be increased at greater rate to justify what Wong once inappropriately called proportional betting. On the other hand there are situation where a small change in perceived edge for the next hand my justify optimal bet jumping from a minimum to the maximum.

See ya next month,
S. Yama

 

S Yama, I agree with you entirely. But please explain your last line:

Can you explain further? Why is proportional betting bad? Why would a small change make you want to bet max?

 

More on the simulation

Much to my surprise, the simulation software I have does automatically produce the type of information you asked for. I don't use simulations often so I was not aware that the software produced these charts. But not to my surprise, no anomalies were uncovered.

Just to refresh memories, I could not force a new shuffle after each 8 hands. Instead I placed the cut card at a point where it would be reached on the 8th hand of a shoe the vast majority of times.

NOTES FOR CHART:
1) Hand Depth = The hand number when starting a new shoe.
2) Bets = The initial bet is $1 per hand. The column marked "Bets" is the total amount bet including Splits and Double Downs

Hand Depth........Bets.........Hands Won......Hands Lost.........Ties
......1..........$31,920,046........43.54%..........47.87%..........8.59%
......2..........$31,917,912........43.53%..........47.88%..........8.59%
......3..........$31,918,132........43.55%..........47.87%..........8.58%
......4..........$31,917,220........43.54%..........47.87%..........8.59%
......5..........$31,919,056........43.53%..........47.87%..........8.58%
......6..........$31,917,958........43.54%..........47.88%..........8.59%
......7..........$31,918,181........43.53%..........47.88%..........8.59%
......8..........$30,246,488........43.53%..........47.90%..........8.57%
......9...........$2,898,007.........43.34%..........48.17%..........8.50%
.....10...................$985.........43.45%..........49.85%..........6.70%

The conclusion I draw is that all percentages are within the expected/normal ranges, as I expected. The win/loss/tie rate is completely normal. There is no advantage in betting larger on the first 8 hands out of a shoe.

 

reply

toonces, toolman - your comments and simulation aren't on track with what I am suggesting - you can not duplicate the result of a sequence through using progression - very different animal - and toolman - you aren't testing what I talked about - it doesn't matter how many hands, total, you win or lose over repeated eight hand sequences - it matters HOW MANY of the SEQUENCES give you positive results - I have said the base odds per hand don't change - and you will get the expected probabilities if you total everything up - what I am saying is that if you track SEQUENCES not hands - you will find that a small majority of SEQUENCES give you positive results - even though you win and lose the same proportion of hands - no existing simulation software allows you to track sequences - I have searched for such -

S. Yama's comments are much more relevant - and he may just be right - I am focusing on one aspect - when many others could be looked at as well - but the entirety of the house edge is based on the fact that the player has to play first on stiffs - and stiffs are very common - if you reduce the number of stiffs - even by a fairly small margin - bj becomes positive ev for the player - I can't think of any other aspect of the game that affects ev so heavily -

right now - throwing out this stuff - I am doing some speculating - for sure - but wouldn't throw it out if I didn't think there was merit to it -

I actually use this in my play - and I actually make money playing tbj - even if not large amounts - a few thousand at this point (net profit - after all buy-ins, rebuys, tips, expenses) - playing in small tourneys - and have played enough tourneys that the profit isn't from getting ploppy lucky in one big tourney - it's from consistently getting to the final table - 29% of the time - and I am not a great player - I ploppy out with the best of them - I focus on strategic play - as that is how I first saw the game when I started playing - and base my play in the early and middle hands on considerations such as this - and it works -

I think that we are coming very close to 'beating a dead horse' here - I am resigning myself to doing some coding and building a simulator for tbj/ebj - that will allow tracking of results for tables and sequences as well as hands - but don't wait up for it - as it may be a long time before I get around to it -

 

That's still not it, I'm afraid

[Beaten to the punch by RKuczek's reply, which says much the same thing. ]

I don't want to give the impression that I believe in the theory, because I don't. It's just that I lack the mathematical rigour to be able to totally refute it on purely theoretical grounds (unlike S. Yama).

But, you really have missed the point. It's hard to find new ways to state the case that RKuczek is putting, and how it differs from your interpretation of it. Maybe somebody else could find a more clear way of puttting it. (I initially misunderstood in much the same way, as it's sometimes been a bit ambiguous.)

No one will be surprised that 43.53% of the hands dealt were won. The question is how were those wins distributed? The suggestion is they will have been clumped together, so that some runs of 8 hands will have been quite a bit below the average and a larger number of runs will have been a little bit above the average. This would balance out overall, following the rule that Ken has dubbed 'preservation of EV'.

 

Min or Max

...See ya next month
Is it February already? lol

Okay, toonces and others, I will be a bit perfidious with my answers to the first part of your request.

Why do I say that what Wong stated about proportional betting is not right for bj tournaments?

Please try to formulate a very precise definition of what is proportional betting. What is its goal? Does it change, how and why?
Then, try to formulate a very precise definition of what function betting in blackjack tournament serves.
And finally compare the two animals.
Is your answer close to: “Because (in vast majority of times) it does not apply”?

As to examples of switching from minimum to maximum bets as optimal play with just a small change of expected value in next hand. Here are two examples. The examples are simplified because it always DEPENDS on countless fine points...

Imagine EBT tournament, final round, it's winner takes all. It's elimination hand. There are two guys, not good players, way ahead of you, and a third player with brl just two minimum bets smaller than yours, and betting after you. Your bankroll is about max bet, so betting max means you’re all-in. You have two very close options.
First option: bet minimum and if BR4 wins you are out of the tourney, if he loses or pushes, then you and two other guys continue to play and because of your good betting position on the last hand you estimate that your chance to win is about 40%. Total chance for winning the tournament - slightly better than 20%.
Second option: bet maximum and if you lose you are out, if you win (and most pushes) you advance, but because of correlation in some cases BR4 wins his bigger bet, but more importantly you end up with worse betting position on the last hand, so you chances for winning with three of you left is about 40%. Total chance for winning tournament – slightly better than 20%
Note about mid range bets: if you lose the other guy can surrender, or take low and than double, or take straight high over you. If you lose you are almost guarantee to be gone, if you win you may still not advance, but if you do you will have smaller bankroll and lesser chance to win the tourney than if you’d bet maximum.
The point is that your optimal bet is to either bet maximum or minimum. Now, even the slightest change in the anticipated expectation for the next hand can determine either maximum or minimum bet, and nothing in between.

The other example is when you have to make a maximum catch-up bet within, let’s say three hands, all other aspects being the same. You count cards; the deck will be shuffled after the next hand. If the offered hand presents a better EV than the average, you make max bet right away, if it is even just slightly worse than the average, you make the minimum bet and wait to fire away max bet right after the shuffle.

Later,
S. Yama

 

Monkeysystem

I think I understand what you are saying, but to make sure ....

Is it that -

Just as RKuczek has pointed out a tendency for 8-hand sequences to have a preponderance of 3 or less stiffs, which he suggests should benefit the player, you are pointing out that there will also be a preponderance of sequences with 0 pushes, which hurts the player.

It feels right to assume that there is a kind of natural balance that means that the net effect of all such skewing is zero, and that's what I have understood S. Yama to be saying (so please correct me if I'm wrong )

 

Another point of view!

Why must I have only two (2) options? Under YOUR scenario and circumstances, the black and white issues are dire and, in my humble opinion, too simplistic. The goal of this hand, and I’m assuming that it is NOT hand 30 (because you talk about winning versus BR1 & BR2), is to advance to the next hand in the best shape possible.

There are two components to this: (1) How far ahead are BR1 & BR2? And (2) how aggressive is BRL? For example, in this case let us put some numbers to the positions shall we?

BR1 50,000 betting 5,000
BR2 65,000 betting 10,000
BR3 25,000 (YOU)
BRL 24,000

Under YOUR scenario BR3 either bets 500 or 25,000. I disagree with your premise. If I were BR3 I would consider a bet of either 1,500 or 12,500. I would NOT bet 25,000. There is not need to go all-in on this hand. In essence you would be giving the low to BRL and it has been previously pointed out that our win percentage is only 44%. Why do you feel the need to risk it all?

Betting 500 leaves you with the least number of options – basically you need the dealer to beat BRL to win. Since BRL is likely to bet 2,000 a split opportunity would be necessary if the dealer has a stiff card showing. A BJ for BR3, with a min bet, isn’t much help because BRL will simply double down.

A bet of 1,500 is still very conservative and leaves BR3 with more options, including surrender, splitting and doubling – pending BRL’s bet and the cards.

A bet of 25,000 essentially bets your entire BJT life on the line. Surrender at that point cripples you. Sure, if you win you climb back closer to BR1 & BR2, but if this is hand 8 or hand 16 you still have an additional 8 or 9 hands to do “catch” the leaders.

Once again in this case we are discussing OPEN bets. If I were BR3 and betting before BRL and had a secret bet, I would use that at this juncture.

With mid range bets – I respectfully disagree. Let me explain why – If you bet max and lose, the other guy can surrender to take the low so there is no difference. If you have a mid range bet then you leave yourself open to BRL taking the straight high over you, however, if BRL attempts to take the direct high and the dealer wins you advance. If you bet max and the dealer wins you go home! With a mid range bet you have options such as splitting (if available with or without doubling after splitting) and there is also doubling down for an amount that would get you the high from BRL. If this case doubling for less, with a face down DD card really puts the screws to BRL because unlike a TBJT if you DD and bust or DD and get crap BRL doesn’t know and their (BRL) decision has to take into account a lot more possibilities. In a TBJT everything is in the open and the decision process for BRL is much simpler for BRL.

In the specific example that I provided, I respectfully disagree. I can understand you rationale but given the intricies of EBJ, including the DD card being face down, I feel that the optimal bet is NOT minimum or maximum. Rather a mid-range bet, usually in the lower half to ½ max bet would be the optimal bet – for EBJ elimination hand (EH). In my humble opinion.

 

EXACTLY! The whole EV discussion is irrevelant unless you win the first table and advance! The question is how are you able to do this? The technique, in my opinion, is irrevelent, the results are what matters.

This concept of more aggressive betting in EBJ versus TBJT is based on the premise that there is a player advantage in the first 8 hands. This is a proposed theory that I personally, don’t adhere to.

I agree that the total sum of the events in the overall picture is more important than the single individual events. It is only when the effect of the single events skew the results of the sequence that more attention needs to be paid to the single events.

For example – consistent betting on hands 1-7 (whether 500, 2000 or 5,000). In this case the overall picture is the summation of the events such that each individual event has equal weight. However in the event of a betting sequence such as min bet then max (all-in) the outcome of the individual event, the max bet, dwarfs the expected sequence of events. This betting sequence would skew the overall results thereby nullifying the expected sequence probability (assuming the player lost) or skewing the sequence to the aggressive side (assuming the player wins/dealer loses).

The initial premise of this thread was – do the cards being dealt reflect real world situations? Since they are being generated from with a RNG or another method, it is my assumption that no, the cards do NOT reflect what one would see when being dealt from a 6 or 8-deck shoe.

 

Skewed or not?

One again I respectfully disagree and here is why.

If I were able to determine that the first 7 hands were to be skewed in such a fashion that the dealer was more likely to break than I could use that knowledge to my advantage. If there were the case I would bet very aggressively, stand more often and likely have a higher BR going into EH1.

The converse would be true if I had the knowledge that I was going to lose 5 of the first 7 hands I would bet more conservatively, hoping my opponents would bet aggressive and thereby having a large BR than my opponents when approaching EH1.

In either instance the knowledge that the short sequence would be skewed one way or another, would be a huge tactical advantage – much as an AP waits for a positive real count before increasing the size of their bets. Does it guarantee a win? NO! But it puts the odds in their favor.

Now if the outcomes are truly random and not skewed, then yes I concur that there would be little need to adjust BJT strategy.

 

A farewell to this thread

I expect this to be my last post to this thread. Just want to summarize the “skew factor” discussions. In an effort to keep this post on the shorter side, I’ll just give a simplified overview of the situation.

RKuczek has argued that the “skew factor” favors the player in the first 7 hands of an EBJ tournament. Therefore, make larger bets during the first 7 hands and most of the time one will be in good shape going into the elimination hand. No proof was given that this idea is valid.

All others (hereafter to be referred to as “opponents”) have argued that although the “skew factor” may indeed exist, there is no known way to use it to the player’s advantage. It is an interesting but useless bit of information. The opponents have used math, logic, and simulations to show that simply betting more on the first 7 hands of a tournament gives no advantage whatsoever – you are still at the mercy of the house edge. To add credibility to the opponents’ side, a couple of the best minds in the world of blackjack have joined the discussion.

I am always open to new ideas concerning blackjack in general and tournaments in particular. My friends in the blackjack community know that. However, any new ideas or theories must be backed up with solid evidence that they are indeed valid along with a practical way of applying those theories to actual play. Since no evidence has been shown that the “skew factor” can be applied in actual play, it must be discounted as another of those theories that sound good but are of no useful purposes. As the old saying goes “If it sounds too good to be true, it usually is”.

Everyone who has followed these discussions will of course make up their own mind. I just hope that decision is the right one.


PS: I would like RKuczek to answer Ken Smith’s questions as raised in posts #31 and #37. A further discussion on that would be interesting.

 

this will be my final post here also - I imagine

not much point in repeating my self -

Ken is right on in his second post - the skewing that produces more positive ev sequences also produces a greater magnitude of negative ev in those sequences which are negative - so the cummulative results are what we expect from live bj - I will repeat this oone last time - arguements based on cummulative results and single hands odds - are not even vaguely responsive to my posts - I am talking about sequnces of bets - and whether the sequence as a whole has a positive or negative ev - I am not totaling up over many sequences - or looking at the individual hands - I am dealing straight out with the sequences as the base unit of analysis - if you tracked 100,000,000 sequnces - of eight hands each - you would find that a little over 1/2 of those sequences would result in a positive ev for the player - and a little under 1/2 would result in a negative ev for the player - and those sequences with negative evs would show quite larger negative evs - about twice the magnitude as the positive sequences -

and I did offer some proof - I listed the probabiltiies for sequences which showed an obvious skewing effect - that occurs in virtually evey discrete probability distribution - when a small number of trials are used -

all I am saying - is that when skewing occurs - you can use that as a basis for a playing strategy - as you can use any probability that you are aware of -

finally - I am not recommending some flat betting scheme - I never 'flat bet' in any tournament - I size bets relative to the other players' bets - are at least attempt to do so - what I am suggesting - is that it will be advantageous - to bet somewhat above the middle of the other players' bets during the first eight hands of an ebj tournament - because the probabilities say that will be to your advantage at the majority of ebj tables you play - and the probabilities aren't an 'arguement' they are real math - and the skewing is a real - and well known - effect - of discrete distributions and small numbers of trials

and finally - yes - I am convinced that the UBT deals are random - and no they don't duplicate the results of a shoe - because shoes aren't shuffled after every round - and you rarely play eight round tables in tbj - what you are seeing is exactly what I have been talking about - with discrete distributions and a short sequence of hands - you get skewed probabilities and more extreme results more often - and this benefits the ploppies who bet wild - in the early hands - because of the direction of the skewing - when you accumulate all the results - over many hands, sequences, tables - you will see the expected probabilities -

 

Still.....

The funny part about this last paragraph is that this assumption about the cards is what started this thread. Personaly I'm not sure I agree or disagree with this last one

 

fgk42

buy an Orion RNG - only $250 bucks - plug the dongle into your computer's serial port - then run off eight hand sequences - you will see exactly the same skewing of results as on UB/Bet21 - it is a function of the short hand sequence - the discrete nature of the probability distribution - and is a reflection of the underlying probabilities - skewing works both ways - more often positive than you expect - but sometimes much more negative than you expect -

in TEC SNGs - I always go min bet - then counter bet - and I win 1 of 3 - thing is - how can you use the skewing to benefit your play - my approach is to bet more aggressively - but this is only reasonable if the other players are betting small or moderate - if they bet big - then go small? - as in a TEC SNG - and hope you have one of the very negative sequences - and they crash out??? - you really need to have several strategies available - and be able to move fluidly between them -

finally - it really is not a debate as to 'if skewing occurs' - the math says it will - both more often positive results than expected - and the negative results - when they occur - being more negative in magnitude than expected - the debate really is - can you use this in some way to improve your chances of advancing - I think you can - S. Yama says doubtful

since we have established that whenever S. Yama and I agree - we have defined "universal truth" - this topic can still be considered as open for debate -

 

Hang on a minute!

That is not my understanding of what has been said so far. In particular, S. Yama wrote -

Maybe I've got it wrong, but my understanding of S. Yama's position is that the skewing of stiffs will not cause there to be an imbalance between the numbers of sequences with positive and negative results, because there is all sorts of skewing of different elements of the game to take into account, some favouring the player and some favouring the dealer, all destined to balance out and yield no overall effect.