Progression betting system is not any worse than

Progression betting system is *not any worse* than flat betting (if the hand was dealt from a fresh deck every time, and etc etc). If you are playing an even game against the house (i.e. 0.0% edge) *for every hand*, it does NOT matter if you use flat betting or any other exotic/clever/"power" systems. Your *expected* return after many many hands will be zero. Now add a small edge for the house, and your expected returns will be some negative amount of dollars after a certain fixed number of plays (without counting cards). Again, that expected value will be *the same* no matter what kind of betting system is used (as long as the average bet (over a large number of plays) is the same for different systems, and etc etc). This is what we call science (math, statistics, or whatever).

I see there are two (very strongly) divided "factions" in AP community regarding progressive systems, and I can see where each side is coming from.

[1] First of all, you cannot argue with (proven again and again and again...) science. There is no "your" science or "my" science. You cannot invent a perpetual-motion engine! Period. You just cannot beat (statistically) unbeatable games by merely using some clever betting systems. I see why some people on this board feel so strongly against these betting systems (so far as to go to suggest to censor any posts related to them).

[2] But, then again, please notice the assumptions (sometimes just noted as "etc etc") in my arguments above. Any theory (we don't use the word "truth" in science. Even the "fact" that a rock thrown in the air never fails to fall onto the ground is called (or described as) Newton's "theory".) is only valid under certain (well-defined) assumptions (or conditions). For example, Newton's theory of universal gravitation is only valid in moderate strenths of gravity, and it breaks down in extreme condistions like in black holes. Likewise, Newton's (another) theory of dynamics (the famous f=ma) is only accurate when the speeds of objects are low (in extreme conditions, Einstein's special theory of relativity is needed to accurately describe the dynamics). Likewise, these progressive betting systems are only "proven" to not work under some (explicit and/or hidden/unstated) assumptions. Can the "dynamics" of BJ be accurately described with a well-defined and *solvable* mathematical model (as a stochastic process)??? I don't know. For one thing, each hand is NOT drawn from an iid (identical independent distribution), and that's exactly what AP exploits: The distribution of cards changes as the deck depletes. I don't know of any theory that proves/disproves any one betting system is better or worse than any others in "real" BlackJack games. My point is, it's an open question until somebody comes up with a rock-solid proof that progression does not work in BJ.

Just my two cents,
~Jack.

BTW (1), if you ask me, I think I personally belong to the first school of thoughts ([1]); you are innocent until proven guilty (that is, the burden of proof is on the side of [2]). But, I'm very open-minded toward [2]. (Actually, I suspect positive progression systems should outperform (slightly, if ever) the flat betting system for exactly the same reason why the card counting/bet spread (is supposed to) work. (Please think about it!))

BTW (2), but then again, with so many simulation softwares etc out there (although I've never used any of them personally, and I don't really know if it's possible to do this kind of simulation), how come nobody on the side of [2] has come up with some solid *data* to prove their systems work. (Remember, the burden of proof is on the proponents of [2]. If you discover a way of time travel, for example, *you* need to convince the rest of the world (that is, if you want to take a credit for it ;-).)

BTW (3), if it matters, I have some formal education in stochastic processes.

BTW (4), if you come up with a working progression system, PLEASE share it with us!!! (But, "it works for me" argument will not be enough. Even if you said, hey, I just won a super-lotto using my 'power system', and waved around your millions of dollars in my face, I would have no interest in your system.)

What I meant to say was:

All betting systems (which are not correlated with the card distribution change) are more or less equivalent as far as the long term average return (or loss) is concerned, assuming the player has an infinite bankroll.

~Jack

I am probably going to regret posting on this subject of progressions. But the issue comes up so frequently here, and there is so much misunderstanding and misinformation about it, that I think it would be worthwhile for me to make some definitive comments about it.

Now, first of all, the proofs that progressions don't work is rock-solid. The proofs are really quite straightforward and simple, if you understand a little probability theory. Perhaps I will write up the formal mathematical arguments about this and post them in the near future. I am currently planning to include them in my book.

The proofs apply to betting systems where you bets are uncorrelated with the game your playing. That is, suppose you have a sequence of random variable X0,X1,X2, � Xn, which give the probability distribution for various negative-EV wagers, and you have a sequence of Bets B0,B1,B2,�,Bn . If B0 is independent of X0, B1 independent, of X1, etc, then we can conclude that your overall advantage will be negative. The proof relies only the linearity of the expectation operator E, and on the fact that E(XY)=E(X)*E(Y).

Almost all progression systems clearly have this property. Progression System for fixed games like craps and roulette certainly have this property.

Now for blackjack, the situation is somewhat more complicated. Card-counting in blackjack is actually "counter-example" for this theorem. It is not a counter-example for what I have stated above, because I have carefully the assumption of independence. But card counting is an example where the bets are not independent, and for which the conclusion fails.

Now it is theoretically possible to have betting systems for BJ which appear to be progressions but where the bets happen to be correlated with the count. This issue has been studied before in the BJ literature. There was an important paper by the late John Gwynn many years ago which looked into this issue. Here is an important but interesting fact: a player using a negative progression in BJ will face a somewhat lower house edge, and a player using a positive progression in BJ will actually face a higher house advantage. The effect is very slight. Several years ago I published sims on Green Chip which demonstrated the inefficacy of using this method for negating the inherent house advantage in the modern game of BJ.

Now having said all this, let me go back to your original point that a progression player will lose at the same percent EV as a flat bettor. This is basically correct, subject to the stipulation listed above. But it does not tell the whole story. EV is not everything. Gamblers also face Variance and Skew. Basically, progressions raise both of these. By raising Varaince, they make it harder for the house to get into the "Long Run" and easier for the gambler to come out ahead on a short-term trip.

There are legitimate arguments which are advanced suggesting that Variance is a friend of the negative expectation bettor. Personally I do not subscribe to these arguments, nor I endorse them. But the are well-informed people who do. For example, there are many authorities who suggest that taking the odds bet in craps is a good strategy for negative EV gamblers. This does basically does the same thing that a progression does: increase the Variance. If you accept it as a strategy, then you may also accept progressions as a legitimate technique for the BS player.

I am not planning to get into extended discussion on this issue on the Free pages. I may answer some questions, particularly if they are needed to clarify my remarks here. But I am not going get into an extended argument or flame war here over it. I will be happy to discuss this or related matters in detail on the Green Chip Theory page.

I have thought of the odds bets as getting even money on the table which would, when averaged with the inherent craps disadvantage, raise overall Ev.

when playing don'ts you place the min bet on the come out and then place odds when you have the advantage over the house. works great with a very low min like $2

taking over a don't bet from another player who is already up and then placing odds, very hi ev.

you are putting more money on the table when you have the advantage, positive ev plays.

same as i do in bj advantage play

although i believe craps has a much lower SD if played smart, than smart bj play can have.

placing on the right side bets is another story. putting more money in play when you are at a disadvantage makes no sense to me.

Math Prof,

Please correct me if I'm wrong, but it seems to me you are just repeating what I said. Your "rock-solid proof" argument only applies to a model with independent distributions of cards, which is not the case for real BJ games. Actually, we both seem to agree on this (even though you sounded like you knew something that I didn't). Please give me a rock-solid proof that a "system" that do not use card distribution change *directly* (such as card counting) cannot outperform the flat betting system (as far as the mean is concerned), if you can, and that was my point of the previous post.

I studied math many many years ago and my math skill is kind of rusty now, but I think anybody with a few math books in his library can easily prove the following conjecture I put forth earlier:

(1) Suppose you have a Markov process with 2-step correlation. (Sorry, I cannot recall any correct terminology here. What I mean is:
P_n == P(C_n|C_n-1,C_n-2,...,C_1)
= P(C_n|C_n-1),
where C_i is the card drawn at the i-th, and P(C) is the probablity of drawing C. (C={A, 2, ..., 10})
(2) The outcome (win/loss) only depends on the probability of cards.
O_n == O[P_n(C)]
where O = {+1, -1}.
(3) Now we have this betting system which determines the next bet solely based on the previous bet and its outcome (+1 or -1), to which most "progressive systems" belong.
B_n == B[P_n]
= B(B_n-1,O_n-1)
(Please note that bet-spreading-with-card-counting cannot be written this way (the second line).)
(4) Expected gain at the i-th step can be denoted as
E_n == E(B_n, O_n)
= E(B_n-1,O_n,O_n-1)
= E(B_n-1,O[P(C_n|C_n-1),O[P(C_n-1|C_n-2)])
(Note that E(B_n) is NOT equal to due to the BlackJack payoff, etc...)
(5) So, my conjecture is:
If a system is defined with
B_n(B_n-1,+1) > B_n-1 and B_n(B_n-1,-1) < B_n-1,
then "the long-term average of E_n (over many trials)" of this system is bigger than that of the flat betting system, which can be defined as
B_n = B_n-1 (But, again please note that E_n != E_n-1.)
(I'm assumming, OK, here comes the "fuzzy" part, ;-) that
P_n is "sufficiently similar" to P_n-1.
I'm stating the fact that a ten-rich deck, for example, will not suddenly become low-card-rich by drawing one card. Once you figure out how to prove the conjecture you will know what kind of restrictions are required for P_n....)

Hope this problem is easy enough not to require many trips to the library...

~Jack

BTW,
> There are legitimate arguments which are advanced suggesting that Variance is a friend of the negative expectation bettor. Personally I do not subscribe to these arguments, nor I endorse them.

I don't know why you are so reluctant to accept this. If the variance goes to infinity the *relative* mean will go to zero, *under the assumption* that the player has the infinite bankroll. In the real worlds, where the casino has much bigger bankroll, the variance acts against the player by increasing the ROR.

Geez, this d*mb BBS software keeps removing my angular brackets!

The following line
(Note that E(B_n) is NOT equal to due to the BlackJack payoff, etc...)
should read
(Note that E(B_n) is NOT equal to < B_n*O_n > due to the BlackJack payoff, etc...)

you have decided before beginning your trip that you will risk only a FIXED TOTAL AMOUNT of money, (let's say $1,000), AND you don't care how long you stand there and play. This means that you will quit gambling at craps for the rest of your trip if you lose the $1,000, no matter how fast that might occur.

In this case it makes more sense to make a series of small pass line bets and then take max odds on each bet if a point is established. Or, you could bet the don't side and lay max odds against the point. Either way, your variance is higher than if you never made any odds bets, but your disadvantage on that fixed total amount of money ($1,000) allocated to playing craps is less than if you just made pass or don't pass bets on each roll and never took odds. You will win or lose faster when you take max odds, but the overall casino edge against you will be lower, sometimes very close to even, if you can take 100x odds.

If you are playing for comps, though, it is better to make a fixed bet each time and never take odds, along with playing at crowded tables only, so you can maximize the TIME spent there at the table for better comps.

See website - TheWizardOfOdds - for a more detailed explanation of this effect, under the Craps section.

AB

Sorry, the first assumption may be too drastic (so drastic it may alter the reality too much). Let's do away with this:

(1) Suppose you have a Markov process with 2-step correlation. (Sorry, I cannot recall any correct terminology here. What I mean is:
P_n == P(C_n|C_n-1,C_n-2,...,C_1)
= P(C_n|C_n-1),
where C_i is the card drawn at the i-th, and P(C) is the probablity of drawing C. (C={A, 2, ..., 10})

So, (1) should be replaced with the following:
P_n = P(C_n|C_n-1,C_n-2,...,C_1)
where n stands for the ordinal of the card drawn from a fresh deck (NOT the ordinal of the trial!!!)
In other words,
P_N = P_n
where
N: N-th draw from the beginning of the game
n: n-th draw from the last shuffle
and
N = n + sum_of m_i
where m_i stands for the penetration of previous shuffles.

MathProf> I am probably going to regret posting on this subject of progressions.

With all due respect, MathProf, this is exactly why I posted my message. I don't believe in cr*ps like "quitting while you are ahead", and "it works for us", etc, but the fact that (some) d*mb people are advocating progressive systems do not mean they are incorrect. I need to see it for myself (either way). Besides, because of this pervasive negative sentiment, even people like you (supposedly educated and intelligent) are confused between the fact and belief.

Anyway, if anybody (mathematically-inclined) is interested, I think we might need one more assumption to prove my conjecture (I'm not quite sure though).

(*) The bet has the lower bound but not the upper bound: That is,
B_N >= B_min for all N
where B_min > 0.

The odds bet does not reduce your losses at craps at all. Imagine two players. One player bets $5 pass line and never takes odds, the other player bets $5 pass line and takes $100 in odds. After a long series of bets, both players lose the same 1.5% off their pass line bets. The guy taking the odds breaks even on the odds bets. Although taking odds reduces the overall hous edge it does not reduce the a players losses and giving odds costs the casino nothing.

Bert

There is a lot of discussion about shuffles being nonrandom. This assumed "nonrandomness" is contrasted with "random" RNG's used for simulations (which by the way or not necessarily random as it looks like from a discussion on bjmath one of the best in the business was using one which may have created biased data. That there is no significant difference between results derived from good RNG's and reasonably complex casino shuffles has been shown numerous times. Casino washes, pickups, types of plugging and stacking, etc. can be totally replicated and have been. Wong, Carlson, Imming, and I am sure others did these things years ago. The more recent studies by Harvey Cohen using more advanced computer techniques have verified the others.

I tend to discount completely the idea you seem to pose that because there are shifting advantages at blackjack and plays are not totally dependent some progression some time might be valid (with the very mild proviso stated later). If the size of the bet is determined by a past outcome or (as in my progression on the level from a starting point) and one is not affected by the instant favorability, blackjack is no different from an totally independent play game. There is just some more complexity but the invariant edge still remains the basic strategy edge if that is what is being played and no account is given to cards previously played.

For a progressive system to work at blackjack IMHO some type of shuffle or pickup would have to result in some type of subtle consistent win loss pattern bias and concurrently the progression being used would have to correspond to that subtle pattern. While not yelling "that cannot ever happen" I do not hesitate to speak loudly the possibilities of that type of congruence happening is in the realm of impossibility. And if it did occur and the shuffle or pickups or whatever changed, then the bias, if any, would be a different one requiring a different progression.

Please take this post as a discussion and not a putdown.

manipulate the time/result relationship. A positive progression may delay or speed up the rate of loss of an individual player. You lose less more often than a flat bettor loses and occasionally win very big. It is possible (but unlikely) for a positive progression player to have a huge win early in his playing lifetime and as a consequence never be behind for a substantial period of time thereafter. Likewise a positive progression player may never hit that big win and be a loser for most of his sessions.

The exact opposite is true for the negative progression player...most win almost everytime they play...a few will get pounded by a long losing streak which happens on occasion.

Dear ML,

I'm pretty new to the BJ community, and I'll look up the articles you mentioned. But, I have no reason to doubt that your proof is flawed in any way. My point was, however, questions like "Is F=ma correct?" are meaningless. It's just a *model* of the nature which only works in certain regimes. I'm pretty sure the progression does not work within the models you considered. But, my question is, Are you models realistic enough? Do your models capture all essential ingredients of BJ dynamics?

Again, as I said, I'm on your side. I'm skeptical about progression myself. But, I just don't understand the atmosphere here where progressionists are treated like Galileo (that is, in the pre-Newtonian period). I know of one message board, where this "blasphemous" word cannot be even spoken!

I agree with you on the nullness of "nonrandom shuffle" effects. (I saw some data in Wong's ProBJ, where card correlation is found to be zero even for *unshuffled* decks.) But, we know of a living-proof that BJ dynamics can be exploited by counting cards (and thereby, indirectly inferring the (changing) probability distribution of cards as the deck depletes). So the question is, can we exploit this without counting cards?

For me, this is an open question.
~Jack

PS: BTW, Does ML stand for Markup Language? Or Mighty Lord? ;-)

in Blackjack Forum in the past. I was able to adapt your approach to counting Aces with an unbalanced primary count and have had success with it.

Now, I see your point in your response and do not argue with it, but I was talking about a player using a predetermined number of dollars
to make his bets, then quitting after he makes $100 dollars worth of bets.

Player A goes to the pass line with $100. He makes $5 pass line bets, then quits after BETTINGexactly $100 total(not winning or losing $100).Over the long run, he will lose about 1.4% of the money he brought, or $1.40, although it might take him a long time to lose that $100.

Player B goes to the pass line, bets $25, then takes triple odds after the first roll of the dice which happens to be a 4. Eventually the shooter sevens out,and Player B loses his odds plus his original bet,total of $100. NOW he walks away, quits forever. Even though he lost everything, wouldn't his overall disadvantage theoretically have been less than Player A? (He could have won after that one bet of $25 plus $75 odds, of course. Either way, he walks and quits FOREVER.In a way, isn't this like a kind of "tournament"?) He bets the same total amount of money ($100), yet has slightly less chance of being behind.

To make it easier for me to visualize this, I imagined two teams of 100 players each, Team A and Team B, who played with above restrictions. Can you show me the "flaw" in this line of thinking?

Thanks for your response.

AB

Progressions are bullshit!and she plays BINGO!

I agree. In fact on the rare occassions I play craps I take odds. I just wanted to point out that in the long haul it does not save you any money.

By the way, this big player in Shreveport bet $500 pass line with 100 x odds and was barred from 2 casinos. He played only at Horseshoe after his barring and won, I'm told, 1 million dollars. He eventually lost it all back. Watched him play a couple of times. Real humbling to see more than my entire BJ bank roll wager on a single roll at craps.

Bert

apperance of the all important -7-

but it will allow you to put more money on the table after you are up on a number playing the don'ts, very important, you have the edge at that point

similar to a split or double down in bj

last night a number of don't players were not taking odds and allowed me to take it on their bets. so my bets were paying true odds on a number that had a higher chance, math wise, for winning. I say that is advantage play, like bj advantage play.

there are many angles to this game that can make it a lucrative one.

but it is true you must spend some time

one good thing is that some of the best advantage plays in craps have never been revealed
in any public forum and are generally kept very private

with the degradation in most bj games advantage bj players should look to craps as a potential new area of advantage play

Casino payoffs for odds bets are precisely the same as making or not making a point. In noncasino craps the even bet on six or eight if any one will fade it gives a slight advantage but even in those games the 4,5,9,10 bets are precise.