Progression strategies and their failure

Hello folks, never posted here before, just stumbled across it because I'm doing a bit of reading on progression betting strategies. My understanding is that they fail, no matter what, in the long run. The question I have however, is, what exactly causes their failure? Specifically regarding up-as-you-lose progression methods, the example I'm questioning is a "Martingale", I think:

Bet 1 unit, if you win, keep that bet aside and reset
If you lose, double the bet

So if you started with 1 unit and lost 10 hands in a row, you would be down 512 units (I think). If you won the next bet, you would be even. Any winnings (1 unit at a time only) are kept aside.

Is the restriction, or downfall to a progression system like this solely based on the table limits (or your own bankroll limitations)?

Sorry if this has been covered before - I 100% understand that progression systems lose, but I'd like to take a concrete reason to my friend who believes that this is a must-win type of system, whether mathematical or logistical in nature.

http://www.bj21.com/bj_reference/pages/10537.html

Thanks Panama Rick,

I've read over Bootlegger's post (it's excellent), which has led me to believe that the progression systems will not work. However, the post doesn't go into enough detail on why specifically they don't work ... I'm looking for a mathematical (or other reason why, if it's not mathematical) explanation on the why's.

Thanks again.

"I've read over Bootlegger's post (it's excellent), which has led me to believe that the progression systems will not work. However, the post doesn't go into enough detail on why specifically they don't work ... I'm looking for a mathematical (or other reason why, if it's not mathematical) explanation on the why's."

Try this link:
Mathematical Proof that Progressions cannot overcome Expectation. by Richard Reid

http://www.bjmath.com/bjmath/progress/unfair.htm

You need to understand the concept of mathematical expectation. If you don't have that concept, I'd recommend the book The Mathematics of Gambling by Dr. Edward O. Thorp, or any text on elementary probability.

One fundamental, useful thing about expectation is that it's additive. In other words, if you have a list of mutually exclusive events, that together comprise the overall event you're interested in, you can multiply them by their individual probabilities, and then add to get the overall expectation. The "law of large numbers" tells us that the expectation is what you can expect to happen "in the long run."

For example: If you have three events, A, B, and C, which are mutually exclusive, and if the occurence of any of A, B, or C means that some improtant event E has occurred, then:
P(A) x Exp(A) + P(B) x Exp(B) + P(C) x Exp(C) = Exp(E), where P(whatever) is the probability that whatever occurs, and Exp(whatever) is the expectation if whatever occurs.

The concept is not limited to three events, it could be 1003 events or 1,000,003. Doesn't matter. Exp(whatever) can be any positive or negative number. Usually, for our purposes, it's a positive or negative dollar amount. Eg. if I bet $5 on the flip of a fair coin, and lose the whole $5 if tails comes up, but win only $3.65 if heads comes up, my overall expectation is 0.5 x (+$3.65) + 0.5 x (=$5) = -$0.675. Heads and tails are "mutually exclusive" -- they can't both happen. But if one or the other happens, we've completed the event in question -- a coin flip.

P(whatever) is always a number between 0 and 1, because P(whatever) = 0 means whatever is impossible, and P(whatever) = 1 means whatever is certain to occur.

What progressionists are saying is that they have a way to divide up an event, where each individual expectation is negative, yet the overall expectation adds up to something positive. Eg. Suppose Exp(A), Exp(B) and Exp(C) were all negative, they are saying that, nevertheless:
P(A) x Exp(A) + P(B) x Exp(B) + P(C) x Exp(C) = something positive

Remember that P(A), P(B) and P(C) are all between zero and one. Can't happen.

ETF

What progressionists are saying is that they have a way to divide up an event, where each individual expectation is negative, yet the overall expectation adds up to something positive. Eg. Suppose Exp(A), Exp(B) and Exp(C) were all negative, they are saying that, nevertheless:
P(A) x Exp(A) + P(B) x Exp(B) + P(C) x Exp(C) = something positive

What's missing from your proof is proof that all the expectations from a series of progression bets are negative. With games like Roulette, Craps and coin-flipping, it should be "intuitively obvious to the casual observer" that they are, because winning or losing a game will have no effect at all on your odds in the next game.

With Blackjack, the situation is not so simple, because the odds are not the same on every hand: Advantage play is possible in Blackjack because the cards that are dealt on each hand are now missing from the remaining deck, which will effect your odds on the next hand, and because the odds will sometimes shift to the player's advantage. If you can detect when you have an advantage and bet more in those situations, it's possible in the long run to overcome your losses in the hands where the house has the advantage.

The lure of playing progressions in Blackjack is that they might, somehow, also exploit this shifting advantage without counting cards. And strictly speaking, neither your simple proof nor Reid's elaborate proof apply to Blackjack because, indeed, there is a small correlation between the results on successive dealt hands from the same deck. To prove that progressions "don't work" in Blackjack, you need to prove that this small correlation doesn't give you enough information about the odds on the next hand to be exploitable.

Wynn has just spent $1.8 Billion on building a new casino/hotel.

But the less sarcastic reason as to why they don't work is because EVERY bet in a casino has a house edge built into it, combining bets that have a negative expectation can not and will not turn them into a positive expectation bet.

There is a difference between the odds of a play-all game and the betting
outcome of the game. Math experts seem to confuse the two.

Counters don't change the odds, only the betting outcome. The dealer or
house is going to win more hands than the player.

A wonger isn't playing the full game, only segments of the game and
therefore is playing to different odds and has the odds on his side.
If a wonger would flat bet he would win long term because he'll win more hands than the dealer.

A progression can overcome the odds and win long term, but it can't change the odds.

"There is a difference between the odds of a play-all game and the betting outcome of the game. The dealer or house is going to win more hands than the player. Math experts seem to confuse the two."

(shrug) The odds of the play-all game are changed by betting more when you have the edge and betting less/nothing when you don't. Perhaps you meant the same thing.

"Counters don't change the odds, only the betting outcome."

That's a pretty loaded statement! For example, there are BJ games with rule variations whereby flat-betting & play-all can give the edge to the play-adjusting player.

"A wonger isn't playing the full game, only segments of the game and therefore is playing to different odds and has the odds on his side. If a wonger would flat bet he would win long term because he'll win more hands than the dealer."

That's not exactly the reason the wonger has the edge -- or "wins long-term", as you say.

(One could say, BTW, that, strictly speaking, the wonger is not "flat betting" but has a "2-size betting ramp". She is betting A in positive-EV counts and B in negative- and/or neutral-EV counts, whereby A=$k and B=$0. That would be extreme nitpicking, however.)

"A progression can overcome the odds and win long term, but it can't change the odds."

(sigh) You seem to be changing your definition of "odds" in the same phrase!

I presume we are talking about vanilla BJ. If by "odds" we mean the game's edge in percentage terms, this cannot be changed by a progression betting scheme (on its own). If by "odds" we mean the player's expectation in terms of money, then a progression betting scheme, under various (mostly unrealistic) assumptions, can theoretically give the edge to a player.

Call him Bill.

A third person keeping track of the number of hands won and lost between the player and dealer and oblivious to the money being bet, would conclude the house won more hands.(facturing out variance).

A progression player can overcome the EFFECTS of the odds(dealer winning more hands),but not the number of hands the dealer will win.

Some progressionists have realistic assumptions and some don't.

Maybe the nomenclature should be changed to avoid confusion. Exactly!

What's missing from your proof is proof that all the expectations from a series of progression bets are negative.

That's part of the premise, not part of the proof. That's the assumption of the progressionists. Read below -- a progression can "overcome" the odds (suuuuuuure it can).

With Blackjack, the situation is not so simple, because the odds are not the same on every hand:

No mention of blackjack at all in the original post.

If you have a situation where you can divide an event into subevents, and some of those subevents have a positive EV, then it's possible, in theory, for a progression to work -- assuming you bet more when a subevent is positive. Then you get into correlation and all the rest of it. But that's not part of the Progressionist religion.

You can use card counting as an example, but counting is not a progression partly for that reason -- some of your bets are positive EV.

In fact, if you have a very, very good blackjack game to start out with (bearly even off the top), it's possible to devise progressions that give the player a tiny edge. But it's nothing compared to what counting can get you (which isn't all that great to begin with).

ETF

and have no discernible specific advantage on a perticular hand.

An example would be to lessen the value of a loss before proceeding further. Player loses a $10 bet and lower his bet to $5 and stays at
5 until he wins and then returns to a $10 bet. Or he may decide to recover the whole $10 with two $5 wins before proceeding to the higher bet again. Using this method of betting, a player never gets caught increasing his bet into a losing streak. There is some value in the concept but not necessarily in a specific hand.

... has less value than betting the absolute minimum on every hand, and playing as sloooooowly as possible. Why expend mental energy on a way to lose money faster?

ETF

I did quite nicely with it. With a little imagination,it can give you
lots of options. One drawback was it made one look like a card-counter. Didn't experience anything you mentioned.

In fact, if you have a very, very good blackjack game to start out with (bearly even off the top), it's possible to devise progressions that give the player a tiny edge.

For many years, the Wizard of Odds had a challenge posted on his site : his $20,000 against the challenger's $2,000 that no progression-type betting system could show a profit against a casino game in a one-billion-game simulation. The original challenge stipulated that the game had to be either Craps, Roulette, or Baccarat, so his money was perfectly safe.

But last October, the Wiz accepted a challenge -- apparently the only serious one in all those years -- to play against a double-deck Blackjack game with S17, DAS, and split to 4 hands, which has a house advantage of about 0.26% (if played to the cut card, not just off the top). He allowed a spread of 1 to 1028.

The challenger failed, and last month the Wiz took down the challenge because he was getting too many e-mails from people asking questions or wanting to argue about the issues without actually taking the challenge.

I didn't know about it until after he had withdrawn the challenge, but I'm pretty sure that game can be beaten with a progression.

Would you like to offer me the same challenge? ;-)

>But last October, the Wiz accepted a challenge -- apparently the only >serious one in all those years -- to play against a double-deck >Blackjack game with S17, DAS, and split to 4 hands, which has a house >advantage of about 0.26% (if played to the cut card, not just off the >top). He allowed a spread of 1 to 1028.

Where did you get that info from? The house advantage for that game is around 0.19% off the top. What do you mean by played to the cut card? Do you mean that when you run out of cards you continue to drawing from the discards? Not very realistic for a challenge.

What if instead of playing to the cut card you play to a fixed number of rounds, say 14/15 (provided that you don't run out of cards). In that case the house advantage would still be 0.19% and you would have to overcome that with a progression. Would you still take the challenge?

Are you the author of the Sage-blackjack?

Regards,
Tim

The 0.26% number is the Wiz's own. It's based on playing to 75% penetration -- 1-1/2 decks -- and I would assume that he based that number on sims, whereas off-the-top numbers are usually derived from combinatorial analysis.

The reason that it's greater than the off-the-top house edge is because of the "cut-card effect," which comes into play if you have a cut card in a fixed position and you play until it comes out in a round, rather than dealing a fixed number of rounds from each pack. Briefly stated, it's because the number of rounds played will vary depending on whether the front of the pack is predominantly high cards or predominantly low cards, and the extra rounds played in some packs will generally be at a greater player disadvantage.

No, I'm not the author of Sage Blackjack.

Sorry, I've misread your post. I thought you said "played to the last-card" instead of cut-card. Now the advantage makes sense.
You didn't answer if you would take the challenge under my conditions.

Regards,
Tim

exposing his system for a very cheap price. The Wizzard comes out ahead either way.

You won't find on any casino the spread estipulated (1 to 1024). So if the challenger won and the system is disclosed nobody will ever profit from it.

I think Mike S. (the Wizzard) should re-open the challenge again. Or is it there something to fear about? ;)

Regards,
Tim