Finally, Winning Progression w Proof

This game is available to me at the Copa in Gulfpot Ms: single deck, S17, DD10,11, noDAS, Late Surrender, 50% penetration, heads up.

The progression is simple, bet 1 unit, if you lose bet 2 units. Always go back to one unit after a win and don't drop to 1 unit unless you win a 2 unit bet.

Count System (card = tag): 2=0,3=1,4=1,5=1,6=1,7=1,8=0,9=0,T=-1,A=0.
PE = 0.65; 78 indices + Insurance

Simulation: SBA, 1,000,000,000 hands
Flat Betting: -0.01% +/- 0.003
Progression: +0.015% +/- 0.004

In this sim there was no betting with the count, just the progression above. This progression also cut BS disadvantage in a short sim, but did not give a winning game. I will later see if edge can be maintained with just Ill 18 indices. Probably we are seeing the effect of the small correlation between losing a hand and winning the next hand known to exist in 1 deck play. I have never seen a sim that proved you could win with it though, especially with such a small spread. Of course the edge here is so small as to be almost worthless.

Counting only for strategy decisions using a strong level-1 count (very important point, IMO) and varying bets only when the progression calls for it.

I wonder how that would perform in a multiple deck game, using a larger spread, say 1-10 units, using that d'Alembert system (up one unit when you lose, down 1 unit when you win), max bet 10 units when you keep losing, and (here's the ringer) Wonging out at any negative count of -2 or more. I would start the progression at an initial bet of 5 units to try to avoid having to bet only one unit in a long winning streak with a positive running count.

I would try to run the sim myself but do not have the SBA software, and my old BCA Dos system does not handle unbalanced counts.

Anyway, just a thought, thanks for the report on your sim! It is certainly the first one I have ever seen that can shows a positive expectation for ANY progression using computer analysis. One billion hands certainly weeds out practically any chance of a false conclusion. I hope Math Prof, DD', and others respond to your post!

AB

In Wong's Prof. Blackjack, I recall that he ran a simulation and showed that the odds of winning a hand following a loss and win were virtually identical. No?

Since the negative correlation between hands is only correlated with the count, and the count itself is an extremely weak phenomena with 8-decks, it is unsurprising Wong's sim found nothing of significance. 1-deck sims show noticeable effects, though nothing of much interest to someone who plays for money.

It is certainly the first one I have ever seen that can shows a positive expectation for ANY progression using computer analysis. One billion hands certainly weeds out practically any chance of a false conclusion. I hope Math Prof, DD', and others respond to your post!

The negative correlation has been recognized for at least fifteen years. I doubt any one wants to get into this territory again.

In the past I've trashed the gambling establishment for pretending the negative correlation between hands doesn't exist. It does. However, at the same time, you have to recognize it is only of interest as a loss limitation method for basic strategists and of no practical value to an advantage player.

So many other fascinating legitimate forms of advantage play exist I see no reason to discuss the progression issue endlessly.

Bert, you did it. You added one-quarter of one-tenth of one percent to EV by using a progression. Nice job. Seriously.

Would you believe that in one one-year period (long, long ago) I added just over 500 times that amount just by targetting dealer error? ;-)

ETF

It all comes down to what your assumptions are when you start calculating. If the idea is logical,and independent thought agrees, the math will just comfirm what you intuitively know. Rock-solid implies no exceptions. Re: mathematics of progressions by MathPro on this page.

I have SBA and do not see how you told the program to up your bet after a loss. Please clarify that, and possibly post the entire SIM results.

This an interesting result. I do need to echo what John May said, and that is that this phenomena has been known for many years. Griffin comments on it in ToBJ, and there was a paper by Gwyn which appeared in BJF.

My recollection (which is very imperfect) was that Gwynn's work showed the negative progression player getting a net edge in the S17 single deck game which existed at the time.

More recently casinos have gone to H17, which gives them enough of an edge that it is hard to overcome just by using "progression" methods. I did some sims which are posted over on BJMath which indicated the impracticality of this for the BS player.

Now in your Sim, you have been able to negative the House advantage by using an excellent playing count, This playing strategy basically gives the flat-bettor an even edge; if you look at the data you see that you really have a statistical tie for flat-betting.

So in one sense, you have a situation analogous to the Gwyn situation: a nearly even game off the top, which can be beaten with a martingale-type approach.

However, there is one more element present here: a depth-charging effect. Your player gains an edge the deeper you go into the deck. Now your progression player only bets 1 unit off the top; the bigger bets come when the playing strategy gives an edge.

It would be interesting to see how the player did if they bet 1 unit on the first round, and then always bet 2 units on the later rounds. I don't recall if SBA can handle that, but it would help to isolate the depth-charging effect from the Martingale effect.

PS: Do you have a cut-card effect. If so, then the result is more impressive.

I did a shorter sim, not nearly 1 billion hands, that showed an increased loss if you increased bet after a win. The depth charge effect should be evident either way, what? Anyway, this was only 50% pen. I will sim 1 billion hands later increasing bet after win.

By the was, the effect is apparent in DD game, S17, DAS, Late Surender, DOA, 50% penetration and the edge is much greater.

It did not work in 6 deck game no matter how big the spread.

Bert

Go to the beting section, change to cover betting. In the next to last row titled "Bet - lost", change bet to 2 across all counts and leave at 1 unit for a win in the "Bet - won" row across all counts.

Bert Nommel

Bert wrote:

I did a shorter sim, not nearly 1 billion hands, that showed an increased loss if you increased bet after a win. The depth charge effect should be evident either way, what?

Are you saying that the positive progression had an outright negative EV, the negative progression had a positive EV. This does suggests that the depth-charging effect is not playing that significant a role here. At least the progression is playing the more serious role.

Doggone it, here I was hoping that I could chip up after a loss while counting and then blame it on the "negative progression" I was using. Oh well, chipping up after wins draws less attention anyway. Thanks for sharing the results of your sims.

AB

...creative endeavour here, there is an upper limit to the effectiveness of the negative correlation-the actual change in % advantage resulting from wins, losses and pushes. Even if you calculate this perfectly you do not have the basis for a practical winning system under any conceivable conditions. Any progression system designed to exploit the negative correlation would only do worse.

On the plus side...its very nice to see this sort of discussion can take place without too much hysteria.

However, there is one more element present here: a depth-charging effect. Your player gains an edge the deeper you go into the deck. Now your progression player only bets 1 unit off the top; the bigger bets come when the playing strategy gives an edge.

I looked at this some years back and some of the results are presented in Get The Edge At Blackjack. I did some sim work on the effects of depth-charging a martingale at single-deck-the conclusion being that even if you reset the martingale at the top of the deck and played with almost no restriction on bet spread the increased variance largely offset the extra gain. The D'alembert or pyramid progression worked rather better, outperforming flat-betting by several tenths of % without increased fluctuation, however it was nowhere near substituting even a 1:2 spread in accordance with the count.

The study had some interest then because some players were making a living flat betting single-deck in the mid-nineties, and this was a superior mathematical and to my mind, cover, approach . However, I doubt any one is trying this at the moment with the decline of favourable SD games in Nevada.

I don't have the slightest idea how someone can explain all this
nonsense with fewer words and more clearly than you did.
Accept my congrats.

Sincerely
Z

I am just a humble guy from the midwest but all this gushing on something that gives such a small difference in edge drives me crazy.

Why would somebody count with 78 indicies and not bet with the count?
(you are already moving the bets 2 to 1!)

I agree with ETfan below that there are far bigger fish to fry.

The thing that drives me mad is that cardcounters spend such large amounts of time on stuff like this for diminishing returns.
(no reward for lots of effort!)

There are some huge edges out there, so big that 0.01% differences become insignificant.

With a 0.01% edge I wonder how many hours of play it would take to be 99% sure of being ahead?
But it sure beats working in Mcdonald?

errrrrr......... actually no it doesn,t by a long way!

D.