Doublet D'Alembert - Gains with added stability

[Colbster]

I mentioned an idea that I had in a post just as a comment a few days ago and I have given it enough thought that I think it has some merit to add to the discussion.  This is nothing more than a twist on an old idea, but it eases the risk profile of a popular progression idea that I am a big fan of already, the D'Alembert (+1 on a loss, -1 on a win).

Rather than increasing every loss and dropping every win, I am waiting for a two-in-a-row win or loss to increase or decrease.  We know that a string of losses can jump up the betting fairly quickly on a traditional D'Alembert, requiring a larger bankroll and max bet/max drawdown tolerance.  For instance, losing 8 straight would take your next bet to 9 and your cumulative loss to -36 (-1,-2,-3,-4,-5,-6,-7,-8).  By waiting for the double losses, our next bet would be only 5 and our cumulative loss would be -20 (-1,-1,-2,-2,-3,-3,-4,-4).

However, if we were to win each of the next 8 to get back to the starting 1 unit bet, we would still have the same net result of +8.  Our double wins will always be +2 units, compared to the +1 for every single win on the traditional method.

I ran a quick 200-spin series just for comparison and they compare nicely.  I won 103 and lost 97 playing Evens.  Flat betting, we are +6 units.  Playing the traditional D'Alembert, we ended at +83 with a max bet of 13 and a maximum drawdown of 67 (We didn't finish the series - I am currently at a bet of 7 units after 200 spins).  With my variation, we are up a very respectable +64 with a max bet of only 9 and a max drawdown of 48 (Ended with a next bet of 6).

This seems like a safer alternative with the same desirable expectations of wins with normal distribution, just without the higher risks associated with a large string of losses.

Like I said, nothing really excitingly new here, just a slight change up to ease the downside of a solid progression method.

[Colbster]

To explain how this works, I just had one of THOSE sessions.  200 spins - 111 Losses, 89 Wins.  Flat betting = -22 units.

Original D'Alembert: -164 unit loss but a maximum drawdown of 512 units at one point, max bet of 34 units

My variation: -116 unit loss, max drawdown of 333 units, max bet of 21 units

Clearly there are times when this is very dangerous to play, as any progression can be.  However, it keeps the risk much more tolerable and offers comparable returns to the typical D'Alembert.

[GLC]

Colbster,  Have you looked at triples? 

If doubles make it safer, triples should carry it even further in that direction.  I know that we can accumulate some losses if we get more double losses and a win than we get double wins and a loss, whereas with doubles, we either have a break even or a double loss.  With triples we can actually gain units if we have more wins than losses between triple losses and, of course, the reverse, we could lose extra units, but in the long run they should break about even.

What do you think?

Maybe you could run it through your spins mentioned above and see how it compares.

[biagle]

what we do if: we lost 2 times on 3u bet and betting 4u first win, second loose? Stay and wait 2 in row win/lose?

[Colbster]

@GLC:  George, I did consider triples.  I dismissed it because you could get the series of LLWLLWLLW that lose units without moving up to cover them by increasing the bet.  Of course, you could also have WWLWWLWWL, but those would be at the lower levels anyway and I would take that series all day long.  The time we spent at a level waiting for a triple could be substantially longer than with singles and doubles and there is a lot of volatility that could happen in the meantime.  I didn't save the spins, but I can add a triple formula to the spreadsheet I'm testing with and see where it takes us.

@Biagle: Yes, chops don't have any impact on the game.  We bet every spin so we are in place to get the double wins which come about every 1 spin in 4 but we stay put on betting when we don't have back to back wins or losses.

[Colbster]

I added in triples to see how they would fare and, at least during the disastrous series described previously, it was much safer.

Triples ended with a -57 unit loss (compared to -116 and -164).

The max drawdown was 137 (vs. 333 and 512).

The maximum bet during the session was 9 (against 21 and 34).

Now, the question becomes how profitable can it be in a winning set.  Results to follow.

[Colbster]

The next 200-spin session is completed with 103 wins, 97 losses.

Single D'Alembert
End +75 (Off of max 92)
Max Bet 16
Max Drawdown 105

Double D'Alembert
End +62 (Max was 67)
Max Bet 10
Max Drawdown 67

Triple D'Alembert
End -5 (Max was only 18)
Max Bet 6
Max Drawdown 60

I think that the poor performance on the triple is enough for me to write it off.  It underperformed flat betting with a large drawdown relative to the maximum profit point.  The double pleased me this session, as the max and end figures were very competitive with the original D'Alembert without quite as much risk.

[Colbster]

Just to validate those results, I ran the same numbers H/L.  Here are those results

Single
End 47 (Max was 70)
Max Bet 18
Max Drawdown 143

Double
End 24 (Max was 37)
Max Bet 9
Max Drawdown 71

Triple
End 24 (Max had been 49)
Max Bet 7
Max Drawdown 70

Again, the single had the best return but carried the greatest risk and bankroll requirements.  Double and triple were very comparable, although triple had given back more of the max by the end of the session.  With no major advantage to the triple over the double, and coupled with the poor performance I listed in the previous post, I think that skipping the triple in favor of the double is justifiable.

Just as a note, betting High during these spins won 102 and lost 98.

[GLC]

Colbster,   As I think about it, the more wins/losses we use, the closer we get to the "bread winner" method as outlined in the "Monte Carlo Anecdotes" book.  It was obvious that triples would be safer.  Not so obvious whether they would return enough units to justify either the time or the risk.

Also, I have a progression posted on the forum based on winning 2 or losing 3 (also, winning 3 or losing 2) that I like quite a bit.

Another question I have is if a bet line of 112233445566778899 etc... has enough recovery power after the 5 or 6 or larger levels to keep from getting bogged down in the hole.

Maybe a line like 11 22 33 44 66 88 11 11  14 14  18 18  etc... would have a better risk/reward ratio.  The equalizer is hitting stop losses or table limits which can't be avoided in the long run.

As with all these progression ideas, the more we're willing to risk, the more we win per spin.  The balancing act we face is how much risk do we want take?

[GARNabby]

This is nothing more than a twist on an old idea, but it eases the risk profile of a popular progression idea that I am a big fan of already, the D'Alembert (+1 on a loss, -1 on a win).

Why not raise/lower it on every other loss/win respectively?  Better still, have a useful trigger for that, if only to mix it up so that the house won't know what to expect next.  For example, poker players sometimes bluff (after drawing one card) only on the red Q-high busted four-flush draws.

As with all these progression ideas, the more we're willing to risk, the more we win per spin.  The balancing act we face is how much risk do we want take?

That's where THEY get you.  The progression bet's force can go as low as the actual house edge (HE), to make the most of it by "treading water".  But you aren't going to come out ahead in the short run, which is the purpose of a progression bet.

[GARNabby]

Has anyone noticed, but this method has a few tricks "up its sleeve"?

[Colbster]

Here's another 200-spin set:

96 wins, 104 losses

Original D'Alembert
Ending -9
Max Bet 17
Max Drawdown 119

Doubles
Ending -2
Max Bet 8
Max Drawdown 58

Triples
Ending -34
Max Bet 8
Max Drawdown 71

I only mentioned the triples because I was too lazy to remove the cells from the spreadsheet but I thought that the results just underline what I stated on the topic earlier.

Regarding the Single/Double D'Alembert, I think it was interesting that the Doubles beet flat betting and the Single D'Alembert.  Max bet and max drawdown were about half that of the original and essentially broke even on a losing session.

[Turner]

This works very nice on my 10 line EC patterns. Thanks Colbster. I havn't considered stretching a D'Alambert.

[GLC]

I think what the results are demonstrating for us is that no matter what bet method we use there's a certain sequence that will give a loss and others that will give a win.  Different sequences will affect singles different than doubles different than triples etc...

It's like the sequence many hucksters use where they front load the beginning with losses and back load the ending with wins to show that with 20 losses and only 15 wins, their system will produce a win.

I'm not necessarily trying to make a case for triples, just pointing out that none of these methods are necessarily better than the others.  It depends on the how the spins are coming at the time you're playing.

Though it sounds like I'm being negative about this idea, nothing can be further from the truth.  I'm a total "gambler's fallacy" zombie and have been for years.

As a matter of fact, my favorite double dozen method of late is based on a double loss.  I play the last 2 dozens to hit.  I don't increase my bet size unless I lose 2 times in a row.  Then I add 1 unit to both dozens.  If I lose 3 times in a row, I add 2 more units to both dozens.  I never reduce my unit size until I reach a new profit. 

[GARNabby]

I think what the results are demonstrating for us is that no matter what bet method we use there's a certain sequence that will give a loss and others that will give a win.  Different sequences will affect singles different than doubles different than triples etc...

Not true.

If you bet a set fraction < 1 of your BR (, and as the BR changes,) and losses and wins even out, then your BR will shrink regardless the order of the L/W outcomes.

So, naturally, the game is to find how that simple observation, itself, is evened out in the grand scheme of things.  Surely, the house does not have a God-given edge in every way (in practice and/or theory)?

It's like the sequence many hucksters use where they front load the beginning with losses and back load the ending with wins to show that with 20 losses and only 15 wins, their system will produce a win.

Turn 'er around is fair play.  (Hint.)