So now for the martingale.

I thinks it's fair to say that anybody using the original 1-2-4-8-16-32-64-128 etc... is asking for trouble. But what about a limited form of martingale.

Koetsch explores this and then goes on to compare everything in some further tables. But let's start at the beginning and compare the flat bet against a martingale x1, x2 and x3.


[attachimg=1]

[attachimg=2]

So with the martingale x1, you are doubling up after the first loss.
With the martingale x2, you are doubling up 1,2,4.
With the martingale x3, you are doubling up 1,2,4,8.

Looking at the tables, you can see the martingale makes a difference. Although you could theoretically lose 375 chips on the martingale x3, it's not very likely. The actual peak loss reached -119 chips. So to keep yourself within the starting stake of 100 chips, the martingale x2 had an actual peak loss in 600 rounds of -71. Koetsch states it's important to remember that because you are now playing the martingale, the house take has more than doubled for the average fully played round. You have to quit when your ahead and get out on one of the statistically available up-swings.

Once again, the rounds where the peak winnings exceed 10,20 or 30 chips is much better than flat betting. For example, the number of rounds which offer the possibiity of winning 10 chips more than doubles from 25 to 56. Koetsch states it's clear that while using an unlimited martingale is indeed a bad bet, in a limited form it can be an asset for a successful betting strategy.

It's also important to look at the reversals with the martingale. The defensive approach of the martingale improves things in this area and is another benefit of using such a strategy.


end of part 5.

The baccarat shoe/s above had a peak drawdown of 24 units on the geometric x3 side which is roughly in line with the average peak loss within a round of 21.

The flat bet component had a peak drawdown of 5 units which falls under the average peak loss within a round of -8.13.

Just as an interlude before part 5 tomorrow, I thought I would share with you guys a very stubborn baccarat shoe. This is a test of flat betting vs the geometric x3 strategy. I bet player only all the way through and there is not one reversal on either flat betting mode or geometric x3. I should also mention so as not to confuse anyone that a reversal is only when a net loss situation reverses to become a net gain.

Looking at this may give someone a clearer insight into things. It was a bit of teaser because hand 100 left me stranded on the geometric x3 side. The next bet would have been 40 and could have ended things with a 5 chip profit and the first reversal, LoL.

Here is some more geometric betting to cover x4 and x5.

[attachimg=1]

[attachimg=2]

Even though a 100 chip bankroll is in use, the statistical results show that a stake of 70 would carry someone through the worst actual peak losses while waiting for the net gain to turn positive. Of course, this is twice the stake needed for the flat betting strategy, but the average peak gain is 3 to 6 times higher. The author always stresses the importance of monitoring the reversals and getting out at the appropriate time. That is so important because not getting out before the 100 games are up invariably shows the casino as winning.

The beauty of the parlaying of bets can be clearly seen in the stats where peak gains exceeds 10, 20 or 30 chips. So if you want to quit with 10 chip winnings, the geometric betting strategy will increase your chances by about 2-3 times over flat bets. For 20 chip winnings, geometric is better by 20-30 times. And for 30 chip winnings, the x5 is nearly twice as good as the x3 geometric bet. Where as flat betting simply can't get there at all. Enjoy playing up your winning guys BUT know when to get out. The problem with the higher you go in the geometric betting is the number of reversals decrease. Some players might feel comfortable only going up to x4 knowing that the average number of reversals will be 2.

The next part will deal with the martingale and the good news is that things get better (especially on the reversals side of things)

end of part 4.

I was reading up on 'regression to mean' tonight having not really looked at it before.

The one thing that struck me is that you could be in for a long wait if you played for it in a traditional sense and didn't have any software that could look for a lot of different opportunities.

So I was thinking how I would attack it if I was sitting in a B+M casino.

One way to speed things up could be to look for missing pairs.

So you have BB, BR, RR, RB.  OO, OE, EE, EO.  LL, LH, HH, HL.

[attachimg=1]

In the picture above, the OE went missing for 17 pairs before a hit and then it went W,W,W,L,W,L,L during the next 14 spins. So suppose you hit it after the first W until you hit two consecutive L's. It returned 6 units profit.

What I like about this idea using all 12 pairs across the 3 e/c's is that you will regularly see pairs going missing for 15+ times which equates to 30 spins. So I suppose that's roughly the same as just a single e/c going missing for 7/8 spins on the bounce which seems to be an acceptable number of missing spins to start looking for 'regression to mean' opportunities.

It's just a suggestion as an alternative to look out for. I will see how it goes next time I am at the casino.

Hello Kav,

Koetsch did use negative progressions as well (martingale with a bit of a variation) and I will come on to them in part 5 after finishing the geometric strategies.

In fact, one particular martingale variant is his favourite and performs very well. It is a bit of an eye opener because a lot of people assume the martingale is probaly the worst progression out there. I suppose it is if you don't have a good understanding of how to use it to good effect.

I will do another couple of parts tomorrow. Thanks.

Part 3 explores geometric betting. This is letting a winning bet ride. So let's go for x3 again. (1,2,4,8) Revert back to 1 unit on a loss.

Here are the results

[attachimg=1]

[attachimg=2]

The theoretical winning limit is rising all the time. It's nearly 4 times what's possible with flat betting. Remember you are only using a bank of 100 chips maximum. Also the average peak gain is now three times what the benchmark flat betting strategy produced.

Winning 10, 20 or 30 chips are all better using the geometric betting strategy compared to the linear bet and flat betting. In 64% of the rounds you can now quit with a 10 chip gain, compared to only 25% with flat bets. In fact, now 25% of the rounds will allow for a 30 chip gain.

The only slight downside is that the reversals have dropped below 3 to 2.53. But that still gives you a chance  to get out of the round without losing. So the geometric bet looks good. Better than the linear bet and much better than the flat bet.

More geometric bets will be explored in part 4.

Hello klw,

I have to admit that after reading many gambling books that I was quite sceptical about the claims in this book. So I went to 'testmystrategy' and loaded as many of these parameters as I could and noted down the results. There were certainly no wild discrepancies and everything pretty much fell in line with what Koetsch states. I have some spare time on my hands for a few weeks and I will do some more testing.

Some of the progressions Koetsch suggests are very interesting and he has a few personal favourites which I have not come to yet. It's a very detailed research and I really like the guys approach to it all. There is nothing stopping anybody putting their own strategies through similar approaches just to see if they can come up with a kind of 'sweet spot' to maximize any potential gains.

Thanks.

Part 1 showed some statistical analysis for flat betting. Now it's time to look at some diferent progressions and see how the results compare vs flat betting.

Now suppose instead of just betting 1 chip for each of the 100 rounds, you add 1 chip to the previous bet every time you win up to a total of 4 chips. You always revert back to 1 chip after a loss. This is called a linear bet.

Here are the results.

[attachimg=1]

[attachimg=2]

There are a few potential gains with the linear bet compared to the flat bet.

1) A higher potential gain of 250 compared to 100.
2) The peak gain has risen to 63 compared to 28.
3) The aveage peak gain has more than doubled from 6.8 to 14.07.

Admittedly the peak loss has icreased to -51 from -34 but still well within the 100 chip maximum.
So by parlaying the winnings, you are using the casino's money to make slightly larger bets and still safely within the 100 chips.

Also the rounds where your net gains can exceed 10, 20 or 30 chips are vastly improved.
There are twice as many rounds where you can gain over 10 chips. More rounds achieve a 20 chip gain than the flat betting stats gained 10 chips. There were no flat betting rounds which achieved a 30 unit gain, however the linear bet strategy achieved this nine times.

How about the reversals? There are still an average of 3 reversals per round.

So all in all, a bit of an improvement and it gets better.

end of part 2.

For the baccarat aficionado's

A shoe played with all decisions arrived at and profit/loss. (all flat betting)

Ended up at +3 less tax. Can't say it was that great a shoe but it wiped it's feet.

Thank you for your reply XXVV,

The book is a kind of statistical analysis of what you can realistically expect with different betting strategies over the short run.

All the examples are based over 600 rounds of 100 games. So that's 60,000 games.

100 games can be considered the short run as it's possible to fit in 100 games over a couple of hours.

As a benchmark, Koetsch started the first example with just one chip each time and then progresses using different types of progressions. He limits himself to 100 chips maximum for each example and lays out the results in a table format.

He looks for what he considers to be the most useful information.

Namely

1) what are the absolute worst and best things that could theoretically happen?

2) what were the worst and best things that actually did happen in 600 rounds?

3) what were the average worst and best things that did happen?

4) what typically happens if you don't get out while your ahead , but instead play the full round of 100 games?

5) during a round, how often can you expect to get ahead by at least 10, 20 or 30 chips?

6) in a 100 game round, how many times does your bankroll net-status typically reverse from losing to winning?

7) how often does this net-status never reverse but remains losing throughout a 100 game round?

So all in all, it's a very detailed and interesting piece of analysis.

Here is the table for the first example just betting one chip for each of the 100 games.

[attachimg=1]

Some further information.

[attachimg=2]

So what statistical evidence can be gathered from that. It seems the average peak gain is only about +7 chips and the average loss is about -8 chips.

Now one of the main points of the book is knowing when to quit. So clearly, if you are ahead by +7 and hoping to get further ahead, you are making a mistake statistically speaking.

The reversals are an interesting part of the statistical analysis. We all know that games of chance swing backwards and forwards getting ahead a few or behind a few.

17% of rounds had no reversals leaving a healthy 83% of rounds with a reversal. What's more, 68% of the rounds had two reversals. So obviously it pays to keep an eye on any reversals you experience. Playing after more than one reversal could be statistically tricky.

That concludes the statistical analysis for flat betting the nearly even chances.

The following chapters explore using different types of progressions and they throw up some very interesting results with regards to the statistics that I have already looked at.

end of part 1.

This is a pretty good book and worth a review/discussion.

The authors views on betting strategies are based on his analysis of more than 12 million games. His findings lead him to believe that you can quit a winner in up to 90% of the rounds of nearly even odds games.

His results show that progressive betting can trump flat betting. I think a lot of us try all kinds of different kamikaze progressions early on in our quest and then mistakingly start to think that we have to find a winning flat betting strategy instead. The key really as the book shows is knowing when to quit and what are reasonable expectations to have.

I will try and cover things in detail a bit at a time.

Just to say as well that you don't have to specifically wait for one of either BB/RR, EE/OO or LL/HH to have more absences than the BR/RB, EO/OE or LH/HL.

Take this picture as an example.

[attachimg=1]

The HH is missing for 3 pairs and the LH is missing for 4 pairs.

The next few results were  L,L,H,L,L,H,L,L,L,L. So a good mixture of alternating LL, HL and LH was giving a good opportunity for any parlay plays.

The Mongoose would have returned 2 quick wins from 3 games.

Stage 1.
bet 1. L win.
bet 2. L win.

Stage 2.
bet 1. H lose.
bet 2. L win.

Stage 3.
bet 1. L win.  end of game +5.

Stage 1.
bet 1. H lose. end of game -1.

Stage 1.
bet 1. L win.
bet 2. L win.

Stage 2.
bet 1. L win.

stage 3.
bet 1. L win.  end of game +5.

3 quick games resulting in a 9 unit profit.

I will run through a few examples to give you guys a better idea of what's going on.

[attachimg=1]

In the picture above, the EE and EO are missing for 4 pairs (8 spins) and 3 pairs (6 spins)

The next few results come out as follows. O,O,O,O,O,E,O,E,O,E.

A few things to note here. The last three pairs hit OE, OE, OE consecutively. When it goes like this for a few pairs, you could just bet for that first O.

If the EE and EO are missing, you don't mind so much when a mixture of either OO and OE appear or EO and OO. Because this situation is great for parlays (ie STAR or Mongoose)

It's when you start getting consecutive hits of either OE or EO like the three pairs circled where you need to be careful with some of the different types of MM out there which require back to back wins. EO followed by OE or OE followed by EO on a loop is still giving you two wins followed by two losses.

You always need to be alert to what's going on and adjust your MM to suit the situation.

Here is my low variance strategy for all even chance bets.

The penny ante idea interested me because I have spent several years working with results in pairs and they fascinate me. Working with 4 groups (BB,BR,RR,RB) can lead to some long absences for one (or even 2) of these 4 pairs.

Now there was a thread last year in the Baccarat section called 'Intervals' where the author went off on a bit of a tangent towards the end. Previous to that, another poster called 'Chef' suggested that the entry and exit points were vital towards some lower variance if someone wanted to create a winning strategy using these 4 pairs.

The original idea was the following.

RR, OO, LL =1.
RB, OE, LH = 2.
BB, EE, HH = 3.
BR, EO, HL = 4.

If 1/2 absent. Bet B1, E1 or H1. (1 means the first result of the pair)
If 1/3 absent. Bet the opposite of the first result on the second result of the pair.
If 1/4 absent. Bet B2, E2 or H2. (2 means the second result of the pair)
If 2/3 absent. Bet R2, O2 or L2.
If 2/4 absent. Bet the same as the first result on the second result of the pair.
If 3/4 absent. Bet R1, O1 or L1.

Now there is nothing much wrong with this but I do think it can be improved with the following.

Take a look at this picture.

[attachimg=1]

You can see that the BB pair has went missing for 8 pairs (16 spins)

Taking BB out of the equation now gives the R's a two thirds to one ratio over the B's. Of course the reverse would also hold true where removing the RR pair would give the B's a two thirds to one ratio over the R's.

So this is a good starting point. Now looking again at the picture, you can also see that the BR has went missing for 6 pairs (12 spins)

So this knocks out another B and one R. So now the ratio left is three R's to one B. That's now boosted things up from 66% to 75%. So you are going to witness a nice stream of R's if BB and BR continue to be absent. The same would also hold true if BB and RB become absent.

The R stream after row 5 is R,R,R,B,R,B,R,R.

That's 6 R's to 2 B's. In other words W,W,W,L,W,L,W,W.

Some nice variance there indeed. Obviously this can be replicated over all three even chances. Baccarat would be somewhat limited because of just the one stream.

I am taking a guess that this is what 'Chef' had in mind because the entry and exit points are vital. You are looking for one of the BB or RR pairs to be missing. But you DON'T want both of those pairs to be missing at the same time.

So it's BB and BR/RB

or

RR and RB/BR

Of course the original idea is still worth looking out for as well.

Looking at the picture again and specifically the Even and ODDS. You can see that the EO has went missing for 7 pairs (14 spins) and the OE missing for 8 pairs (16 spins)

Here is the rule.

If 2/4 absent. Bet the same as the first result on the second result of the pair.

You can see the last 7 pairs were all double results.

So there you have it. This works wonderfully well and the new idea really gives things a boost.