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Here is one of the most detailed explanations on the 'penny ante' concept that I have found.

It deals with triples and quadruples.

You will find this in Chapter 5 titled 'Nontransitive Paradoxes'

Chapter 6 titled 'Combinatorial Card Problems' is interesting as well.

Here is the link to the book.

http://www.logic-books.info/sites/default/files/k12-time_travel_and_other_matematical_bewilderments.pdf

The question is can you find a way to make penny ante work in roulette?

[Rolex-Watch]

Many years ago I spent a long time trying to get this "penny ante" to work with Baccarat and was unable, from memory because the house has to declare a path in terms of B or P, which obviously it doesn't, so it is a non-starter. 

Thanks for the link to the PDF....

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Thanks for the reply Rolex-Watch.

Here is the thing though! A passage in Chapter 5 in the book says ''For doublets the waiting time is 4 for HT and TH and 6 for HH and TT.'' Now either I am not understanding it properly or it suggests playing RB/BR in roulette or playing BP/PB in baccarat would be preferable to playing RR/BB or BB/PP straight of the bat. Beats me. The obvious way for me to find out I suppose is to test it over enough results to see if this edge does indeed materialize.

[horus]

OK, I have read through it all again and I think I understand now why it can't be used for roulette or baccarat, LOL. It's interesting though all the same. I get carried away with these sorts of things. I suppose logic dictates that all the casinos would have been closed down years ago by a few shrewd mathematicians if this did actually work.

All is not lost however, I will continue on this thread with a few other ideas I have which hopefully are a bit more worthy.

[horus]

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.

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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.

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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.

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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.