Now let's consider the 8 possible outcomes of any 3-hand pattern regarding the mechanical B-B-P betting plan:

For "probability of success" I refer to any sequence capable to produce at least one win.

1) B-B-B. Such sequence is one of the second best, meaning that the probability of success is 100% but it gets just an overall +1 profit (minus vig).

2) B-B-P. The best sequence to get, the probability of success is 100% and the profit is the best we can hope for (+3 minus vig)

3) B-P-B. The probability of success (PoS) is 100% but it leads to a negative overall profit (-1 plus vig)

4) B-P-P.Again the PoS is 100% still it is one of the second best patterns to get (+1 minus vig)

5) P-P-P. PoS of 100%, overall profit -1 unit (no vig)

6) P-B-P. PoS of 100%, overall profit +1 (minus vig)

7) P-B-B. PoS of 100%, overall profit -1 (minus vig)

P-P-B PoS = zero, no profit.

For every 3-hand sequence the PoS is 87.5% proportionally splitted into three different steps of any single 3-hand sequence.

Actually the PoS is higher than 87.5% as patterns #1, #2, #3 and #7 will happen slightly more often than what a 50/50 game suggests.

As you can notice, the purpose to introduce a single P on any 3-hand sequence is oriented to reduce the negative variance.

Thus any PPP or PPPP or PPPPP... patterns will form at least one winning hand no matter what.

On the other side, the BB pattern is more likely than the BP pattern so any BB or BBB or BBBB or BBBBB... patterns will produce at least one or more consecutive winning hands.

The PoS is related about the probability to get at least one winning hand per every 3-hand pattern dealt.

Again the B-B-P mehcanical strategy in terms of PoS will lose only whenever a P-P-B pattern will show up precisely on the very first spot.

Odds dictate that most of the time such pattern will show up isolated or in clusters of two.

After that cutoff point we simply should quit the attack.

Of course the PoS implies the use of a 1-2-4 progression but we'll see that we don't need to utilize the full progression as a careful regsitration of what happened so far might help us to spot the situations where the most likely situation should come out more often than not.

Now I run 10 pc generated shoes and I randomly choose the #3 shoe from the list.

Here's the shoe (ties ignored):

PBPPBBPPPPBBBPPBBPPBPBBBBBBBBPBBPBPPBBPBBPPBPBPBBBPBPPBPPBBPPPBPPBPPPPPPPBP.

Splitting into 3-hand patterns we will get:

PBP -++

PBB -+-

PPP --+

PBB -+-

BPP +-+

BBP +++

PBP -++

BBB ++-

BBB ++-

BBP +++

BBP +++

BPP +-+

BBP +++

BBP +++

PBP -++

BPB +--

BBP +++

BPP +-+

BPP +-+

BBP +++

PPB ---

PPB ---

PPP --+

PPP --+

PBP.-++

-++-+---+-+-+-++++-++++-++-+++++++-+++++++-+++--++++-++-++++--------+--+-++.

Luck favored this attack as BBP were well higher than PPB but notice the distribution of single + and clustered + as well as single - and clustered -.

Interesting to notice that P doubles were 8 and P 3+s were only 3.

A new shoe is:

PPBBPPPPBPBBBBBBPPBPPBBPPPBPPBBPPBBPPPBPBBBPPPPBBPPBBBPBPPBPBPPPPPBBBPPPPPP

Again we split the outcomes in tranches of 3:

PPB ---

BPP +-+

PPB ---

PBB -+-

BBB ++-

BPP +-+

BPP +-+

BBP +++

PPB ---

PPB ---

BPP +-+

BBP +++

PPB ---

PBB -+-

BPP +-+

PPB ---

BPP +-+

BBB ++-

PBP -++

PBP -++

BPP +-+

PPP --+

BBB ++-

PPP --+

PPP --+

---+-+----+-++-+-++-++++------+-++++----+-+-+---+-+++--++-+++-+--+++---+--+

This shoe wasn't so lucky as PPB>BBP, anyway we got some hints about the distribution of WL signs.

More on this next week.

as.