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IF High[0] < High[1] OR High[0] < High[2] THEN High[0] < Math.Max(High[1], High[ 2])

which follows from High[1] < Math.Max(High[1], High[ 2]) and High[2] < Math.Max(High[1], High[ 2]) and the transitivity of "is smaller than".

The individual conditions are not stochastically independent

Also you mention eight different patterns that are possible with the expression. You forgot one, there are nine patterns, in detail :

a + (NOT b) + c + (NOT d)
a + (NOT b) + (NOT c) + d
(NOT a) + b + c + (NOT d)
(NOT a) + b + (NOT c) + d
a + b + c + (NOT d)
a + b + (NOT c) + d
a + (NOT B) + c +d
(NOT a) + b + c + d
a + b + c + d

And these 7 patterns would not qualify:

(NOT a) + (NOT b) + c + d
(NOT a) + (NOT b) + c + NOT(d)
(NOT a) + (NOT b) + (NOT c) + d
a + b + (NOT c) + NOT(d)
a + (NOT b) + (NOT c) + NOT(d)
(NOT a) + b + (NOT c) + NOT(d)
(NOT a) + (NOT b) + (NOT c) + NOT(d)

That means that out of 16 possible 3 bar patterns based on the comparison of the current bars high and low with the prior 2-bar high and prior 2-bar low, there are 9 patterns that qualify as 3-bar triangles while there are 7 patterns that do not qualify.

The probability for a 3-bar triangle is not > 50%

Now your statement that this does not make any sense is based on a heuristic interpretation of probability. If there are 9 patterns that qualify and 7 patterns that do not qualify, this does not mean that the probability for a triangle pattern is 9/16 = 56.25% !

The reason is that the 4 conditions a, b, c & d are not stochastically independent. If you know that the current bar's high is smaller than the previous bar's high, this increases the probability that the current bar's high is also smaller than the high of the bar two bars ago. Therefore the probability of High[0] < High[1] && High[0] < High[2] is smaller than the sum of the probability for the single events.

And here is some more fun, comparing LBR triangles to Toby Crabels NR7 and IBNR4 bars.

Today's regular session for ES 09-13 has so far produced 80 price bars. Out of these

- 2 bars are inside bar narrow range 4 bars (these are always LBR triangles)
- 3 bars are narrow range 7 bars
- 3 bars are inside bar narrow range 7 bars (these are always LBR triangles)
- 13 bars are triangles (16.25%)

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London

Futures Experience: Intermediate

Platform: Amibroker, Multicharts

Favorite Futures: ES

Posts: 26 since May 2011

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Why do you think I intended to entertain you. As you discovered yourself I awaken you.

yes, I did, the obvious one, a and b and c and d

And you went to far to assume what I was thinking. What I meant is that it is impossible for a pattern like this to have a positive expectation in any market other than when showing isolated selections of it. Just backtest it in a portfolio and look at the results.

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I agree that the pattern alone cannot be profitable. LBR suggests to limit the (average true) range of the last bar and add the requirement for a low ADX reading. But their relative frequence would not invalidate 3-bar triangles as an element for a setup.

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London

Futures Experience: Intermediate

Platform: Amibroker, Multicharts

Favorite Futures: ES

Posts: 26 since May 2011

Thanks: 20 given,
8
received

The matter concerns whether some arbitrarily selected pattern by some author has merit, especially when no backtesting results are presented but just hand waving arguments of adding some other filter and some other indicator. These are things someone reads in books written in the 1980s. This is internet and Twitter age. Anyone trying to figure out how to trade using such absurd constructs is doomed. This is the matter of importance, not whether I missed one possible variation of the pattern. All of the Boolean logic will be of no help to you if you do not know what the premises are.

We agree that a single, simple pattern will not make a trader rich. But a triangle has a meaning, it might point to a consolidation and reduced volatility. It is not a bad idea to detect consolidations and low volatility conditions, as this increases the probability for a larger move to follow.

Of course this is also true for ascending, descending or symmetrical triangles or for other well know consolidation patterns such as flags and pennants. Therefore I would not reject to use such tools as filters to keep me out of high volatility (high risk) trades, when entering a position.

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The indicator allows to display various patterns as described by Toby Crabel in his book "DayTrading with Short Term Price Patterns and Opening Range Breakout", and you can also display the triangles as described by Linda Bradford Raschke.

To display the triangles please set

Drawing method = Detail
Display three bar triangles = true

also see chart attached.

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