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A range bar is closed (then new bar formed) once price has 'ranged' more than 'x' ticks from its high to low on that bar.
If a tick is 0.01 and you have a 6 range, it means 6 ticks (0.06) in price between the low of the bar and high of the bar. Price can open, go up some, down some, back and forth, but only once the high-low is >6 ticks will the bar close and a new bar open.
Does the logic behind range bars imply that the formation of bars themselves depends on where to start counting? If this is the case, what's the use of them?
Yes, for instance if you have a 24/7 chart and your chart only goes back to Tuesday, and your friend Bob has a 24/7 chart and his goes back to some other date, then when your range bar closes and his range bar closes will be different (almost certainly).
The use of them is they are always the same measurement and price is allowed to move up or down unlimited within the range bar size, so they are simply a unique option that some traders prefer for their "smoothness".
I use a 5 tick range bar when trading TF. 5 is not a magic number, it just happens to be half the ticksize of the TF. I use range bars because it allows me time ( I'm old and slow) to set a stop limit order where the next bar will start. If the market moves the opposite direction, I cancel the order.
I'm just a simple man trading a simple plan.
My daddy always said, "Every day above ground is a good day!"