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There are several instances found across numerous codexes that state something along the lines of "...you may reroll a single hit, wound, save or damage roll..." or some variation, usually through a Warlord Trait. I'll use the Imperial Knights one as an example:

Page 112, Codex: Imperial Knights wrote:Cunning Commander: Once per battle phase, you can re-roll one hit roll, wound roll, damage roll or saving throw made for your Warlord...

With abilities such as this, do you have a single re-roll that you can use on any of the specified effects, or can each effect be re-rolled once througout the course of the game?

 Valkyrie wrote:
There are several instances found across numerous codexes that state something along the lines of "...you may reroll a single hit, wound, save or damage roll..." or some variation, usually through a Warlord Trait. I'll use the Imperial Knights one as an example:

Page 112, Codex: Imperial Knights wrote:Cunning Commander: Once per battle phase, you can re-roll one hit roll, wound roll, damage roll or saving throw made for your Warlord...

With abilities such as this, do you have a single re-roll that you can use on any of the specified effects, or can each effect be re-rolled once througout the course of the game?

It says "or", not "and/or". You only get one roll total, which may be used on any of the listed effects.

Single reroll

Ah I thought that was the case, if so it's a pretty crappy trait. I know you get an extra CP out of it but compared to Landstrider, Ion Bulwark and Champion of the Household, it's rather underwhelming, hence why I raised the possibility of there being more than 1 re-roll.

I think it is intended to offset the cost of using the Exalted Host Stratagem to make a Knight a Character which also gives them a Warlord Trait. You can then use that CP to purchase a Relic for the Knight.

So for with this Warlord Trait it cost one CP to take a Knight in a SHAD, make it a Character and give it a Relic.

It is "Once PER Battle Phase" in the example given.

There are 6 "Battle Phases" in each players turn, giving you 6 potential rerolls per player turn.

The rules never refer to the Phases of the Turn as Battle Phases.

OP misquoted the rule:

Once per battle, you can re-roll one hit roll, wound roll, damage roll or saving throw made for your Warlord. In addition, if your army is Battle-forged, you gain an additional Command Point.

 Ghaz wrote:
OP misquoted the rule:

Once per battle, you can re-roll one hit roll, wound roll, damage roll or saving throw made for your Warlord. In addition, if your army is Battle-forged, you gain an additional Command Point.

I was only quoting the bit relevant to the question.

 Valkyrie wrote:

 Ghaz wrote:
OP misquoted the rule:

Once per battle, you can re-roll one hit roll, wound roll, damage roll or saving throw made for your Warlord. In addition, if your army is Battle-forged, you gain an additional Command Point.

I was only quoting the bit relevant to the question.

You misquoted the rule making it look like its usable every phase, which is not true.

 p5freak wrote:

 Valkyrie wrote:

 Ghaz wrote:
OP misquoted the rule:

Once per battle, you can re-roll one hit roll, wound roll, damage roll or saving throw made for your Warlord. In addition, if your army is Battle-forged, you gain an additional Command Point.

I was only quoting the bit relevant to the question.

You misquoted the rule making it look like its usable every phase, which is not true.

Whoops, you're right. My mistake.

The warlord traits with that ability are often doubled up with the on a 5+ you get a CP back when you use a stratagem, so it does offset.