
518 P.2d 767 (1974)
Harrison Leroy HUTCHINGS, Appellant,
v.
STATE of Alaska, Appellee.
No. 1788.
Supreme Court of Alaska.
February 1, 1974.
*768 Susan Burke, Asst. Public Defender, Herbert D. Soll, Public Defender, Anchorage, for appellant.
Robert B. Downes, Asst. Dist. Atty., Fairbanks, John E. Havelock, Atty. Gen., Juneau, for appellee.
Before RABINOWITZ, C.J., and CONNOR, ERWIN, BOOCHEVER and FITZGERALD, JJ.

OPINION
BOOCHEVER, Justice.
Harrison Leroy Hutchings was convicted of selling a stimulant drug in violation of AS 17.12.010. He asserts on appeal that the trial judge erroneously excluded impeachment evidence.
Jimmie Clements was employed as an undercover police officer in January of 1972. He testified at Hutchings' trial that in the early morning hours of January 15, he was in the Gold Rush Bar when Verna Hofhines, another undercover agent, introduced him to Hutchings. According to Clements' account, Hutchings sold him what Hutchings represented to be 100 tablets of "speed" for $35. Subsequent analysis disclosed that the tablets were amphetamines. A few days later, Clements saw Hutchings in a parking lot and pointed him out to a police officer as the man from whom he had purchased the tablets.
Clements identified Hutchings at trial. However, the only other person present, Verna Hofhines, testified categorically that Hutchings was not the man she introduced to Clements the morning of January 15. On cross-examination, defense counsel sought to elicit from Clements the fact that he had been discharged from the police force and was seeking reinstatement, reasoning that Clements might have been attempting to curry favor with his superiors by giving testimony helpful to the prosecution.[1] An objection to this line of inquiry was sustained on the ground that it constituted "improper impeachment", presumably in accord with the district attorney's argument that the dismissal and efforts to be reinstated were immaterial and irrelevant. It is this ruling that appellant assigns as prejudicial error.
Recognizing the role that motive may play in coloring a witness's testimony, this court has always endorsed a broad scope of inquiry into the possibility of bias. In Whitton v. State, we wrote:
What we are speaking of is bias  "the slanting effect upon human testimony of the emotions or feelings of the witness toward the parties or the self-interest of the witness in the outcome of the case." Because this human tendency is so common and well known, reasonable latitude must be allowed in the cross-examination *769 of a witness, and also in the introduction of extrinsic testimony, to bring out facts and circumstances which, when tested by human experience, tend to show that the witness may be biased.[2]
And in R.L.R. v. State, we directed that:
[G]reat liberality should be given defense counsel in cross-examination of a prosecution witness with respect to his motive for testifying.[3]
We take this opportunity to reaffirm the principle that undue restriction of investigation of bias is an abuse of discretion which requires retrial.[4]
We ruled in Whitton that defense counsel should have been permitted to ask a prosecution witness whether he had been promised immunity for testifying on behalf of the state, or whether he expected immunity or leniency. Similarly, in R.L.R. v. State, we held that the trial judge erroneously circumscribed the permissible scope of impeachment by refusing to allow defense counsel to inquire into the circumstances under which the prosecution witness's employment as a police informer arose.[5] These decisions bear closely upon the case at hand. Indeed, the facts of R.L.R. are so akin to those of the case at bar that we regard it as dispositive of this appeal. There, as here, the only evidence connecting the defendant to an illicit drug sale was the testimony of a police informer; and there, as here, a line of questioning which might have indicated a prosecution bias was excluded. It is true that in R.L.R., defense counsel sought to ascertain whether the informer-witness hoped to avoid or mitigate criminal punishment by testifying for the state, while here reinstatement with the police force was the potential source of prosecution bias; but this is a distinction without a difference. What is material is that the opportunity of the witness to achieve either of these objectives could serve as a powerful motivation to shade one's testimony, either unconsciously or intentionally. This being so, the appellant should have been allowed to explore the possibility of bias presented by the fact of Clements' discharge and his subsequent efforts to be reinstated.
We believe that an articulation of the standards used to assess the relevancy and materiality of evidence offered to show bias is necessary. To be of sufficient relevance for admission, testimony, documents or other evidence must have some tendency in reason to establish a proposition material to the case.[6] The offered evidence need not, of itself, prove the fact it purports to aid in determining; it need only "render the desired inference more probable than it would be without the evidence. ..."[7] When evidence is offered to impeach a witness by showing bias, the same rule applies. There are no special rules of "proper impeachment" for bias. The credibility of witnesses is always a material issue, so the only question of materiality or relevance when evidence is offered to impeach for bias is whether the evidence tends in reason to demonstrate the existence of some fact, state of mind or condition that a reasonable person would take into account in assessing the credibility of the witness under attack. As we pointed out above, the balance must be weighed in favor of admissibility where impeachment for bias is the object.
The state argues that the testimony defense counsel attempted to elicit might *770 also have been construed by the jury as evidence of a bias against the State, since the jurors might have reasoned that Clements resented being discharged. But the State misapprehends the entire thrust of appellant's contention. It was not Clements' discharge, but rather his endeavor to be reinstated, that tended to raise the spector of bias. Even if Clements had been angered by his dismissal, we suspect that he would have been reluctant to manifest his displeasure while he was trying to recover his old position. Nor would we hold otherwise if the attempted impeachment was two-edged. Where testimony relevant to a showing of bias may aid or injure either party, each of them is entitled to introduce it into evidence; whether to do so or not is purely a matter of trial strategy.
The state also argues that even if the trial court did abuse its discretion[8] in excluding the bias evidence, the trial judge did not commit reversible error,[9] because the erroneous ruling did not appreciably affect the jury's verdict.[10] Clements was one of two persons who could have identified Hutchings as the purveyor of illicit drugs. The other, Verna Hofhines, asserted at trial without reservation that Hutchings was not the man who had sold Clements amphetamines. We believe that evidence tending to impugn Clements' testimony probably would have been considered by the jury in its deliberations, and we cannot therefore agree that the exclusion of the bias testimony in this case was harmless error. We accordingly find it necessary to remand the case for a new trial.
Reversed and remanded.
NOTES
[1]  Appellant also argues on appeal that Clements might have been trying to demonstrate that he was an effective police officer by procuring a conviction.
[2]  479 P.2d 302, 316-317 (Alaska 1970) (footnotes omitted).
[3]  487 P.2d 27, 44 (1971) (footnotes omitted).
[4]  Id.
[5]  See also Doe v. State, 487 P.2d 47, 58 (Alaska 1971) for a comparable holding.
[6]  McCormick, Evidence, § 185 at 436 (2d ed. Cleary 1972); see Hartsfield v. Carolina Casualty Insurance Co., 451 P.2d 576, 578 (Alaska 1969).
[7]  McCormick, Evidence, § 185 at 437 (2d ed. Cleary 1972) (emphasis original, footnote omitted); see Mutual Life Insurance Co. v. Hillmon, 145 U.S. 285, 12 S.Ct. 909, 36 L.Ed. 706 (1892); cf. Hartsfield v. Carolina Casualty Insurance Co., 451 P.2d at 578.
[8]  In Lewis v. State, 469 P.2d 689 (Alaska 1970), we said that an evidentiary ruling will only be reversed where an abuse of discretion has occurred. See R.L.R. v. State, 487 P.2d at 44.
[9]  Crim.R. 47(a) provides: "Any error, defect, irregularity or variance which does not affect substantial rights shall be disregarded."
[10]  This was the non-constitutional harmless error standard we adopted in Love v. State, 457 P.2d 622, 634 (Alaska 1969).
