
625 F.3d 673 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
Kevin Tommie HALL, Defendant-Appellant.
No. 09-3165.
United States Court of Appeals, Tenth Circuit.
November 16, 2010.
*675 Madeline S. Cohen, Assistant Federal Public Defender, (Raymond P. Moore, Federal Public Defender, with her on the briefs), Denver, CO, for Defendant-Appellant.
Terra D. Morehead, Assistant United States Attorney, (Lanny D. Welch, United States Attorney, with her on the brief), Kansas City, KS, for Plaintiff-Appellee.
Before HARTZ, ANDERSON, and TYMKOVICH, Circuit Judges.
HARTZ, Circuit Judge.

I. INTRODUCTION
Kevin Tommie Hall was convicted of robbing a bank in November 2006 and committing the related crimes of brandishing a firearm in relation to a crime of violence and being a felon in possession of a firearm. He was not a novice, having robbed at least four banks in the past and having twice been convicted of the offense. He appeals his most recent conviction on the ground that the jury was improperly told about his prior offenses.
The indictment against Mr. Hall in the United States District Court for the District of Kansas alleged that he had been convicted of two prior feloniesbank robberies in 1984 and 1992as predicate crimes for the charge of being a felon in possession of a firearm. Mr. Hall stipulated that he had two prior felony convictions, thereby making it unnecessary for the government to put the two convictions into evidence. During voir dire of the jury panel, however, the district court inadvertently read to the jury the entire indictment, including the specific bank-robbery allegations. Mr. Hall moved for a mistrial, but the motion was denied. On appeal Mr. Hall challenges that denial. He also complains about his cross-examination by the government concerning the details of a prior bank robbery and a prior attempted burglary and about portions of the government's closing argument that referred to his bank-robbery history.
We affirm. The denial of the mistrial was harmless error because the 1984 and 1992 bank robberies were admitted into evidence at trial. We reject Mr. Hall's contention that if the district court had not erroneously mentioned the prior convictions, he would not have testified in his own defense (so that the prior convictions would not have been admissible). He did not make that contention in the district court, and the record clearly shows that he had made the decision to testify even if the prior convictions were admitted. Moreover, even if the district court's error induced Mr. Hall to testify, the error was harmless because Mr. Hall would undoubtedly have been convicted had he not testified. As for Mr. Hall's other two issues, neither was raised below and we hold that he has not established plain error.

II. BACKGROUND
Testimony at the trial established the following.

A. The Robbery, the Chase, and the Physical Evidence
At 1:36 p.m. on November 7, 2006, a masked man carrying a pistol-grip shotgun robbed the MidAmerican Bank and Trust in Leavenworth, Kansas. The robber had entered through a rear door, hurried to the teller station, and demanded money *676 from teller Debbie Smith. Smith gave him money from several different drawers, including marked bills with prerecorded serial numbers. The robber put the money in a white plastic bag and left through the rear door. He walked briskly to a nearby parking lot, got in a car, and drove away.
Mary Garrison, who worked in a neighboring office building, was walking to her car to get a bottle of water when she noticed a white male sitting alone in the passenger seat of a four-door bluish gray car. She then saw a taller white male wearing dark clothing run to the car, get into the driver seat, and speed away. When the police arrived a "a minute or two" later, she described the car and told them the direction in which it had driven off. Trial Tr., Doc. 150 at 125.
At 1:41 p.m. the Lansing, Kansas, Police Department sent out an alert notifying officers of the bank robbery and describing the suspect vehicle as "a four-door blue vehicle occupied by two white males." Id. at 136. At 1:56 p.m., 20 minutes after the robbery, Manuel Olmos, a Lansing police officer, was driving in his marked patrol car when he saw a blue sedan with two white males coming toward him. He made eye contact with its occupants, and his eyes and theirs "just fixated on each other and ... we just kept looking at each other... as we passed each other." Id. at 141. The officer turned his car around and began to follow the vehicle.
A chase ensued, with speeds exceeding 100 miles per hour. The blue sedan ran stop signs, sped through intersections, drove in emergency lanes to get around other vehicles, and passed a funeral procession at a high rate of speed. Eventually, the blue sedan came to a stop in a parking lot in Kansas City, Kansas, after officers placed "stop sticks" in the road to deflate the car's tires. Id. at 191. The vehicle's occupants were arrested at gunpoint. Mr. Hall was the driver and James Morrison was the passenger. The blue sedan was registered to Mr. Hall. Mr. Hall was clothed almost entirely in Harley-Davidson apparel; he was wearing a Harley-Davidson shirt, a pair of Harley-Davidson jeans, and black Harley-Davidson zip-up boots with a lace on top. He was also wearing a black belt with a large Harley-Davidson silver buckle on which a gold-colored eagle was depicted.
Several items related to the robbery were recovered along a rural gravel road on the route of the chase. One of the pursuing officers had noticed dark clothing lying by the side of the road and radioed its location. Another officer searched the area and found a black hooded sweatshirt and a pair of brown gloves.
Farther up the road, members of a Westar Energy crew installing overhead power lines had seen police cars pursuing a blue sedan. As the sedan raced by, the crew foreman observed that the passenger "looked like he was changing his shirt or something he was, kind of humped in the seat, his arms were like somebody was taking off a shirt or putting one on." Id. at 215. A crew member working in an aerial bucket when the sedan passed saw a black object fly out of the passenger-side window. Police searched the area and recovered a ski mask. A forensic scientist was able to obtain a DNA profile from the mask that was consistent with Mr. Hall's DNA. Only 1 in 35,160 people would have a matching profile.
Another officer searching along the gravel road found a white plastic bag containing $14,440, including the marked bills from the bank. (A later audit of the teller's drawer showed that $14,541 had been taken.) On the bag was the Harley-Davidson logo and the address of a Harley-Davidson store in Blue Springs, Missouri. The day after the robbery, police *677 officers discovered a dark, pump-action shotgun with a pistol grip in a roadside ditch by the gravel road.
After arresting Mr. Hall, officers searched his car and found in the back seat a receipt from a Wal-Mart in Lee's Summit, Missouri. The receipt showed that at 11:14 p.m. on November 6, 2006, the night before the robbery, someone had purchased a three-hole mask, cigarettes, and a pair of gloves. Surveillance footage from the store showed Morrison and Mr. Hall arriving at the Wal-Mart in the blue sedan at 10:50 p.m., both men entering and exiting the store, and Morrison purchasing the items listed on the receipt. Morrison was wearing a distinctive black-and-orange jacket, which police officers found in the back seat of Mr. Hall's car.
Officers also obtained surveillance tapes from the bank. One showed that Morrison had conducted a transaction at Smith's teller station only six minutes before the robbery. Morrison was wearing a Harley-Davidson hat.

B. Mr. Hall's Alibi
To rebut the case against him, Mr. Hall presented an alibi defense. The predicate of the defense was that he was not positively identified by any witnesses at the robbery scene. We therefore summarize the eyewitness descriptions and other identification evidence before reciting his account of his whereabouts.
Mr. Hall is white and 6'2" tall. At the time of his arrest he was 46 years old, weighed about 210 pounds, had a shaved head, and wore a mustache. Although most of the eyewitnesses were consistent in their descriptions of the robber as relatively slender, approximately six feet tall, and wearing dark clothing and a dark ski mask, and teller Smith said that he was wearing "a black belt with a silver buckle," id. at 79, there were some inconsistencies in the eyewitnesses' physical descriptions of the robber and not all descriptions matched Mr. Hall's true appearance.
One eyewitness described Mr. Hall as 5' 10" (but admitted that was just a guess), and another who admitted to seeing the robber for "[m]aybe about ten seconds," id. at 96, estimated that he was between 5'7" and 5'10" tall. One witness estimated that the robber weighed 165 pounds, while another described him as weighing between 175 and 200 pounds. At least two witnesses described the robber as young, though one based her opinion on the sound of his voice, and the other assumed that the robber was in his 20s "because he was so thin." Id. at 116. Three witnesses described the robber as having hair, but one admitted that what she thought was hair could have been a hat, another (who reported seeing hair coming out the back of the mask) testified that she saw the robber only for a matter of seconds before she got under her desk, and the third stated that because she "didn't see any long hair ... coming out of the ski mask," she assumed that he had short hair. Trial Tr., Doc. 151 at 485. Also, neither of the witnesses who saw the robber after he had left the bank and rolled up the ski mask mentioned seeing a mustache. One witness indicated on a police form that the robber wore tennis shoes, although it was pointed out at trial that the tennis shoe was the only option on the form depicting a lace-up shoe above the ankle. Finally, two witnesses observed that the robber had a tan or dark complexion.
In addition, some of the forensic evidence did not implicate Mr. Hall. The government's expert identified two "possible" hairs inside the recovered ski mask, but did not conduct DNA tests on either of them. Id. at 403. She did find some DNA on the recovered shotgun, but both Mr. Hall and Morrison were eliminated as being *678 its source. Further, the police were unable to find any fingerprints on the shotgun, and the recovered money was not examined for fingerprints.
Mr. Hall filed a notice of alibi defense one week before trial. It said that he would be the sole alibi witness and that at the time of the robbery he was "near a halfway house for recently released prisoners" in Leavenworth, Kansas. Suppl. R., Vol. 1 at 48. Given that he was seen driving the getaway car 20 minutes after the robbery, he needed to explain how he happened to enter the car in the interim. His explanation was that the robber was a man named Lee, who (with Mr. Hall's permission) had driven off with Morrison about 45 minutes before the robbery and returned the car to Mr. Hall a few minutes after the robbery. He testified as follows:
In 1992 Mr. Hall pleaded guilty to a bank robbery committed in 1990. He remained incarcerated until he was released to a halfway house in Leavenworth, Kansas, in August 2005. A few days later he got a job as a welder, making from $600 to $700 per week. After three months in the halfway house, although still on supervised release, he moved to Topeka, Kansas, and lived with his mother before moving in with a girlfriend, Sherry Lorence. He bought a Harley-Davidson and a car.
Mr. Hall incurred two DUI charges during the first half of 2006. As a result, his probation officer required him to wear an electronic monitoring bracelet and imposed an evening curfew. He lost his job in late September 2006 and borrowed money from his mother.
In early November 2006 Mr. Hall had a fight with Lorence. He went to Kansas City, Kansas, where he stayed in motels and with his sister, Connie Lunsford. He was aware that being in Kansas City was a violation of his supervised release, but he assumed that he would be heading back to prison anyway because of the pending DUI charges, so he "just left." Trial Tr., Doc. 148 (Hall Testimony) at 12.
While in Kansas City, Mr. Hall hung out in bars. It was in one such bar, on Saturday, November 4, three days before the robbery, that he met Morrison. The two men met again on November 6. During their night of drinking, they met Lee, who was shorter than Mr. Hall, but taller than Morrison, was "half white, half Mexican," weighed between 165 and 170 pounds, had medium-length brown hair, and was in his late 20s. Id. at 27. Mr. Hall had never met Lee before.
Mr. Hall drove Morrison and Lee to a hotel. After Lee and Morrison carried Morrison's belongings to a room, Morrison returned to the car and asked Mr. Hall to drive him to the store for cigarettes. On the way Mr. Hall noticed that the license-plate light on his car was not working, so he decided to drive to a nearby Wal-Mart to fix it. In addition to cigarettes, he purchased a screwdriver and a hooded sweatshirt for Morrison. Morrison asked for the sweatshirt because the jacket he was wearing belonged to Lee and he needed something to keep warm since "he didn't have a place to stay." Id. at 29. For the same reason, Morrison separately purchased gloves and a ski mask. Mr. Hall then took Morrison back to the hotel, where Morrison got $18 from Lee to repay Mr. Hall. Mr. Hall then drove to his sister's house to spend the night.
Mr. Hall drove back to the hotel the following morning and picked up Morrison and Lee. Morrison needed a truck to get some of his belongings from his former residence, so Mr. Hall volunteered to give him a ride to Lansing, Kansas, where Lee knew someone who would lend them one. En route, they stopped at the hospital where Mr. Hall's sister Connie worked, *679 and she gave him $20. Mr. Hall then drove to a liquor store and purchased a pint of Wild Turkey.
Lee, however, was unable to borrow a truck in Lansing, so they drove to Mr. Hall's former halfway house in Leavenworth. Wanda Wing, Mr. Hall's former girlfriend, was staying there. He wanted to speak to her and thought she might be willing to lend them a truck. Upon their arrival, he asked a woman who was sitting outside to ask Wing to come out and speak with him. While the three men waited for Wing, a staff person came outside. Mr. Hall turned away, knowing that he was not supposed to be associating with residents of the halfway house. Morrison thought that the staff person was staring at Mr. Hall's car, so Mr. Hall suggested that Morrison and Lee take the car elsewhere while he waited across the street for Wing to come out and talk. Morrison and Lee left between 12:30 and 1:00 p.m. Wing never came out to speak with Mr. Hall, though he saw her through a window.
Morrison returned with the car, but not Lee, about an hour later. He said that they were to meet Lee at the Dillons store, so Mr. Hall got in the driver's seat and began driving there. While stopped at a red light, he saw Lee a few cars ahead of them driving a pickup truck, and he tried to follow him.
A few moments later a police car passed Mr. Hall, who noticed that the officer was looking at him "like he saw something, saw a ghost or whatever, that's how hard he looked at me." Id. at 37. Thinking that there might be a warrant out for his arrest because he had violated the terms of his supervised release, he "tried to get away." Id. at 38. By the time he caught up to Lee's truck and pulled along side it, Morrison was "act[ing] like something was really wrong." Id. at 39. Morrison "kept looking back and he kept telling me, hurry, go, go, go, and that's what I was doing." Id. Mr. Hall first asked what was going on when Morrison pulled out a three-quarter inch stack of five dollar bills and put it in a tote bag, but Morrison just told him to drive. Without asking any other questions, he complied. As they passed Lee's truck, Morrison threw the tote bag in the bed of the pickup. Just after that Mr. Hall encountered a police vehicle, which gave chase.
Mr. Hall did not know why he initially was running from the police, but he was scared. He "started figuring out that something was really wrong" when Morrison "started throwing stuff out" and continued imploring Mr. Hall to "go, go, go." Id. at 42. At one point, without saying a word, Morrison reached into the backseat, pulled out a shotgun from underneath Lee's jacket, and brought it toward the window. Not knowing what Morrison was going to do, Mr. Hall grabbed his elbow and the gun discharged. Morrison then threw the gun out the window. He also threw out the window a white, plastic bag that was tied shut. It was only then that Morrison told him that "Lee might have robbed something." Id. at 44. But Mr. Hall did not stop. He knew "that when you run from the police, that you're going to get beat down when they pull you over. So I wanted to go somewhere where there was a lot of witnesses so nobody would get shot or beat or any of that stuff. I just didn't want to be stopped out in the country where there was nobody around." Id. After his arrest Mr. Hall did not tell the police about Lee or that Lee and Morrison had dropped him off at the halfway house; he is not a "snitch" and does not tell on people. Id. at 47.
Trial testimony corroborated parts of Mr. Hall's alibi. Lorence confirmed that he had been living with her from August to November of 2006, and that he had left *680 without permission from his probation officer after she had a fight with him in early November. Mr. Hall's sister Connie remembered his visiting her at the hospital on November 7, and stated that he was accompanied by Morrison and a clean-shaven man in his early to mid-30's with dark hair and a dark complexion. She also testified that Wing had called her in December 2006 and said that, from a window, she had seen Mr. Hall outside the halfway house on the day of the robbery, but because it was getting close to count time she was afraid she would get in trouble if she went out to speak with him.
Despite this corroboration, the alibi had serious holes. For example, how did Lee get the truck that he was driving just before the police chase, and why would Lee give all the money to Morrison (except for $101 from the teller's drawer not accounted for in the bag found by the road)? But the government did not rely solely on those holes and the strength of its case in chief; it also undertook to rebut the alibi through additional evidence.
Wing testified that although she had spoken with Mr. Hall during the summer of 2006, she had not had any further contact with him before the robbery. She went back to the halfway house in early November 2006 after having violated her supervised release, but she could think of no way that he could have known she was there on November 7.
Wing also recounted how Mr. Hall had tried to convince her to be an alibi witness. After he had been arrested for the bank robbery, she saw him while at the halfway house. As she was smoking outside, he yelled to her from the recreational yard of the federal detention facility, which is part of the same complex, telling her that his sister Connie was going to call her. Connie called the same day and told her that Mr. Hall was in the detention center, that his mother needed to talk to her "more about it," and that he "needs you to help him." Trial Tr., Doc. 151 at 529.
Mr. Hall's mother called Wing in early 2007, after she was released from the halfway house. The two had lunch together and Mr. Hall's mother handed her a letter from Mr. Hall. Wing "didn't really" read the letter. Id. at 531. She later agreed to meet a second time with Mr. Hall's mother, who gave her another letter from Mr. Hall and told her "some things that I needed to do. Like I needed to have a watch on.... And she gave me a watch to wear so I could say something around two o'clock I was with him, seeing him at the half-way house." Id. at 531-32. Also, Mr. Hall mailed two or three letters for Wing to her brother's house in Kansas City, Kansas. Mr. Hall's letters said that she "could really help him out because they couldn't really identify him at the bank. They had a description wrong." Id. at 535. The letters instructed her to say that she was with him at the halfway house at approximately 2 p.m. on November 7, 2006, and that two men had dropped him off and left him talking with Wing. But two o'clock is count time at the halfway house, so she could not have met with Mr. Hall then; and she was not about to go along with the story because she "didn't want to get up here and lie and go back to prison again." Id. at 536. Wing denied telling Connie that she had seen Mr. Hall on November 7. She did, however, admit on cross-examination that she did not keep Mr. Hall's letters or give them to her probation officer or any police officer.
The government also attempted to rebut the alibi testimony using evidence of Mr. Hall's prior crimes. Because this evidence goes to the heart of his issues on appeal, we defer summarizing that evidence until our discussion of those issues.


*681 III. DISCUSSION
Mr. Hall's issues on appeal concern disclosure of his prior offenses. He claims that he was entitled to a mistrial when the district court informed the jury during voir dire that he had previously been convicted of two bank robberies. He also argues that the prosecutor engaged in misconduct when she elicited information about his prior bank robberies and an attempted burglary on cross-examination, and when she brought up those robberies during closing argument.

A. The Court's Mention of Prior Convictions During Voir Dire
Mr. Hall complains of the district court's denial of his motion for a mistrial after it disclosed to the jury during voir dire that he had two prior bank-robbery convictions. The disclosure was made as the court read the indictment to the jury.
Count 3 of the indictment, the felon-in-possession count, stated that Mr. Hall "had been convicted in 1984, of Bank Robbery... and, in 1992, of Armed Bank Robbery and Use and Carry of a Firearm in Connection with a Crime of Violence." R., Vol. 1 at 31. To avoid the prejudice to him from informing the jury of the specific offenses that he had been convicted of, Mr. Hall stipulated with the government that he was a prior convicted felon prohibited under federal law from owning or possessing firearms. See Old Chief v. United States, 519 U.S. 172, 117 S.Ct. 644, 136 L.Ed.2d 574 (1997) (defendant charged with being a felon in possession of a firearm may stipulate to the fact of his prior conviction and thereby preclude the government from putting on evidence of the conviction to prove the predicate felony). The court therefore should have informed the jury only of the stipulation. The court, however, read the indictment to the jury verbatim.
Defense counsel brought the mistake to the court's attention and moved for a mistrial. He conceded that he had always intended to bring up Mr. Hall's 1992 conviction in voir dire, but he was concerned by the court's reading of the 1984 conviction. The prosecutor did not oppose a mistrial. The court, however, thought a mistrial was unnecessary. It observed that the evidence of the convictions might be admitted, because it had not yet ruled on the government's pending motion under Federal Rule of Evidence 404(b), to allow evidence of Mr. Hall's prior robberies to prove preparation, common scheme or plan, and identity. Although the prosecutor then informed the court that she was abandoning her Rule 404(b) motion, she said that if Mr. Hall testified, she might seek to elicit the prior convictions to impeach Mr. Hall on cross-examination under Federal Rule of Evidence 609, which permits evidence of conviction of a crime to attack a witness's character for truthfulness. After a recess during which it reviewed the law, the court decided to deny the motion for a mistrial "on the assumption that the government's case is overwhelming," Trial Tr., Doc. 149 (Excerpts from Voir Dire) at 6; but it left open the possibility that Mr. Hall could renew his motion.
It is not disputed on appeal that the district court erred in disclosing the prior convictions. And declaring a mistrial at that very early stage of the trial would probably have been the advisable course. But that conclusion does not end our analysis. We will not reverse a conviction if the alleged error was harmless. See Fed. R.Crim.P. 52(a). An "error is harmless if it did not affect the substantial right of the accused." United States v. Patterson, 561 F.3d 1170, 1172 (10th Cir.2009) (internal quotation marks omitted). A nonconstitutional error affects a substantial right if it *682 has a "substantial influence" on the trial's outcome or creates a "grave doubt" as to whether it had such effect. United States v. Rivera, 900 F.2d 1462, 1469 (10th Cir. 1990) (internal quotation marks omitted). Mr. Hall's concern is disclosure of the 1984 conviction. But because, as we shall see, evidence of that conviction was later admitted at trial anyway, the disclosure of that conviction during voir dire did not affect Mr. Hall's substantial rights. The district court's error was therefore harmless, and its failure to grant a mistrial did not prejudice Mr. Hall.
Evidence of the 1984 conviction was elicited during Mr. Hall's testimony. Just before he began testifying, defense counsel stated his intention to bring out the 1992 conviction on direct examination (presumably to avoid the evidence having greater impact if first elicited during the government's cross-examination) and asked if the court would be willing to take a break before completion of direct testimony to rule on whether the government could impeach him under Rule 609 with the 1984 conviction. The court agreed, and defense counsel then proceeded to question Mr. Hall about the 1992 conviction for a 1990 bank robbery. In fact, he also asked Mr. Hall about two other bank robberies in August 1990which the government had agreed not to prosecute in exchange for his 1992 guilty plea. Mr. Hall admitted that he committed those robberies and that he had pleaded guilty to using a firearm in connection with one of them.
During the anticipated break the parties debated the admissibility of evidence of Mr. Hall's 1984 conviction. In addition to arguing that it was admissible as impeachment under Rule 609, the prosecutor argued that it was admissible to rebut a contention of defense counsel in his opening statement. Defense counsel had said:
We indicated in voir dire that Mr. Hall had committed bank robberies before and he'll tell you that. And he will say that he spent a lot of time in prison for that. And he would not in 2006 at this time of his life, rob a bank by using his own car and parking right behind the bank with his own tag, that there's no way on earth he would do that.
Trial Tr., Doc. 150 at 23-24. This argument, the prosecutor asserted, opened the door to questioning Mr. Hall about prior bank robberies that shared similarities with the MidAmerican Bank robbery. She noted in particular that in two of the prior bank robberiesthe one in 1984 and one in 1990Mr. Hall had driven his vehicle to the robberies, had used a mask or otherwise concealed his identity, and had used a gun.
The court ruled that the 1984 conviction was too old to be admissible for impeachment under Rule 609, but that evidence of prior robberies could be used to rebut the contention by defense counsel in his opening statement. When defense counsel asked for clarification of the ruling, the court stated: "The only ones I'm letting in are where he was driving a car that he wasand it would refute [defense counsel's] argument." Id., Doc. 148 (Hall Testimony) at 55.
Defense counsel then elected to bring out the 1984 conviction in Mr. Hall's direct testimony. He admitted to having used his mother's car in the 1984 bank robbery, but asserted that at his present stage in life, he would "never park [his] own car out back behind a bank and go in and rob it." Id. at 58.
Thus, evidence of both the 1984 and 1992 bank robberies was admitted at trial. The district court's mention of these during voir dire told the jury nothing that it did not later learn, so Mr. Hall was not *683 prejudiced. Denial of his mistrial motion was harmless.
Perhaps anticipating this response to his argument, Mr. Hall contends that the prior-crime evidence was elicited only because he elected to testify, and that he would not have testified if the court had not mistakenly mentioned his 1984 conviction during voir dire. We are not persuaded.
First, Mr. Hall never suggested to the district court that his decision to testify might be affected by whether it would lead to admission of the 1984 conviction. His pretrial notice of alibi stated that he would testify. At that time the district court had not ruled on whether the 1984 conviction would be admissible under either Rule 609 or Rule 404(b). Mr. Hall suggests that if he had known that the government would abandon its motion to introduce evidence of the 1984 conviction under Rule 404(b), he would have chosen not to testify. But that suggestion is not credible. He was certainly aware that if he testified, he would be impeached with evidence of the 1992 conviction (defense counsel never argued against its use for impeachment and even told the court at the time of the mistrial motion that he intended to mention the 1992 conviction during voir dire) and presumably counsel had also been preparing to elicit on direct examination that Mr. Hall had committed two other bank robberies in 1990. Even if Mr. Hall thought that evidence of the 1984 conviction would be harmful and he would prefer to have it excluded, it is impossible to believe that the threat of the admission of that evidence would deter him from testifying when the admission of evidence of his three other bank robberies would not. The additional impeachment could not have been a significant factor in his deciding whether to testify.
In any event, were we to assume that Mr. Hall would not have testified if the district court had not mistakenly mentioned the 1984 conviction in voir dire, he is still not entitled to relief. The court's error that allegedly compelled him to testify is ground for reversal only if there is a "grave doubt" that the outcome of the trial would have been different had he not testified. Patterson, 561 F.3d at 1172 (internal quotation marks omitted). But we are convinced that he would have been convicted anyway. As he stated in his notice of alibi, he was the only witness who would testify to the alibi. And without the alibi defense (probably, even with it), the evidence was so overwhelming that any reasonable juror would have found him guilty. In other words, any error in inducing him to testify was harmless.

B. Evidence of Prior Robberies and Attempted Burglary Elicited During Cross-Examination
Mr. Hall next contends that his cross-examination by the prosecutor exceeded the scope of what the district court said it would permit regarding his prior offenses. The prosecutorial misconduct, he argues, deprived him of due process and a fair trial. In our view, however, the complained-of cross-examination was too trivial in importance to have prejudiced him.
After the prosecutor elicited Mr. Hall's admission that he had used his mother's car to commit the 1984 robbery, she began to question him about other similarities between the 1984 robbery and the charged offense:
Q. And when you went in there, you had something covering your head, correct?
A. Uh, I think I had a pillow case over my head, yeah, that's correct.
Q. Okay. And you had a gun, correct?
*684 Trial Tr., Doc. 148 (Hall Testimony) at 61. Defense counsel did not object, but the court called the prosecutor to the bench and advised her that it had not intended to allow questioning about the details of the prior robberies, only whether or not Mr. Hall's cars were used in their commission. The prosecutor responded that she would "move on." Id. at 61-62.
The prosecutor then asked Mr. Hall about his attempted burglary of a gas station in June 1990, two months after completing his prison sentence for the 1984 bank robbery. He admitted that he had parked his own car in the parking lot of the gas station. She next asked Mr. Hall about the three August 1990 bank robberies that had already been brought out on direct examination. He admitted that in committing one of the robberies he had used a car that was registered to his mother but belonged to him. He also admitted to having worked with an accomplice in those robberies, and committing at gunpoint the one to which he pleaded guilty. Again, defense counsel did not object.
On appeal Mr. Hall argues that this questioning exceeded the limits of what the district court had set. Defense counsel, however, failed to object in district court to the cross-examination that he challenges on appeal. Therefore, we review only for plain error. See United States v. Caraway, 534 F.3d 1290, 1298 (10th Cir.2008). "Plain error occurs when there is (1) error, (2) that is plain, which (3) affects [the defendant's] substantial rights, and which (4) seriously affects the fairness, integrity, or public reputation of judicial proceedings." Id. (internal quotation marks omitted) The defendant has the burden of establishing all four elements of plain error. See United States v. Gonzales, 558 F.3d 1193, 1199 (10th Cir.2009).
We agree with Mr. Hall that the prosecutor's questioning about his prior offenses went beyond what the district court had approved. But he has failed to establish the third element of plain errorthat the error substantially prejudiced him. In light of the history of his criminality that was properly presented to the jury, we fail to see how the jury would be influenced by the additional evidence that he had an accomplice, used a gun, or wore a mask during a prior robbery. The obvious reason why defense counsel did not object at trial is that it was not worth the effort. Cf. United States v. Short, 947 F.2d 1445, 1455 (10th Cir.1991) (prosecutor's questioning that exceeded the scope of the court's evidentiary ruling and brought out details about the defendant's prior conviction was harmless error in light of the "overwhelming evidence" against the defendant and defense counsel's failure to "request the court to strike the testimony or to give a limiting instruction").

C. References in Closing Argument to Prior Convictions
Finally, Mr. Hall takes issue with the prosecutor's closing argument, which, he claims, "reinforced the impact of her improper cross-examination," Aplt. Br. at 49, and impermissibly used the prior convictions to support his guilt. He argues:
In closing argument, the prosecutor reinforced the impact of her improper cross-examination by arguing, "we know, because of the testimony yesterday, that he's committed four prior bank robberies, two of which he got away with." She added, "this argument that he would have been smarter, you know, he had a 50-50 shot at going there, robbing it and getting away." She later reminded the jury, "You know that the defendant was a convicted felon, you know about his past," then urged the jury to convict Mr. Hall. And in her rebuttal closing, she argued, "He keeps going *685 and he keeps going. He thinks he's going to get away. He's gotten away before." Twice, she referred to Mr. Hall as a "multi-convicted felon."
Aplt. Br. at 49-50 (citations omitted). Again, however, defense counsel raised no objection at trial to the closing arguments. We therefore review for plain error. See Caraway, 534 F.3d at 1298.
The first two remarks quoted in Mr. Hall's brief are from the following discussion by the prosecutor:
In the defendant's opening statement there was an argument that Kevin Tommie Hall would have been smarter than to go to the bank in Leavenworth, Kansas driving his own vehicle to rob a bank. Well, we know, because of his past experience, that he has on at least three occasions driven his own vehicle to go commit serious felony crimes. Two of those were, in fact, bank robberies by his own admission. And we know, because of his testimony yesterday, that he's committed four prior bank robberies, two of which he got away with.

And so this argument that he would have been smarter, you know, he had a 50-50 shot at going there, robbing it and getting away. And so kind of think through and process all of those thought processes that the defendant would have had back on November 7th of 2006.
Trial Tr., Doc. 151 at 592 (emphasis added).
In our view, these comments were not clearly improper. Read in context, the prosecutor was arguing that Mr. Hall's prior criminal history would not necessarily have taught him that it was foolish to take his own car to a bank robbery, because half the time that he had done that, he had not been caught. "Prosecutors have considerable latitude to respond to an argument made by opposing counsel." United States v. Hernandez-Muniz, 170 F.3d 1007, 1012 (10th Cir.1999). Because the comments do not satisfy the second condition for a plain-error reversal (that the error be plain), they do not justify relief for Mr. Hall.
The third remark was made at the end of the prosecutor's opening closing argument. She said:
You've got the evidence sitting right over there on the table. You know that the defendant was a convicted felon, you know about his past, and based upon all of the evidence that you've heard in this case, we're asking that you find him guilty of all three counts.
Trial Tr., Doc. 151 at 604 (emphasis added). Again, if there was error, it was not plain. The prosecutor was seeking a conviction on all three counts, one of which required proof of a prior felony. It was not wholly out-of-bounds to mention an element of the offense in closing argument.
The remaining challenged remarks arose in the prosecutor's rebuttal closing argument. The first mention of Mr. Hall as a "multi-convicted felon" was in the following passage:
[Defense counsel] said the reason he didn't tell Agent Gothard about Lee was because he didn't want to snitch anybody out. Here you have an individual who's a multi-convicted felon and he's being accused of a serious offense and he's not going to tell that there was a third person there? Knowing full well that he's a suspect in the case? How much sense, honestly, does that make?
Id. at 626. We think it within the limits of proper argument to suggest that an innocent person with a long criminal record would promptly state his alibi to avoid further legal difficulty.
The next challenged comment was spoken in the following context:

*686 Instruction Number 20 is the aiding and abetting instruction. If you remember, during the course of the defendant's testimony, he said, yeah, we're driving and there's all this stuff being thrown out, I don't even know it was being thrown out, but at some point he realized there was stuff being thrown out and so he says something to Morrison and Morrison said, yeh, well, Lee just robbed something.
Does Hall pull over at that moment and say, hold on, whoa, I don't want any part of this? You know, he drives by that funeral procession, you talk about the best place to pull over and say I give up would have been right there.
And what does he do? He keeps going. He keeps going and he keeps going. He thinks he's going to get away. He's gotten away before. He ditched the evidence. And it's not until he's stop sticked and he can't go anymore that he finally stops. Not because that's the safest place to stop, but because he can't get away. He knows he's caught.
Id. at 629 (emphasis added). This was proper argument to support an aiding-and-abetting conviction (obviously a fall-back theory) by pointing out that even after Mr. Hall knew that Morrison had been involved in a robbery, he continued to assist in Morrison's flight.
Finally, the prosecutor again referred to Mr. Hall as a multi-convicted felon at the end of her rebuttal. She said:
And then he's talked to, he admits to you or tells you today, I lied to the police, but you need to believe what I told you under oath after being a multi-convicted felon. Based upon all the evidence we're asking you to find the defendant guilty of the three counts because he is, in fact, guilty.
Id. at 629-30. The clear import of the comment is that Mr. Hall, as a multi-convicted felon, is not credible. The comment, which is consistent with the rationale for Rule 609, was not clearly improper.

IV. CONCLUSION
We AFFIRM Mr. Hall's conviction and sentence.
