If you’re fond of shenanigans, laced with high jinks and tomfoolery, the Cal-Stanford football rivalry is your oasis. Just as Saturday’s Big Game in Palo Alto brings to mind historic moments on the field, it reminds us there’s nothing quite like the juvenile humor of collegiate intellectuals.

In a matchup dating to 1892, this is the event that brought you a gridiron full of peaches, a kidnapped mascot, brazen acts of thievery and the subtle weaponry of a fake newspaper — all of it fundamental to the spectacle. We’re not talking about Ohio State vs. Michigan, USC vs. Notre Dame, or LSU vs. Alabama, the type of confrontations so often associated with national acclaim. It’s more like Harvard-Yale or Army-Navy, in which the teams usually aren’t so great, but the spirit is an ongoing treasure.

Like many hot-blooded rivalries, this one is replete with bonfires, after-hours graffiti and old-fashioned insults. What has always stood out, though, is something especially clever, an episode that leaves the victims marveling, “Damn ... they really got us this time.”

Perhaps the most ingenious of them all occurred in the days following the 1982 Big Game in Berkeley, always shortened to “The Play.” In the waning moments, rocket-armed quarterback John Elway led Stanford on a drive that resulted in a field goal, and an apparent 20-19 win, with just four seconds left. All that remained was the ensuing kickoff.

In a sequence that remains incomprehensible to this day, the desperate Bears lateraled the ball five times on the return and found themselves confronted by oblivious members of the Stanford band, blaring out the strains of triumph, on the field of play. It ended with Cal’s Kevin Moen trampling a trombonist to reach the end zone — and somehow, the whole chaotic shambles was ruled a touchdown. Make it 25-20 Cal (the extra point seemed quite unnecessary) and the wildest finish in the history of college football.

In the days that followed, angry Stanford students felt there had to be something illegal on that play, and they had a precious ally in the school newspaper. Sports staffers Adam Berns and Mark Zeigler produced a replica, four-page “Extra” Daily Californian that looked exactly like the real thing, right down to the type faces, logos and advertising styles. With the Daily Cal due to hit the racks that Wednesday, “We were really on a tight schedule, having to put out our own paper, too,” Zeigler, now in his 34th year with the San Diego Union-Tribune, said in an interview this week. “We had to pull two all-nighters, and I flunked a midterm because of it. But Adam told me, and I’ll never forget this line: ‘In 20 years, when we’re sitting on my yacht in the Greek islands, you’re not going to remember this midterm. You will remember this plan.’ He never got the yacht, but he was right.”

Armed with 15,000 copies of the bogus paper, about a dozen Stanfordites set out for Berkeley before dark. “We got real lucky, because when we got there, we found out their paper (distribution) was really behind,” Zeigler said. “We had a couple hours without having to worry about that.”

To say the least, Berns and Zeigler took great delight in watching Cal students open their paper to read the screaming headline: “NCAA Awards Big Game to Stanford.” Upon further review, the story claimed, a referee had “signaled the play dead” long before the touchdown. A heavily doctored photo was offered as “evidence” and there was a phony interview with Cal coach Joe Kapp, muttering, “This has to be the worst moment of my life ... Why now, why me, why Cal ... why did it have to happen to my boys?”

As the scene unfolded, “I saw a cheerleader cry,” said Zeigler. “A football player just sat down and buried his head. It wasn’t like there was Twitter or Instagram, where we’d get so quickly exposed. We were there for probably an hour, just watching people react. Looking back, it’s pretty cool to have been part of that. Kind of what college is all about.”

And whatever happened to that Stanford trombonist, who went from playing “All Right Now” to crashing flat on his back in the end zone? His name is Gary Tyrrell, now retired after a career in finance and living in Half Moon Bay. It’s amazing, he said this week: “Barely a month goes by when it doesn’t come up. I’ll get introduced to someone and it’s like, ‘This is my famous friend, Gary,’ and the story gets told once again. As long as they treat me in good spirit, I’m OK rolling with it.”

Tyrrell recalled standing in a TSA line at San Francisco International Airport, en route to Hawaii and “wearing an aloha shirt that had sort of a guitar motif on it. Gentleman behind me goes, ‘Excuse me, sir — shouldn’t that shirt have trombones on it?’ I was like, ‘Have we met?’ Turned out he recognized the name from the tag on my backpack.”

The ill-fated trombone now rests in a glass case at the College Football Hall of Fame in Atlanta, immortalized in public view. Tyrrell was an accomplished player as a student, heading up the band’s trombone section in his junior and senior years, “but I don’t play now,” he said. “The last time was at the 2000 Tournament of Roses parade. (Stanford played in the Rose Bowl that year.) I marched with the band there, figuring it would be a nice way to cap the career.”

The tradition of The Axe, the symbolic trophy given to Big Game victors and the source of much chicanery over the years, dates to a Cal-Stanford baseball game on a rickety San Francisco field at 16th & Folsom in April 1899. Stanford had embraced an “Axe Yell” at sporting events — “Give ’em the axe, the axe, the axe.” On this occasion, a yell leader named Billy Erb unveiled a standard 15-inch lumberman’s axe — the perfect tool, he figured, for chopping up a straw man, dressed in blue-and-gold ribbons, that the Cal people had placed in the stands.

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After a testy exchange of postgame words, a group of Cal fans seized the axe and sprinted away, passing it from student to student on a frantic chase through city streets. According to “Golden Bears” author Ron Fimrite’s definitive history of Cal football, “A delivery wagon was hailed which carried the thieves to a butcher shop, where most of the handle was sawed off so that the Axe might be better concealed. Finally, with the truncated Axe tucked into his trousers, Cal’s Clint Miller sneaked aboard a ferryboat bound for Oakland, the Berkeley boats being watched more scrupulously by police alerted to the theft.”

At this early stage, there were no thoughts of handing the Axe over to Stanford if Cal lost the Big Game. It was safely stashed at the American Trust Company in downtown Berkeley, displayed only at pep rallies and then returned to its vault by armored car. But on April 3, 1930, a sensational heist transpired. As the armored car drove up to the bank and the Axe’s official custodian, Norm Horner, stepped onto the street, he encountered a group of Stanford roughnecks posing as newspaper reporters and photographers. Flashbulbs popped from the ancient cameras, temporarily blinding Horner, and gang member Howard Avery wrestled it from his grasp.

At that point, reports indicate that either a smoke or tear-gas bomb went off, enshrouding the area. Stanford had at least four getaway cars ready — one carrying the Axe and the others sending police and Cal people in the wrong direction. Quite a triumph for a group that came to be known as “The Immortal 21.” But a dangerous precedent was set, and in 1933, the two schools agreed that the Axe would belong to the Big Game winner.

Switch now to the early morning hours of Oct. 17, 1998. With the intent of stealing signs after dark on the Stanford campus, five members of Cal’s Theta Chi fraternity happened to notice the outfit worn by the Stanford Tree mascot being taken away from the “Cardinal Chaos” event and stashed in the Band Shak, home of the Stanford band. At around 4 a.m., with the place apparently empty, they entered through an open window and made off with the 10-foot-high costume on a joyous ride back to Berkeley.

Now calling themselves the “Phoenix Five,” the men claimed responsibility for the theft in the Daily Californian and submitted a letter, supposedly signed by the Tree, lamenting that he felt “liberated” and “sick of the Farm. The Phoenix Five have introduced me to the outside world, where people are different and actually like their school.” Cal enjoyed two weeks of lively publicity before the culprits agreed to return the Tree.

It was last seen during halftime of the Stanford-USC football game, destroyed in a tree shredder by Cardinal band members claiming it had been “contaminated.”

Bears vs. Cardinal Who: Cal (5-5, 2-5 Pac-12) vs. Stanford (4-6, 3-5) When: 1 p.m. Saturday Where: Stanford Stadium TV: Pac-12 Network Radio: 810, 104.5, 680, 1050

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There is no simple formula to the execution of a memorable Big Game prank. Technology has played a role, as have misdirection, misinformation and the occasional uniform change. A look at some of the better efforts:

• In 1997, a Cal engineering student named Alex Smith attended all of Stanford’s home games. Strange as it seemed, he had a master plan to hack into the stadium sound system and be heard through the referee’s microphone. During the season-ending Big Game, Stanford was flagged for an infraction — and the fans heard this: “Penalty ... excessive arrogance ... Stanford sucks!”

• A berth in the 1980 Peach Bowl was at stake for Stanford. In the era before bags or packs were inspected, Cal students brought thousands of peaches into Memorial Stadium and spent most of halftime using slingshots and other devices to hurl them onto the field. “By the time the Stanford band ended its show,” read the account on californiagoldenblogs.com, “the place looked more like a fruit salad.” With Cal students chanting “Hey Stanford, eat my peach,” the 2-8 Bears beat John Elway-led Stanford 28-23. No peaches for them.

• The Stanford band donned blue-and-gold outfits for an excursion into San Francisco during Big Game week in 1950, pretending to be their Cal counterparts. They played the Bears’ fight song for hours, intentionally off-key. (Although many Stanford passers-by said they still sounded better than the Cal band.)

• On another San Francisco excursion, the Stanford band played a few numbers in a fancy hotel and then repaired for lunch. A member of the Cal band happened to be lurking in the background and, seizing the moment, coaxed a hotel waiter to surrender his uniform. Moving through the crowd with a tray full of water glasses, and excusing himself for having a particularly clumsy day, he spilled water on one band member after another.

• In 1993, Cal promoted its football team with the slogan: “Everyone’s getting into Cal.” In its pregame performance for the Big Game, the Stanford band announced other slogans Cal had considered, including “Cal: It’s easy to spell.”

• In 1991, folks driving along highways 101 and 280 noticed that the signs leading to the famed Palo Alto learning institution read “Stanfurd.”

• Thanks to a resourceful plot, Stanford people managed to have the Cal band’s charter buses canceled in 1983. It wasn’t until halftime that the members arrived, putting a damper on their ceremonial entrance.

• Innocent times: In 1973, three Stanford fraternity members telephoned Cal coach Mike White, asking if the Axe could appear during a writers’ luncheon at Ming’s restaurant in Palo Alto during Big Game week. With the request confirmed through White’s secretary, they dressed as Cal football players, waited outside the restaurant and made off with the Axe after a brief scuffle. (That was the last theft of the Axe, the final tally reading four successful missions by Stanford, three by Cal).

Bruce Jenkins is a San Francisco Chronicle columnist. Email: bjenkins@sfchronicle.com Twitter: @Bruce_Jenkins1