Kyle Shanahan, the NFL’s most conservative head coach, spent two weeks in Las Vegas and became a gambler.

And after he had a big, bold bet pay off early in the fourth quarter, the 49ers’ head coach made the mistake that so many others in Vegas have done before him:

He let it ride.

There’s a reason Las Vegas keeps growing, folks. The house — or, in this case, the Mahomes — always wins.

The Niners’ decision to take the ball first in overtime was puzzling to anyone who knew the NFL’s new overtime rules, which, like in college football, effectively guarantee each team a possession.

In the college game, you always want the ball second. The idea is that when you’re second, you know what you need to do when you have the ball. You can counter or even overtake. It’s the same as being the home team in baseball — there’s an advantage to being at the plate in the bottom of the ninth.

According to Shanahan, though, the Niners had put their brains together and decided that the first or second possession didn’t matter. They wanted the third possession of overtime, possibly giving them a sudden-death victory.

It’s an exciting bit of galaxy-brained game theory that ignores, or at least aggressively overlooks, the far more real possibility that by taking the ball first, you put the game in Patrick Mahomes’ hands.

Also, a touchdown on your offensive possession is the only guaranteed route to that third possession for San Francisco. (And “guaranteed” is a stretch — who knows, if the swashbuckling Chiefs might have gone for a two-point conversion after a matching touchdown.)

Ultimately, the Niners kicked a field goal to start overtime.

And while there’s value in resting a tired defense and compounding the team’s offensive momentum from late in the game, the plan was still fundamentally flawed.

Mahomes beat the Niners by going right through that gap in the logic.

“What I can’t live with is when I do stuff that I didn’t plan on doing or that I didn’t do, and second-guess myself,” Shanahan said. “I’m proud of what we did today as a coaching staff and as players in terms of we worked and we did everything we planned on doing. We just didn’t get it done.”

No, they didn’t.

And while taking the ball first in overtime was merely another small thing to add to the Niners’ list of transgressions Sunday, it will likely remain the most prominent in the minds of Niners fans, if only because it was the last transgression.

Shanahan had rolled the dice earlier in the game and won. It’s a fundamental reason the Niners had an overtime to play.

The 49ers’ offense had sputtered for the game’s two middle two quarters. Early dominance had turned into a 13-10 deficit to start the fourth.

And facing a fourth-and-3 on the Kansas City 15-yard line, Shanahan went against analytics, the football gods, and his own history and decided not to kick the field goal.

Instead, he put all his chips on quarterback Brock Purdy, who had been struggling to complete passes, and tight end George Kittle, who had not caught one in the game.

It was the biggest bet of his football life.

And it paid out.

Not only did Kittle make the catch in the flat and extend the ball for a first down, but Purdy found Jauan Jennings for a 10-yard touchdown pass two plays later. The Niners were back on top.

It wasn’t just a bold move by Shanahan — it was downright brash.

But we’re not celebrating that incredible Las Vegas moment on Monday because Shanahan’s next bet didn’t cash.

Las Vegas is a town built by losers who thought they had a hot hand. Add Shanahan’s 49ers to the list.

I’m sure the 49ers had ample statistical justification for taking the ball first in overtime. All gamblers think they have an edge.

And amid that justification, I’m sure there wasn’t much difference between the two choices — it was a coin-flip decision made after an actual coin flip.

Amid such tight margins, the Niners went with the option that gave Mahomes yet another chance to beat you, straight up.

Sure, the Niners had held Mahomes in check all game. All those opportunities he had to bury San Francisco in regulation came up short.

But the whole world knew that if the Niners gave him another shot at their neck, he wouldn’t miss.

And he didn’t.

It’s not how much you were up in Vegas; it’s how much makes it to the plane.

And the 49ers hopped on a plane empty-handed.

Source: www.mercurynews.com