In this situation, the numbers are pretty clear: For the Chiefs to have any chance of winning, they have to go for it. A decision so easy, a human could make it.
Here's the full breakdown of my calculations:
Option  Chance of converting 
Chance of winning
Before play

After play  Change  

Go for it4th and 10, own 32  31%  <1%  8%  +8%  
Punt  <1%  <1%    
Field goal tryA really, really long kick  <1%  <1%  <1%   
Along with some circuitry to come up with a win probability for every game situation, all you need to figure out what you should do next is an estimate of how likely you are to make a field goal or convert a first down.
My estimates for these are based on the results of thousands of similar plays, but you may think you're smarter than I am. This chart shows you how changing those estimates would change my recommendation.
Punt  97% of the time 
Go for it  3% of the time 
Field goal try   
Alex Smith incomplete pass to the left intended for Albert Wilson.
To estimate a team’s chances of winning, I use a mathematical model that accounts for a whole lot of variables — including the difference in score, the time remaining in the game, and the number of timeouts each team has left. On top of that, I have models for the likelihood that a team makes a field goal and the likelihood that it will convert a first down.
By combining all of this information, I can come up with the best decision a team can make, according to math.
If you want even more details about the numbers behind my decisions, my full model is available on GitHub. Help make me better!