My offer for gas money is made after the tournament is over. I would not offer my $20 minimum at the beginning and then be exposed to a 5 minute run and troll the rest of the day.
I always make the offer after the tournament, when I can fully evaluate the day's runs that were made.
If the boater runs 5 minutes from blast-off and trolls the rest of the day, I would explain to them that with that small of a run on the big motor, I don't feel obligated to provide gas money. Each situation is different and you have to evaluate each individually. You also have to take into account the attitude the boater had during the day in response to recommendations you were ASKED for by them. In one tournament on my local lake, I had the boater make a run that didn't produce, but he took my advice and made the run. I felt that I should give more based on his taking my advice. What you have to realize is the scale is a sliding scale based on the day.
Don't lock yourself into something that is not fair to you before the tournament starts. Always see what runs were made, even to the point of seeing the gas gauge before blast-off and comparing it to the idle into weigh-in. I have used this technique and guessed the amount of gas used and made my offer based on this.
So far, I haven't had any issues when making the offer of gas money to the boater using my techniques. I do admit that I am over analytical when it comes to giving someone money that I have worked hard to get into my bank account.
All the boaters I had this past year on the BFL, every single one came up to me at successive tournaments and asked how I did that day. To me, I had gained respect from the boater by being a good net man and paying my share of the expenses of the day we shared together on his boat.
To me, the biggest thing you can do when fishing draw tournaments is gain respect from your partner as an angler and a person. Your reputation will grow whether you catch fish or not.