My favorite mental visualization I came up with: imagine driving from New Jersey to Florida (substitute with a long drive you had). Mine was about 1,200 miles which at 60 miles per hour is 20 hours. That's 72,000 seconds of mind-numbing driving.

Now if during the entire, exhausting, 20 hours of driving, you press a button, and it falls within the "danger zone" that lasts 15 seconds, you lose.

The above example is better when looking at lottery winning chances (worse than 1 in million) - where you can imagine having to throw a quarter out of the window, hoping for it to land within the proper 1 inch section of the road.

I like this example because it gives you visceral feeling - allowing you to think in terms of lengths of road or length of time to compare various odds.