Shaun,
Have you compared your formula with actual results?
I normally just multiply the win prices of the three placegetters to get an indication of the likely trifecta dividend - obviously it over-states the result if you have very short-priced favourites winning but generally its in the ball-park.
Your example of horses at $4, $5 and $10 paying only $82 appears to be a very unfavourable result.
Or is the DS formula what he considered the true odds to be?