My English is not great, but hopefully you understand.
Lets assume that we have a Joe Public betting on events and he goes as linemakers hope, winning 50% and losing 50% of his bets, always bets with a same stake and nothing but parlays. So he is losing money because there is the vig and a lot more vig with parlays.
What kind of odds he gets on straight wager when he's parlaying teams with a 20-cent line? In this case all teams have -110, just make it simple. With a 20-cent line bookmaker commission
is about 4.55%. 100-4.55 is 95.45% and this is how much bookmaker pays out on every wager. 100*0.9545=1.909 and Americans knows that as -110. Everytime you make 2 team parlay you have to calculate 0.9545*0.9545 and with 3 team parlay 0.9545*0.9545*0.9545 to solve the vig.
True odds on single wager with a 20 cent line and the original odd was -110 and Commission 4.55%.
2 team parlay -135 (Commission 8.90%)
3 team parlay -152 (13.04%)
4 team parlay -171 (17.00%)
5 team parlay -195 (20.77%)
6 team parlay -225 (24.38%)
If you think you can make money in a long run betting -225 on single wager when true odd is -110, 6 team parlay is perfect for you.
What a about dime line (10 cent line) -105/-105. Bookmaker commission is 2.4% with a dime line, so 100-2.4=97.6%. Calculating with a same way:
True odds on single wager with a 10 cent line and the original odd was -105 and the vig 2.4%.
2 team parlay -116 (4.74%)
3 team parlay -123 (7.03%)
4 team parlay -130 (9.26%)
5 team parlay -137 (11.44%)
6 team parlay -145 (13.56%)
A free tip for sportsbooks. Offer dime line on parlays, you will get more people betting parlays because they see -105 instead of -110, not a rising vig. You might have some smart people betting NCAA parlays, but with NFL and NBA you won't lose.