Quote:
Originally Posted by Didace
The house edge isn't actually reduced.
As a percentage of your total bet it is. For example, suppose you are offered a bet where your win probability is 50%. You can place either a $10 bet which will pay $9.50 if you win or you can place a $110 bet which will pay $109.50. The second option is equivalent to a 10x odds bet on craps - you place a bet 10x the original one and get a fair payout.
Now in case 1, your EV is 0.5(9.5 - 10) = -0.25. Since your bet was $10 this represents a house edge of 2.5%. In the second case your EV is 0.5(109.50 - 110) = -0.25, same as before as you correctly point out. This time though the house edge is based on your 110 bet and is 0.23%. The numbers are certainly different for craps, but the idea is the same. The house edge as a percentage of what you bet is reduced by making a bet with no house edge.