I am sorry that you fell for this hook, line and sinker.
While there is no "house advantage" on the odds bet, there is also no "player advantage." But (and this is very important) the odds bet is linked to the passline bet and the house IS ALWAYS MORE LIKELY TO WIN THE PASSLINE BET. Therefore, the house is MORE LIKELY TO WIN THE ODDS BET even if the odds bet is paid with NO HOUSE ADVANTAGE.
The fact that the odds bet has no house advantage with the payoff does not mean you have an equal chance of winning it. In fact, you have less than an even chance of winning it.