5speed is correct here, I was going to quote & correct you JimmyRustles but I missed the + button and forgot, it was late
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Any O2 sensor is not accurate until it warms up, this goes for Narrow and Widebands. When you cold start your car, modern day O2 sensor will heat itself up with the heating element inside of itself. This helps it read the AFR's are more accurately and sooner then non-heated units. This also prolongs the life of the sensor majorly, otherwise it would get clogged with exhaust soot.
On our chassis until the O2 sensor is not warmed up, it will not enter closed loop. This will vary on the O2 sensor that you are using. If you use the original Thimble style O2, you will have longer times before you hit closed loop. I switched out to a newer Plano style O2 and on my OBD2 car it would go into closed loop a lot sooner.
To reiterate, Open loop across board when cold, once O2 is warmed up (1-5 minutes) goes into closed loop across board.
Now we do have cold enrichment tables too, if your above 122*F and in closed loop, that enrichment table becomes 0, and ECU uses O2 feedback (source TunerCode docs). While if you don't have an O2 your generally going to run 576-256 points of enrichment on a stock bin. Thus not running an o2 is hurting your gas mileage in that area.