The 1 ohm resistor value is stupid. The LED calculator assumes that you tested and sorted all the LEDs into groups with exactly 2.0V for each LED and that the power supply is exactly 12.0V. Do you think that ebay tested and sorted the LEDs? No way! They simply guessed that some will be 2V.
But if your LEDs are 1.8V then the six have a voltage of 10.8V and the remaining voltage of 1.2V causes a current of 1200mA which will instantly destroy the LEDs.
5 LEDs with a voltage of 1.8V have a total voltage of 9V. If the remaining 3V causes 30mA then the resistor value is 3V/30mA= 100 ohms. If the LEDs are all actually 2V then the current is 20mA which is only a little dimmer.
Thanks for the clarification!
I completed the LED project today, and it was successful. My friend who received it really liked it a lot.
I learned from this thread that none of the pieces are exact. I had never tested forward voltages before on LEDs, and was surprised that most of the LEDs were below their rating at 1.75V.
I didn't like how some of the light series were brighter than others, but as I think Dana noted above, if I really wanted the lights to all have the same intensity I should use constant current drivers.
Thanks everyone for the help!