installing Windows 8.1 pro
Will I install windows 8.1 pro in a 500gb hdd in which I store games or a 80gb hdd to run win8.1 fast
Unless 80 GB drive is special like SSD or WD 10k or 15k rpm or similar it will be much slower than a modern 500GB hard drive
So just use the 500 GB drive assuming this drive is new or empty
If you use the 80 GB drive you will have to ensure you install as much as possible on the 500GB drive and regularly check for free space
Perhaps you meant to make a 80GB partition where you'd install windows and have a 2nd partition to store games and such? if so yes, it's always a good practice to separate OS on a dedicated partition.
Just make sure to install games on the 2nd partition, else your OS partition will fill up too quickly.