Like you said OP, my mind will urge me to make my winnings double. Perhaps, it is because that my thinking is that I have done it successfully so there is a chance that I can pull it off again. But if it was a huge jackpot price then I would get out of gambling immediately and buy the things that I could not have or afford when I am broke and leave gambling for good.
If it was a jackpot better to leave right away and enjoy all the money that you've got, opportunities comes once in a while make sure you make a good use out of it. People have differences interpreting the situation.
For normal gamblers they will take the advantage and quit, while for those addicted gamblers they won't stop chasing for more winnings instead of quit for a while and try to whinning up and enjoy the moment.