re: Poker & How many hands is a "good sample size"
Considering top pros go through 100K-150K break even stretches but boast a 2.5-3ptBB/100 winrate, you have to get in about 1 million hands to be certain you are within .5 of your winrate.
It's a tough one to answer completely, but for purposes of improving, I think playing 20K hands, then reviewing, then 20K, etc is a good way to go.
I know I've had 9K break even stretches at 5NL followed by 11K stretch with a near 10ptBB/100 winrate.
The game just has far more variance than most people realize, which is why bankroll management and emotional control are essential to success.