Thanks for the added info!
You've selected great games for 3 year olds. I'd quietly point out that the rules of the game make it more fun to learn. I've found that really little guys like this feel like 'losers' and will do much to prevent being the loser. I am not about to suggest no competition. BTDT and it's not good. I used 1st Winner, 2nd Winner (and so on) and allowed each child to finish if they chose to.
Also in general, if you make a mistake like dropping something, break something by mistake or lose a game -- point it out. "Opps! Will someone help me clean up the mess I made?" or, "Oh well, good for you, your are the 1st Winner!" Laugh about it, don't be mad and model how you hope these children will learn to play. Being a 'good sport' and trying our best are learned.