The best choice is tennis, you can bet on 1.01 odds with 1 btc in Grand Slam, usually when Novak Djokovic, Roger Federer and Andy Murray first round's odds are 1.01. Safe bet.
Ok! Let me calculate for you, with 0.01 BTC at 1.01x, you will only get 0.0001 BTC as your profit. It's not including with the fees, if you don't want withdraw it now, you must win in 3 bets with 1.01x odds, this is only for pay your fees, you still profited nothing. Is that worth?
You could lose in 1.01 odds too, there is no "safe bet" in gambling.
you can sports betting with 0.01 btc you have to find a good match as select the team that has the greatest chance of winning despite having little odds at least have has a low risk for losing
Greatest chance doesn't guarantee you can make profit from that, like you said, it still has low chance for losing too