You get better chances, if you pay the transaction fee :-D. I just played all 0.01 0.05 and 0.1 .. and of course, the biggest one did not have the fee included -> lost that one.
In the case I'm thinking of I paid 0.0015 in fees, the initial bet only paid 0.0005, but still the initial bet got into a block before I did. Both transactions hit blockchain.info long before the block was found. The miner just decided to include the tx with the smaller fee rather than mine for some reason.