Like very paid for hobby you have to balance out what you can reasonably afford and budget for it.
Work out how much you can reasonably afford and by that I mean after everything else and leaving money for other hobbies as well as putting some away in savings and without touching what is already in your bank account
Then when you have worked that out work out how often you can afford to punt on that amount. Then just stick to it.
Find other things to do that don't cost money. Have a wank, go for a walk, meet up with mates. Anything to stop you spending money you cannot really afford.
Some people have addictive personalities so find it quite easy to get addicted to their hobby be it punting, gambling or anything else. You just have to be able to say "I cant afford it this week".
At least with a budget you will look forward to your punts more and will probably find you enjoy them so much more too