Generally you can keep your bitcoins safe by keeping your wits about you and not falling for something that seems too good to be true, the same as with government currency. Cryptography and multisignature architecture will provide end to end trustless gambling solutions.
In some ways betting with bitcoin sportsbooks is safer than government currency operators because you do not have to provide your personal information and credit card details that they can store to charge later without your consent or sell on to criminals.
avoid bitcoin gambling scams
Choose operators carefully
Operators could simply disappear with your bitcoins, as has happened with multiple bitcoin dice investment scams. However a government currency sportsbook could do the same thing. The big online gambling sites have spent years building their reputation and make thousands of bitcoins on their trustworthy names. This means simply stealing ฿1 from your account that you would probably bet with them anyway makes no sense as they can make more money operating normally and cultivating a good reputation.
Only bet with the biggest and best bitcoin operators who are all highly ranked here on Bitedge.
General internet security
Even if you are with a trustworthy gambling site you could still be the victim of bitcoin theft if your computer and internet connection are not secure. However this is also true for your personal bitcoin wallet, you credit card and your internet banking so this is not a particular risk for bitcoin betting. To mitigate this risk
Do not click on unknown links in emails or suspicious websites
Use strong unique passwords
Use 2 factor authentication
keep your computers antivirus and firewall up to date
For even better security, particularly over wifi, see out list of the best Bitcoin Accepting VPNs.
Be especially skeptical of any cold calls or emails you get about betting syndicates or trading software that promise guaranteed profits betting online, these are usually scams. Remember if it sounds too good to be true it probably is. You can read about some typical betting scams at the Australian government run Scamwatch Sports investment scams page.
The top sportsbooks recommended here are very safe and trustworthy operators with a track record of security and integrity.