This is a fun topic. I'm a security researcher and actively look for exploits in casinos and other crypto spaces daily. I can't give nonpublic details, but I can talk about some of the more common things I find.
The BitMillions exploit detailed here (
https://bitcointalksearch.org/topic/bitmillionscom-scam-386711) was publicly known for a few days before the site operator fixed it. Keno, lottery, and bingo games tend to be vulnerable to similar exploits.
Craps games from various operators are often vulnerable to two different but similar attacks sometimes seen in physical casinos. A large pass bet is placed on the come out roll and then picked up or significantly reduced if a point is set. Alternatively, a small don't pass bet is placed and then increased and odds laid depending on the point. For example, if the point is 4 you might increase your bet 100x while if it's 8 you might leave the bet alone. These types of slightly +EV rather than instant win exploits are among the most sought after for bad actors as they generally look like normal gameplay.
Games in which multiple bets are placed on a board like roulette or sicbo can often be exploited. A developer will perform a sanity check to see if a bet falls within its limits and this prevents a person from placing negative losing bets. The proper way to do this is the check that each individual bet falls within limits, but sometimes a developer will take the sum of all bets and make sure it's above some minimum. This means you could place a bet of -90 on 0, 50 on red, and 50 on black to usually make 90 units per bet. You might also lose 3340 units if the ball hits 0. There may be ways to mitigate or eliminate that downside, such as betting a negative on -1 instead of 0. Various casinos and development studios have been vulnerable to this.
Sports betting sites are not immune to exploits either. Odds on single events can sometimes be manipulated in favor of the operator, so not very useful, but parlays can sometimes be made with the same event multiple times.
The most dangerous exploits I've found are pf seed leaks. These come in a few flavors. In the early days of bitcoin, dice sites would often generate a file with multiple years worth of daily seeds which were used site wide. The scheme here was hash(server seed + client seed + global bet number) to find the winning number. A popular dice site was vulnerable to a directory traversal attack which allowed the seed file to be read. As another example, there is a crash script available now that leaks the server seed whenever a player does a cash out. To exploit, a person sets up two accounts, once places the minimum bet and cashes out immediately, while the other places a large bet, waits for the cashout message of the first player, finds the outcome of the game from the leaked seed, and cashes out immediately before that point.