Can a player place a bet on himself for winning a sports event? For example a tennis player places a bet on himself for winning a match or a Grand Slam tournament? Obviously he can't place bet on losing a match cause that's an easy cheat, but placing it on himself winning is different.
Major League Baseball certainly does not allow players (or managers) to bet at all on the sport. You may want to look up Pete Rose and his banishment from baseball because of his betting habits. It is considered one of the bright lines in MLB. I believe all other US leagues also have harsh rules against players and coaches betting on games.
This usually doesn't apply to bets in other sports or "regular" casino gambling (Michael Jordan had stories written about his gambling habits). And small locker room bets seem to be tolerated, i.e. you will have stories of players "putting money on the board" for wins.
I don't know about laws, but sports leagues generally bar players from engaging in gambling that is in any way related to their sport. You might think that there is a conflict of interest only in placing a bet against oneself, but while the conflict of interest is not quite a direct with regards to betting on oneself, it still is there. For instance, one could play poorly for several weeks, moving the odds in one's favor, then bet on oneself and start playing better.
A player betting on themselves is a bit like a CEO buying their own stock. While it is easy to see why shorting one's own stock is questionable, going long can also be unethical, as a CEO is privy to insider information. Similarly, an athlete can be considered to have "insider information", in that they know how healthy they are, how healthy their teammates are, etc.