As common types of bets that can be placed on a horse race with six horses are:

1. **Win bet**: This 🎅 is a bet on a horse to win the race. If the horse comes in first place, the bettor wins 🎅 the amount stated in the odds.

2. **Place bet**: This is a bet on a horse to finish either first or 🎅 second. If the horse comes in first or second place, the bettor wins the amount stated in the odds.

3. **Show 🎅 bet**: This is a bet on a horse to finish either first, second, or third. If the horse comes in 🎅 first, second, or third place, the bettor wins the amount stated in the odds.

4. **Across the board bet**: This is 🎅 a combination of win, place, and show bets. The bettor bets on a horse to win, place, and show. If 🎅 the horse wins, the bettor collects on all three bets. If the horse comes in second, the bettor collects on 🎅 the place and show bets. If the horse comes in third, the bettor collects on the show bet.