More Players:

This game works well for up to 3 players. To prevent Player 3 from having a big disadvantage placing ponies, consider placing ponies in this order: Player 1, Player 2, Player 3. Then Player 3, Player 1, Player 2. And finally Player 2, Player 3, Player 1. (Or just play 3 total games, letting each player have a turn placing first.) You might also consider continuing play after the first pony wins and declaring a second-place and third-place winner.

Sum or Difference:

After you roll the dice, choose whether to add or subtract the numbers that come up. Even if the sum or difference of the dice won't result in one of your ponies advancing, you can try to prevent one of your opponent's ponies from moving forward. This variation changes the best pony to place your bets on dramatically!

Four Dice:

On your turn, roll four dice. Separate them into two pairs however you like. The sum of each pair determines which pony to move up.

Probability:

Play a few rounds together, and have children record how far each pony advanced at the end of each game. After several rounds, ask which numbers seem to have a better chance of winning. Which numbers did especially badly? (5, 6, and 7 seem to come up a lot, whereas 2 and 12 don't, and 1 is actually impossible.)

Explore why numbers closer to 7 are rolled more often than numbers like 2 or 12. For instance, notice that 7 can result from 1 + 6, 2 + 5, or 3 + 4, whereas 12 can only result from 6 + 6. It's tempting to conclude that this shows rolling a seven is 3 times as likely as rolling a 12, but it's actually 6 times as likely. Make a chart to see all the possible outcomes of adding two dice.

Help children to produce, then interpret this chart, which shows that there are 36 equally possible outcomes. 6 of these are a sum of 7, so 7 is the best pony to bet on, with a probability of 6 out of 36, or 1/6, of being rolled. A 12, on the other hand, only has a probability of 1/36 of coming up on a given roll.

Drawing the Race Track:

Dividing a paper into 12 lanes is a good opportunity to practice some spatial reasoning. It's usually easier for us to visualize splitting something in half, or even in thirds, than it is to visualize splitting into fifths or sixths. Since 12 can be split in half with no remainder, we can start by dividing our paper in half. Now we know the top and bottom half will each need to have 6 lanes. We could split these in half and then thirds, or thirds and then halves.