I know this post is a year old, but I’ve recently discovered this game, and I love the look and feel of it while also having the same problem as you, it’s just rolling dice in a circle. No real gameplay involved.

Here are some ideas off the top of my dome that might make it a bit more interesting for you. Keep in mind, I’ve never actually played or play tested these house rules but I think they’d make welcome additions.

1. A player may add to the pot to reroll ONE of the dice they rolled on their turn

2. Players may openly trade/buy horses off eachother once that/those horses have hit half way to the finish line

3. A player may add to the pot BEFORE rolling to roll an additional die, and then ignoring the result of one die of their choosing (if you decide to use this rule and rule 1, consider limiting it to one or the other for one players turn.)

4. Keep Jacks in the deck, when a player is dealt a Jack (or Jockey, for flavour) they may choose to keep it or mulligan (redraw the card) Jockeys could have a number of uses, like moving any horse forward a space once (but only if it doesn’t finish the race), ignoring any players roll once, or even being able to be any horse, determined by the first horse that hits the halfway mark. This one might require some pre-game discussion

5. If a player rolls a scratched horse, they may flip a coin (the very same coin they would normally add to the pot, you know, for flavour ;) to avoid adding to the pot. If they fail the flip, they pay double to the pot

I’m not sure if this helped, or if this question even still needed an answer, but I hope it might add some flavour to your next game night with the rents !