Plug in your current conditions in Imp's Adventure and click Run. It will produce a chart from 100k simulations and what percentage of those simulations ended up in which reward bracket. You can use this on the last day of the event to see if it will be worth it to spend the gems and/or money to buy additional dice. To help answer this, you can put in how many gems each reward tier is worth to you and it will calculate the expected gem value based on the chances.
The best strategy, and the one the simulator uses, is to use lucky dice to land back on the Lucky Hut to get constant free movement. The exceptions are: Don't use the lucky dice if you are 1 spot away. And don't use the lucky dice if you are on the Karma Hut.
At the end of the event, any unused dice will be converted to 2 stars. Using the dice usually gets you more stars than not using them. But if you're guaranteed the next tier by not using them, then it's up to you to decide whether to save them and get the guaranteed reward, or use them and attempt to get to the tiers further away.
You can use it to fully upgrade your Starry Mushrooms. Prioritize upgrading the third Starry Mushroom. If they're all fully upgraded, use it to get to the Wishing Hut for a free ordinary dice.
It takes the sum of the values of the tier it's on and all previous tiers and mutliplies it by the chance of reaching that tier. If the expected value of any of the tiers you have not reached yet is higher than the amount of gems you would spend to purchase dice, then it's a good bet. But nothing is guaranteed so it's up to you to decide whether the risk is worth the reward.
If your current stars are already within the range of a tier, the value of that tier is set to 0. The values are to help you decide whether to buy additional dice. If you've already gotten the rewards for a tier, you should ignore the value of that tier in making that decision.