The Wonderland Board

So I was bored earlier, and decided to look up some logic games. I ended up finding a particularly creative one that can be played with dice, called Petals Around The Rose.

How it works is one player, dubbed the Potentate of The Rose - who knows the game's workings - rolls five die. They can tell the other player three things:

• One - The name of the game is significant.
  Two - The answer to any roll is going to be either zero or an even number.
  Three - The answer to any roll.

That's all the information that is supposed to be disclosed. The other player has to figure out how to obtain the right answer - in other words, the logic of the game. However, they are urged to keep the logic secret when playing with others, so as not to remove the thinking process.

After six successful guesses in a row, the player can be considered a Potentate as by then they should understand how the game works.

One of the statements that circulates along with the game itself is that the smarter someone is, the more trouble they'll have on this puzzle. I know why this is myself, but so as not to give anything away, PM me with a guess if you have one.

Also, please don't post the game's secret here, 'kay?

I know this one. It took me months (maybe even more than a year) to figure this one out. I only understood it when I looked at an actual rose.

There's a more mathy way that has different logic behind it but always arrives at the same results. However, you have no chance to figure it out without looking it up somewhere since it's kinda random.

The proper way is much more logical.

Wow. Only now do I see how much overanalyzing I did.
I even tried coming up with an algebraic expression for it, but it got shot down after a while.
And now, since I see it, I think I'm an idiot, of course. x3