So I could be doing something wrong, I am not perfect, but I simulated both the wheel and card game a million times. The card game is WAY better. In the card game you have a guaranteed method of 20 shards, provided you can afford them, the wheel only guarantees 4.

By my stats if you play the wheel up to the 200 spin prize, you have an expected 5.2 shards and 21384 gems spent, that's about 4.1K gems per shard. To keep playin past that is only worse cause now you only have the 1.6% for 1 shard and 0.04% for 2 shards

But on the card game which is actually fair, there are no shenanigans, see my other thread for that lol. the expected cost is just 2700 per shard, 54K for all 20 shards. Also, every card is 1/9 chance of being the Shard, so if you have very limited gems, you can choose between playing one round as far as you can to get the hero, and there's actually no statistical disadvantage between just trying the half of first pick 1/9 shot twice as many times. In fact after running millions of trials on that, when you have limited gems the only difference between playing that last partial round, or as many half price rounds is that you get twice as many other rewards. However, that's just the statistical outcome, its not a guarantee. Yeah run a 1/9 a million times you get a number close to 1000000 / 9 But at the individual trial level, you totally can pick wrong 20 times in a row, though unlikely.