Talk:Arcane Sprocket/@comment-136.1.1.103-20140617205352/@comment-25468619-20141127124701

Statistically, you are worse off if you use anything below 100% chance. Sure it feels nice to get 'more hippos' than you were supposed to (9x10% yielding 2 hippos vs 1 x 100% (9 enchanted sprockets) for 1 hippo), but in the long run (most people are playing the game in the long run) you will get less overall hippos that way.

You can calculate the odds for 0 hippos for 1-9 sprockets at a time for 18 sprockets total:

1 at a time - 15% of 0 hippos (0.9^18), expectation value .1*18 = 1.8 hippos

2 at a time - 13.4% of 0 hippos (.8^9), expectation value .2*9 = 1.8 hippos

3 at a time - 11.8% of 0 hippos (.7^3), expectation value .3*6 = 1.8 hippos

4 at a time - 10% of 0 hippos (.6^4.5), expectation value .4*4.5 = 1.8 hippos

5 at a time - 8.3% of 0 hippos (.5^3.6), expectation value .5*3.6 = 1.8 hippos

6 at a time - 6.4% of 0 hippos (.4^3), expectation value .6*3 = 1.8 hippos

7 at a time - 4.5% of 0 hippos (.3^18/7), expectation value .7*18/7 = 1.8 hippos

8 at a time - 2.7% of 0 hippos (.2^18/8), expectation value .8*18/8 = 1.8 hippos

9 at a time - 0% chance of 0 hippos, expectation value 2 hippos

So, always go for 100% hippo chance for maximum profit with the sprockets, all others will yield you less hippos in the long run. :)