Frank the Frog

Dave the duck's four-legged frog friend Frank is trying to cross a pond using lily pads numbered:

0,1,2,…,10

He starts on pad 0. His goal is to reach pad 10 or beyond.

Each time Frank jumps:

with probability 1/2, he jumps forward 1 pad; with probability 3/10, he jumps forward 2 pads; with probability 1/5, he slips backward 1 pad.

If he is on pad 0 and slips backward,he stays on pad 0.

But the pond has two cursed pads:

If he lands on pad 4, a fountain instantly shoots him to pad 7. If he lands on pad 8, an angry goose instantly scares him back to pad 3.

These instant moves do not count as jumps.

Starting from pad 0, what is the expected number of jumps Frank needs to reach pad 10 or beyond?

Give your answer rounded to 3 decimal places.

The contest ended at 8:16 p.m. AEST on Thursday 2nd July. All submissions will be unofficial .