I've never pretended to be mathematically sound but I'll do what I always do and throw computing power at it until it cracks under the strain.
I wrote a program that used random number generation to return a win according to the percentages you defined, then when a win was encountered paid out the dividend you suggested. I invoked this randomness not once, not twice, not ten times, not..., well a million times actually. And over a series of a million $1 bets I got the following results.

22% strike rate, $4.80 divvy, Profit $56,624, Worst run $294.40
Second time I tried it I got $58814 profit (see Crash, there's nothing wrong with the system if you show a little persistence) and had a worst run of $304.20
If I'm betting a dollar and the worst monetary loss I got at any point was about $300 in a million bet run I suggest a three hundredth of your bank is a safeish amount to bet.

On the other figures I got:

6% strike rate, $17.20 divvy, Profit $26668, Worst run $1369.60
Second time through $36816 profit, worst run $1710.60
Better not stake this one too aggressively.

I'm not entirely happy with the results as all the dividends are the same size which could cause some minor differences. So since you didn't give us a figure governing the variability of the dividends I'm now trialling a new approach involving 1,000,000 worker ants with different sized grains of sand on their backs running against each other up a variable slope. Unfortunately getting results depends on me weighing the resulting piles of sand on the kitchen scales and negotiations with the misses have fallen over on that front. Therefore until I mow the lawn and take the garbage out I can't give you the definitive answer and can only advise caution with staking your new systems.

Best of luck,

KV