How to trade these probabilities?

I'm trying to figure out if it is possible to be profitable to trade a particular probabilities scenario.

Here is the scenario -

Suppose every day in a 2 hours time frame the price of a instrument would range from -2 to 4 only ( 7 ticks range)

Here are the probabilities of each price getting hit during the 2 hours

4 - 40%
3 - 50%
2 - 60%
1 - 100%
0
-1 - 100%
-2 - 60%

Suppose

1. Each tick is worth $100
2. You have a $5000 account
3. Trade the next 100 days
4. You can enter only 1 lot for each trade
5. You have to minus $20 for commission for each trade
6. All positions would be closed at the end of 2 hours regardless of the price level at that point, you can have profit target and stop loss to exit earlier
7. The price always start at 0 at the beginning of the 2 hours

If the trade decision is that you must decide to take either a long or short position at price - 0 only at the beginning of the 2 hours, what is the most profitable way to trade these probabilities over the course of the 100 days?

A. Do you take a long or short position for each trade?
B. What would be your profit target and stop loss?

Suppose you are allow to enter a 2nd lot at any time and price during the 2 hours. Would this make a significant difference and how would you trade this 2nd lot?

Is there a simple way to calculate the most profitable way to trade these probabilities?

Thanks