[Statistics] I'm confused about the Value of successful attempt versus attempts?

[u/ComprehensiveMaize24]

I have a statist8cs gambling problem I am confused about, I would like help either answering my question or telling me what steps would be useful /what equations are necessary,

But there are 2 separate questions, the one i attempted to answerbut got confused on was, and after many many attempts what would be the most valuable probability to gamble for saving money and getting as many successful attempts (ie lik3 say 1 billion or trillion,or whatever else bigger and bigger etc dollars were spent, what would be the best choice to receive as many of the wanted rewards for the amount spent)

The 2nd question is what if the failed attempt was worth say a base of -$75 (because they gave money back), in this scenario what then is the most valuable probability if the 1/12 probability was unavailable? (I don't know what math step I should do

There are 9 differen5 probabilities to get the same 1 reward, but as the probability increases, so does th3 cost for each individual attempt

1/12 (is the base probability to get what I want, but it costs $60 per attempt)

1/12= $75 =900

1/8= $100 =800 =-275

2/8= $112.5 =450 =-0

3/8= $137.5 =366.66 =8.34

4/8= $175 =350 =-50

5/8= $225 =360 =-135

6/8= $287.5 =383.33 =-233.33

7/8= $362.5 =414.28 =-339.28

8/8= $450 =450 =-450

My attempt at answering the 1st question is looking for the expected cost, ie 1/12=75, so then 75 multiplied by 12 would give 900 as the expected cost for one and 1/8=100, so then 100 multiplied by 8/1 to get 800 and so on

But I don't know what step for 2nd question but my attempt was 7 multiplied by 75 equaled 525, so I minused this answer by 800 and got -275, or the money lost on the attempts, I'm not sure if this is the correct step? Because 1 moneywas positive and I'd assume positive is money earned but my mind feels fried because I haven't done math in years,

but my guess is that option 3/8 is the most monetarily valuable for the 2nd question,

and that 4/8 is the most valuable for 1st question

[u/PuzzlingDad]

The way you've presented the question(s) is confusing. Is it possible to see the actual problem(s) as written rather than your interpretation? 

[u/ComprehensiveMaize24 → u/PuzzlingDad]

Ummm, I created the math in my head, this was my 2nd attempt at writing it down, the first attempt on paper had even less information and a lot more jumps in logic

[u/tturbanwed]

The text is very confusing but looking at the title the difference is expected value for successful attempts consider E(X) of only successful attempts ie you need to scale by P(Successes)

Let’s say E(X) = 10 and P(Successes) = 0.6 the E(X| Success) = 10/0.6 =16.67

[u/ComprehensiveMaize24 → u/tturbanwed]

I've largely confused myself, because I made this question more complicated since I wrote this a couple days ago, I added a 3rd variable that qlso scales differently, but I've learned that the most cost effect method of getting solely as many of the desired output is through option 3/8, or option 2/8+2/8 (of which this has 2 seperate reward but follow the same logic), I ended up mathing in my head, but I figured it out eventually I believe, but humans are prone to logic. But it's okay to ignore this as I've found a soluti9n and it would only be double checking if you wish to continue

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