I'll start off by saying that this is probably not deemed an adequately advanced question for this site, and I'll probably phrase this poorly, I apologise if I do.
Suppose there is a $5 \times 5$ grid
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On this grid, coins will be placed on some of the squares, and bombs will be placed on the remaining squares. You do not know the location of these coins and bombs as they are placed randomly. You gain money exponentially with every coin uncovered and you can decide when to cash out your winnings. However, if you hit a bomb, you do lose everything.
You can decide how many bombs there are on the board and winnings also increase exponentially as the amount of bombs increases.
Suppose that as you pick a coin, the amount of money you will win by picking another coin increases by 3%. So if you were to pick 6 coins without touching a bomb you would have made an extra 18% of your money. If there are more bombs on the board then the starting increase is 3% higher, so for example if there is only 1 bomb on the board then the increase is 3% to start with, if there are 2 it is 6%, and so on (for every coin uncovered the increase is still 3% though).
What is the best strategy here? Is it best to do many games with a higher chance of winning or fewer games with a lower chance of winning?
The optimal move is to retire immediately after getting the first coin.
Assuming there are a $nxn$ grid, with $m$ coins and $m$ bombs, multiplying your earnings by $a=1.03>1$ each time you win a coin, starting with $m=1$ money, then the probability of win | lose | nothing at the move $1$ is: $$ p_{win}(1)=p_{lose}(1)=m/n^2\\ p_{nothing}(1)={n^2-2m \over n^2} $$
At the move $i$, if you had $m_i$ wins, the expected utility will be: $$ \mathbb{E}u(i)={m-m_i \over n^2-i+1}a^{m_i+1} $$
This utility expectation function has a saw like curve, increasing per each blank hitted, reaching its first saw maximum when $m_i=0$ i.e. no prior wins, and immediately having its first sharp decreasing after picking the first coin. If you do not lose in the process, of course.
For $n=5$,$m=12$, $\mathbb{E}u_1=12/25a$ at the move 1.
Hence the best choice is playing until you win a single coin and restart.