Does this mining mechanic add genuine choice to my game?

Question

To be concise, I am designing a game based on resource/risk/conflict management. Units will be carrying around several piles of resources, which also power and boost actions like movement, attacking and mining.

I want the resource acquisition to be tactical/exciting as well. My current idea is going up to a resource node, setting its difficulty to a 2-6 number, and expending resources to roll as many dice as resources expended. Dice that come up greater than or equal to the difficulty yield difficulty resources each. As such, a roll of [6 5 2 2] against a node of diff 5 yields 2*5=10 resources, with 4 expended to roll. A net gain of 6.

My question: Does resetting a node's difficulty provide a genuine "steady stream vs risky motherlode" choice?

I've modelled this process, and the means vary less than expected while the maximums and deviations burst up as difficulty goes up. Does this mean there is genuine choice?

The modelled process

Answer 1

Instead of modeling you can compute these results exactly. If you roll n dice at difficulty d, the variance will be [d * n * (d-1)/6 * (7-d)/6], and the mean net gain will be [d * n * (7-d)/6 - 1]. Both scale linearly with n, so here are the mean (measured in Net Gain Per Die) and variance for each value of d:

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| d | Mean | Variance |
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| 1 | 0    | 0        |
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| 2 | 0.7  | 0.3      |
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| 3 | 1    | 0.7      |
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| 4 | 1    | 1.0      |
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| 5 | 0.7  | 1.1      |
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| 6 | 0    | 0.8      |
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As you can see, there's definitely some actual choice here. 6 looks pretty useless (and 1 is entirely pointless - even if you didn't explicitly disallow it in the rules, no one would have reason to pick it), but the others are all somewhat reasonable and come in pairs - e.g. assuming you want the maximum average output (1 resource), do you want the lower variance that 3 offers or the higher one of 4? And are you willing to pay a little in expected output (down to 0.7) to get the extreme consistency of 2 or the extreme variance of 5? I'm not sure how much practical difference this will make to your game though; I'd have to know more about the game first and it'll also be a matter of opinion.