Note: The game is underspecified; it doesn’t mention if fractional credits exist.
– If fractional credits exist, the player can’t get wiped out if not betting 100% of their credits, so they bet 90% (or 50% or 99%) at each step and then play “infinite” rounds.
– If payout is rounded (down), then going below 5 (10) credits makes it impossible to make a profit. To reduce the chance of that happening as much as possible, the player should bet 10 in every step, making wipeout extremely unlikely (and in fact it gets unlikelier the bigger the stash grows).

To me it’s not even relevant if the player is utilitarian. Any reasonable moral system would use the same strategy.

“A utilitarian is offered a coinflip with an 0.1% chance of multiplying utility by a million, and a 99.9% chance of destroying everything.”

I think that example captures the message you wanted to highlight with this post, that most people wouldn’t approve of an approach that ignores risk in favor of maximizing expected value.

Of course there are better strategies than (B) as well.

What’s happening here is that there are an infinite number of strategies, and many of them have an infinite expected payout. In your story, you’re effectively comparing:
(C) bet 100% of available credits, an infinite number of times
(D) bet 10% of available credits, an infinite number of times
and your claim is that a utilitarian “has to choose (C) because it has higher expected utility”.
But both (C) and (D) have infinite expected utility! Neither of them is higher! They’re both infinity!

Also, (C) and (D) are both much worse than the strategy a utilitarian would *actually* use, which would be:
(E) choose a target number T, like 10^30. Bet 10% of available credits, and repeat until you have 0 credits or T credits, and then stop.

Once a target number T is chosen, now all the numbers are finite, and it becomes possible to compute expected values without getting confused. At that point we can notice that we should be doing Kelly betting.

Agreed, it does in real life – but by definition, utilitarians don’t care about risk (or risk of ruin), they just care about maximizing expected value! So I don’t think the Kelly criterion solves this for the puzzle itself.

I think the experiment could be strengthened. Let’s consider a player who must choose to bet all credits or withdraw from the lottery and retain the credits, while keeping the probabilities (99% and 1%) and changes in credits (times 1.1 and lose everything) the same. A utilitarian seems to be required by the expected value theory to always bet because the potential gain is larger than the potential loss. By the loss I mean the credits that the player loses as a result of the bet. I believe this loss is real but the article deals only with the average number of credits returned to the player, not the average amount they will have available after the bet which seems more relevant to me. As in the previous example, however, the utilitarian is invariably destined to lose the bet sooner or later.

What I think solves the problem is either something akin to diminishing marginal returns from utility or minimalist theories that are primarily focused on reducing suffering, not increasing pleasure. The decision-maker from the latter group will simply bet as long as there’re enough sentient beings who can be alleviated from suffering. Once the limit is reached, it’s not possible to increase credits (that is, utility) by 10%. At the stage when the utility can be increased utmost by around 2%, the player is indifferent between betting or leaving because they will not, on average, increase the number of utility (eg. 1000*1.02*0.99-1000*0.01 ≈ 1000).

As far as I can tell, this solution to this problem should not create paradoxes of this nature, but I might have made mistakes in the math calculations, so please do point them out to me. Thank you.

There’s an another way of thinking about it that also shows this, which is looking to the logarithmic value of the utility, that is, how many times you double it (or halve it, in the negative case) from the baseline. Again, we note that we can play forever. What’s the optimal strategy from the POV of getting to some desired level in less time (so you don’t get bored)? If you math it out, it’s around risking 99% of the tokens every round, which needs 24.4 rounds of play to expect to double the current tokens.

At that point, one can contemplate possibly more interesting questions, like ‘if there is more utility than happiest-ever-for-everyone-alive-now, does it engage something like Homestuck Trickster Mode for everyone, or is it applied to future generations?’ and ‘if it does save for later generations, how does our utilitarian tear themselves away from “I’ve made everything glorious and beautiful for everyone for a million years, but with just an hour more, it could be two million years, would it be wrong to stop?” and the like’.

Given the rules, and the fact that the human population is finite but the amount of game repetition is infinite, you actually have a solution, just not in the nature of pure maximalization. Amazing essay, got me thinking a lot.