Is a chance of a single day of happiness worth suffering days for?

Introduction: The All-Star Superman Dilemma

Recently, I came across a moment from the All-Star Superman comic series, Superman prevents a young woman from taking her own life. He manages to stop her, not by a show of power but by giving her autonomy and empathy. He tells her of a terminally ill friend who chose to end their life, a decision he understood but didn’t approve of. His core message was a simple but an appeal to hope: if there is even the “slightest chance” of having one more happy day, one should choose to live.

This forced me to think. There have been times, I felt this too. This scenario forces a confrontation with one of life’s most difficult questions: how do we weigh suffering against joy? So I decided to take a look into this argument from two angles:

1. The Certainty Scenario: Is a single, guaranteed happy day worth enduring 99 days of sadness?

2. The Probabilistic Scenario: How does the introduction of chance alter the calculation and the meaning of the choice?

By examining this dilemma through the lenses of utilitarian philosophy, psychology, and probability theory, perhaps I can find wisdom in this advice.

Analysis 1: The Certainty Scenario (1 Happy Day vs. 99 Sad Days)

Let’s first assume a guaranteed outcome: a 100-day period containing exactly one happy day and 99 sad ones. Is this a worthwhile experience?

The Happiness Trade-off: A Quantitative Imbalance

Classical utilitarianism attempts to measure the morality or value of an action by its net outcome on happiness. Using a “hedonistic calculus,” we can assign values to the experiences:

• Let the value (utility) of a happy day be +X.

• Let the value (disutility) of a sad day be -Y.

The total value (V) of this 100-day period would be:

$V=(1\times X)+(99\times -Y)=X-99Y$

For this period to be considered “worth it,” the net value must be positive ($V>0$).

$X-99Y>0⟹X>99Y$

So for the experience to be logically worthwhile under this framework, the single happy day must be more than 99 times more intensely positive than each sad day is negative. From a purely quantitative standpoint, this seems like an exceptionally bad deal.

The Limits of the Model: Is Utility Linear?

Before proceeding, it’s crucial to acknowledge a key assumption this calculation makes: the linearity of utility. This model treats emotional value like a simple bank balance, where one day of +100 joy is assumed to perfectly cancel out 100 days of -1 sadness.

This is a oversimplification for creating a model, but it may not reflect psychological reality for two main reasons:

• Diminishing Marginal Utility: In real life, experiences often have a diminishing impact. The first day of suffering might feel devastating, but by the 50th consecutive day, a person might become emotionally numb or adaptive. The negative utility of each subsequent sad day might not be constant.

• Non-Comparable Magnitudes: Is a day of profound, life-altering joy—like finding forgiveness, falling in love, or achieving a lifelong goal—truly just “100 times” better than a sad day? Or is it a qualitatively different state of being that defies measurement on the same scale? Some experiences may transcend simple quantification.

So, why use this model? Because while it isn’t a perfect mirror of emotion, it provides a valuable framework. It forces us to define the terms of the problem and clarifies the sheer scale of the trade-off Superman’s proposition implies. It establishes a baseline that highlights why a purely mathematical view is insufficient on its own.

What the Numbers Miss: Memory, Meaning, and Hope

Human experience, however, is not a simple ledger of positive and negative entries. A purely mathematical view misses the qualitative nature of our lives.

• The Peak-End Rule: Research by Nobel laureate Daniel Kahneman demonstrates that our memory of an event is not an average of every moment. Instead, we disproportionately remember the peak (the most emotionally intense moment) and the end. A single, transcendentally happy day could serve as a powerful peak that re-contextualizes the memory of the preceding suffering, making the entire journey feel meaningful.

• The Power of Hope: In this guaranteed scenario, the 99 days of sadness are experienced with the knowledge that a happy day is coming. This is not just suffering; it is suffering with a purpose and an end in sight. Hope acts as a buffer, changing the subjective experience of the negative days. It is the difference between being lost in a dark cave and navigating a dark tunnel towards a visible exit.

• The Asymmetry of Joy and Suffering: The value of happiness is not merely the absence of sadness. A day of profound joy—falling in love, achieving a lifelong goal, finding peace, or creating a beautiful memory with a loved one—can provide a sense of meaning and purpose that suffering alone cannot erase.

Conclusion for Scenario 1: While a simple cost-benefit analysis suggests the 100-day period is a net negative, this view is incomplete. The psychological impact of a peak positive experience and the sustaining power of hope can make a single day of joy valuable enough to justify a long period of hardship.

Analysis 2: The Probabilistic Scenario (“The Slightest Chance”)

Superman’s actual advice is more realistic and powerful because it deals not with certainty, but with chance. The decision to live is a bet on the possibility of a future happy day. This can be modeled using the concept of Expected Utility.

Modeling the Decision with Expected Utility

Expected Utility (EU) is a framework for making decisions when outcomes are uncertain. It is calculated by multiplying the probability of each outcome by its value (utility) and summing the results.

$E(U)=(P_{\text{happy}}\times U_{\text{happy}})+(P_{\text{sad}}\times U_{\text{sad}})$

• $P_{\text{happy}}$: The probability of a future day being happy.

• $U_{\text{happy}}$: The utility (value) of that happy day.

• $P_{\text{sad}}$: The probability of a future day being sad ($1-P_{\text{happy}}$​).

• $U_{\text{sad}}$​: The disutility (negative value) of that sad day.

A rational actor would choose to continue if the Expected Utility is greater than zero ($E(U)>0$).

The Power of an Asymmetric Payoff

The key to Superman’s argument lies in the potentially immense value of $U_{\text{happy}}$. For someone in deep despair, the value of a truly happy day isn’t just a minor uplift; it can be life-altering and feel almost infinitely precious. Let’s assign illustrative values:

• Let the disutility of a sad day be $U_{\text{sad}}=-1$.

• Let’s assume, as per our previous analysis, that a truly happy day is 100 times more impactful, so $U_{\text{happy}}=+100$.

Now, let’s find the break-even probability ($P_{\text{happy}}$) where it becomes rational to take the bet:

$E(U)>0$

$(P_{\text{happy}}\times 100)+((1-P_{\text{happy}})\times -1)>0$

$100P_{\text{happy}}-1+P_{\text{happy}}>0$

$101P_{\text{happy}}>1$

$P_{\text{happy}}>\frac{1}{101}\approx 0.0099$

Thus, If you believe that a single day of profound happiness is worth more than 100 days of sadness, you only need a ~1% chance of that day occurring to make the choice to live a rational one.

If the value of that happy day is even higher—say, 1000 times more meaningful—the required probability drops to just 0.1%. Superman’s “slightest chance” implies a probability that is small but non-zero. As long as the potential payoff of happiness is sufficiently large, the bet is always worth taking.

Overall Conclusion

Superman’s advice to the suicidal girl is not an empty platitude. It is a sophisticated argument that implicitly understands both the weight of suffering and the logic of hope.

• It acknowledges that human experience cannot be reduced to a simple sum of good and bad days. The quality and meaning of our peak experiences can retroactively justify the struggles required to reach them.

• It frames the choice to live not as a guarantee of happiness, but as a rational bet on its possibility. By highlighting the immense, asymmetric payoff of a potential happy day, it shows that even a slim chance can be enough to give life a positive expected value.

Ultimately, the argument is a call to reject the certainty of nothingness in favor of the uncertainty of life, because within that uncertainty lies the possibility, however slight, of profound joy. It is a validation of hope, grounded in a deep understanding of both mathematics and the human heart.