Branching Life Explorer.
Pick a small, invented situation and make two choices. At each step you’ll see a few things that could plausibly happen next, what they assume, and what you might learn. The point isn’t the score at the end. It’s who the person on each path is becoming. Nothing here predicts anyone’s real future.
Choose a situation
It's a weekday evening. Work is done, nothing urgent is waiting, and you have two free hours before bed.
Alternative paths
Every faint line is a path you could take. This is a map of alternatives, a tool for thinking about choices. It is not a picture of parallel universes.
Your path in words
- Start You have two free hours tonight.
- Now: What do you do with the two hours?
Step 1 · Tonight
What do you do with the two hours?
Each choice leads to a few things that could plausibly happen. None of them is the right answer.
Payoff view · formal model
The teammate game
This part uses the teammate scenario. An evening on your own has only one decision-maker, so there is no game to solve: game theory needs at least two people whose choices affect each other.
Two players: you and your teammate. You choose to Support or Blame. At the same time, they choose to Own up or Hide it. Each cell shows how good that outcome is for each of you.
Nash equilibrium: a combination of choices where nobody gains by changing only their own choice, given what the others do. It is a stable point, not necessarily the best outcome for everyone. Here the word is used only for this small, made-up game, never for a real-life outcome.
Teaching numbers
A one-off project under pressure. Blaming protects you whatever your teammate does, and hiding protects them whatever you do. So you both end up worse off than if you'd supported and they'd owned up. (Game theorists call this a prisoner's dilemma.)
| You ↓Teammate → | Own up | Hide it |
|---|---|---|
| Support | ||
| Blame |
Teaching numbers only rank how good each outcome is for each person; higher is better. An underlined number is that person’s best reply to the other’s choice. An orange outline marks a Nash equilibrium. Select any cell to check it.
The check, in words
Start from: you Blame, teammate Hide it.
- If you switch from Blame to Support while they Hide it, you get 1 instead of 2, so you would not switch.
- If your teammate switches from Hide it to Own up while you Blame, they get 1 instead of 2, so they would not switch.
Nobody gains by changing only their own choice, so this is a Nash equilibrium.
Stable, but not the best for everyone: if you Support and your teammate owns up, you would both get more (3 and 3 instead of 2 and 2).
Pure equilibria
One: you Blame and your teammate hides it.
Mixed equilibrium
No mixed equilibrium: Blame is always better for you and Hide it is always better for your teammate, whatever the other does, so neither of you has a reason to mix.
Change the teaching numbers
Changing a number switches to “Your own numbers”. Pick a preset above to go back.
If you’ll work together again
In a single round, blaming can be the stable choice. But teammates usually meet again. Suppose you both start out cooperating (you Support, they Own up) and each follow one simple rule: keep cooperating as long as the other does, and if they ever let you down, stop cooperating for good. Game theorists call this rule a “grim trigger”.
- Keep cooperating
- R ÷ (1 − δ) = 3 ÷ 0.4 = 7.5
- Break trust once, then face blame for good
- T + δ × P ÷ (1 − δ) = 4 + 0.6 × 2 ÷ 0.4 = 7
At 60%, keeping trust is worth at least as much as breaking it (7.5 vs 7), so cooperation can last.
Cooperation can last when δ ≥ (T − R) ÷ (T − P) = (4 − 3) ÷ (4 − 2) = 0.5.
T = 4: what you get for blaming while they own up (the temptation). R = 3: what you get when you both cooperate. P = 2: what you get once trust has broken down. These are teaching numbers in a model, not a rule about real teammates. The point is narrower: trust is easier to keep when people expect to meet again.
What is science? What is metaphor?
Three ways to look at the same branching picture. Only one of them is physics, and none of them is a prediction.
Underneath the story, this explorer is a small decision model. Here is everything it assumes, in plain words.
- States
- Where you are, plus the one thing you carry forward. In “You have two free hours tonight” the things you can carry are: momentum, a clear question, tiredness, a closer friendship, a good mood, a friend's trust, energy, restlessness, a new idea. Right now you are at the start, carrying nothing yet.
- Actions
- The choices at each step. Right now: study a difficult idea; connect with a friend; rest.
- Teaching probabilities
- The chance of each next state, given the state you are in and the choice you make. They are made up for teaching, and each set adds up to 100%. For the current step:
Choice Next state Teaching number Study a difficult idea It finally clicks 30% Some progress, and a sharper question 50% Stuck and drained 20% Connect with a friend A long, honest conversation 45% Easy fun and a lot of laughing 40% They're having a hard time, so you mostly listen 15% Rest You actually recover 55% You scroll and end up restless 30% Your mind wanders and an idea shows up 15% - Decision tree
- Two rounds of choices, each with two or three possible results, drawn as the branching diagram above. Real life has far more choices and far more rounds.
- Markov decision process
- A decision model where what happens next depends only on where you are now and what you choose, not on the whole history of how you got there. That is why the second decision looks only at what you carry forward. Real people carry far more than one thing.
- The game
- Two players with two choices each, chosen at the same time, with fixed payoffs that both know. With the current numbers, the Nash equilibrium is: you Blame and your teammate hides it. The payoff view above works it out step by step.
- What the model leaves out
- Feelings that don’t fit one label, people changing what they want, luck that isn’t on the list, and everything that happens between the two steps.
Continue in the map
- Life as an Evolving GameThe personal idea behind this explorer.
- Decision Trees & Branching FuturesHow branching choices are drawn and reasoned about.
- John Nash & EquilibriumThe maths behind the payoff view.
- Hugh Everett & Relative StatesThe physics, kept separate from the metaphor.
- Personal Reality as an Evolving JourneyLife as a journey that changes the traveller.
- Guided journey: A Life Across BranchesA ten-stop walk through these ideas, from games to physics.
Nothing here predicts anyone’s real future. The situations are invented, the numbers are made up for teaching, and nothing you choose is stored or sent anywhere.