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I’ve learned (and re-learned) a lot from tutoring middle-schoolers in math at Top Honors<\/a>.1<\/sup> For example, if a math problem is too hard to solve in your head, I counsel my student to draw a picture<\/b>. That’s one of the best features of decision trees: it allows you to draw a roadmap for complicated, multi-stage decisions. Trees help you to manage two key complications: uncertainty and path dependency.<\/p>\n Let’s start with uncertainty. We’ve already discussed<\/a> how the outcomes of our decisions are uncertain because they depend on people and things over which we have little or no control. The outcome of your decision to buy home A rather than B or to invest in stocks rather than bonds will depend on the actions of your family and neighbors on the one hand and capital markets on the other. That’s one reason why you can’t tell the wisdom of a decision by the outcome.<\/b> It’s the decision process that matters. <\/b><\/p>\n For any decision you make today, not only are outcomes uncertain, but also the ultimate results will depend on future decisions you make.<\/b> For example, let’s say home A is on a larger lot, which will give you options to put in a pool, greenhouse or (my favorite) astronomical observatory. You’d make these improvements based on how your family’s interests evolve. Home B doesn’t offer these valuable options. If B didn’t have any other advantages over A, you’d be wise to choose A. But, if B had more sunlight and was better situated for solar power or a green roof, then you get a situation that a decision tree can help with.<\/p>\n The chart below is a hypothetical decision tree I prepared for my class at City College of New York<\/a>.<\/b> Decision 1 is a choice between immediately creating an online financial wellness app or starting with a lower-cost offline prototype. Assume we take the upper branch and build the online version first. We invest $75,000 and have a 25% chance of success, which is worth one million dollars and a 75% chance of failure, which is worth zero. The weighted average of these values is $250,000. Subtract the $75,000 cost and you get a net value of this decision of $175,000.<\/p>\n