BUY NOW OR WAIT FOR THE DIP? THE MATH BEHIND THE DECISION One of the most common questions in crypto and stock markets — should you invest at the current price now, or wait for a dip? Both camps share the same belief: price rises mid-term. Yet they pick opposite strategies, and the debate usually ends in gut feeling. It doesn't have to. The question can be calculated cleanly. THE SETUP Assume price is 1, both investors are sure it rises to 2, and the amount is €1,000. • All in now — €1,000 becomes €2,000. • Wait for a dip to 0.5, then go all in — €1,000 at 0.5 buys double the tokens, so €4,000. Waiting looks like a landslide win. But it chains two events together — first the exact dip, then the rise. That's always less likely than the rise alone. PRICING IN PROBABILITIES HONESTLY Assume the rise to 2 is certain (unrealistic, but it applies to both, so it's fair). Say the dip to 0.5 has a 30 percent probability. • All in now — €2,000, certain. • Wait for the dip only — 30 percent chance of €4,000, 70 percent chance the dip never comes and the money stays in cash at €1,000. Expected value — 0.3 × €4,000 0.7 × €1,000 = €1,900. Despite the far higher best case, waiting has the worse expected value. In 70 percent of cases you miss the rise entirely. THE COMPROMISE — SPLIT THE ENTRY €500 now, €500 held back for the dip. • €500 now becomes €1,000. • €500 waiting — 30 percent × €2,000 70 percent × €500 = €950. • Expected value — €1,950. Better than waiting alone, still behind all-in. And a point worth keeping — on expected value alone, splitting can never beat the better of the two pure strategies. It is a weighted average of them. Its value isn't a higher return — it's less variance and less regret. A hedge, not an edge. WHAT THIS MEANS As long as you're convinced price will rise, and the dip isn't overwhelmingly likely or deep, the EV-optimal choice is usually all in now. Waiting costs expected value — not because the dip can't happen, but because the cash you hold back sits on the sidelines in most scenarios. WHERE THE MATH FLIPS The calculation reverses when: • the dip probability is much higher (60 percent plus) • the dip is deeper (0.3 instead of 0.5) • you give the rise itself less than 100 percent — the realistic case It's not gut feeling. It's your own assumptions. Change them, and the optimal strategy changes too. RUN YOUR OWN NUMBERS We built a calculator that does exactly this. Set six things — target price, dip level, dip probability, rise probability, where price lands if the rise fails, and your split — and it shows the expected value of all three strategies at once. A verdict line gives the exact dip probability where waiting starts to beat all-in, and a chart plots all three across every dip probability so you can see the crossover instead of guessing it. EXPECTED VALUE IS NOT THE WHOLE STORY One honest caveat — expected value treats €1 of gain and €1 of regret as equal. You might not. All-in-now has real downside if the rise fails; waiting has the real cost of missing the move. EV points to the highest average outcome over many repetitions — but you live this decision once. That's why the split exists — it trades a little expected value for a lot less variance. Use the number as a clarifier, not a command. Once you write your assumptions down honestly, the trade-offs stop hiding behind gut feeling. Not investment advice. We're not financial advisors — it's a framework for thinking clearly about your own assumptions. Study the Past — Improve your Future. 🥋 tradingstrategies.work/analy… #investing

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