When exactly should we doubt that chance is at play behind a series of events? [duplicate]

Question

My question is more general, but perhaps we can use a specific example.

Suppose I draw cards 100 times. In one of those times, I get dealt a royal flush. Let's call this scenario A.

Suppose now that I draw cards 3 times. In each case, I get dealt a royal flush. Let's call this scenario B.

Of course, scenario B calls for an explanation, but I am curious to find out the reason behind this. Is this because scenario B is more unlikely than scenario A given chance or is it because a supposed designer would be more interested in have more of an incentive to deal royal flushes in scenario B compared to scenario A?

Answer 1

You ask 'when exactly' as if some exact principle applies. Why do you assume that? In reality we are confronted with countless circumstances in which we need to assess whether an event has happened for one reason or another, and there is no exact formula. Let's take two scenarios to illustrate the point.

1. You are having a friendly game of poker. The cards are yours- no-one else has touched them before he game. Your friend wins three rounds on the trot, each time with a royal flush. Your friend did not deal any of the winning hands. You were playing for points, not money, so your friend had nothing to gain by cheating. You know your friend to be scrupulously honest. Your friend seemed more surprised than anyone else at the incredible run of luck.

2. You are having a high stakes game of poker. A stranger wins a huge amount of money by winning three hands each with a flush. The stranger dealt on each of the three occasions. The cards were in a pack brought to the game by the stranger. The stranger has been acting furtively. The stranger has a criminal record for fraud. The stranger was caught cheating at golf. The stranger has a bandaged wrist. The stranger is wearing a thick baggy jacket even though it is sweltering in the room. The stranger is known to be in debt with loan-sharks and is desperate to get money. The stranger has a talkative friend who keeps distracting you with chitchat while the friend is dealing but not at any other time. You spot identical packs of cards in the stranger's pockets.

Now, in which scenario are you more likely to doubt that the extraordinary run of the cards is pure luck? Scenario 2, I assume. Can you say that there is any single factor which allowed your doubt to be triggered with exact justification? No. The point is that you would take into account a wide range of factors and have some form of a hunch as a consequence. There is no all-or-nothing tipping point which takes you from believing it is chance to doubting it. The inherent improbability of three flushes is the same in both scenarios, so that by itself is clearly not enough to dominate your assessment.

Answer 2

The two proposed reasons, un-likeliness and a supposed designer intent, are not on the same level. Un-likeliness is neutral in teleological terms, and just rests on having very rarely, if ever, observed scenario B - it would be more of a quantitative thing. But thinking about a designer is teleological in nature, there is someone who has an intent so that scenario B happens. What would be reasons to assume that there is someone with a specific intent in scenario B? Maybe we are psychologically wired to assume that rare occurrences are usually the result of an agent's actions, so we tend to want to find an agent and their motives. Which doesn't mean there necessarily is, but we would biased in that direction from our experience. One rational thing to do though, would be to try and eliminate other possibilities first. Maybe the deck is rigged? Maybe there is a flaw in the dealing process? Something else?

But in general, un-likeliness should be enough to trigger further investigation. Isn't that what we do all the time? When something appears very rare or improbable, it becomes more salient and we pay attention to it.