I totally agree with "Anon", and others who made similar points in the Circular Altruism post. Context matters! Is it a one-time choice, or an iterated choice? Is there an upper limit to the number of deaths, or no limit? Are the 500 the number of people on the sinking ship/last people on planet earth, or possible victims from a much larger pool? You can only do the math and make a rational decision when you have ALL the numbers from the relevant context.

The first steps of rationality lie not in separating problems from their context, but in determining what context is relevant.

Eliezer, can you explain what you mean by saying "it's the same gamble"? If the point is to compare two options and choose one, then what matters is their values relative to each other. So, 400 certain lives saved is better than a 90% chance of 500 lives saved and 10% chance of 500 deaths, which is itself better than 400 certain deaths.

Perhaps it would help to define the parameters more clearly. Do your first two options have an upper limit of 500 deaths (as the second two options seem to), or is there no limit to the number of deaths that may occur apart from the lucky 4-500?

I'm afraid I don't follow the maths involved, but I'd like to know whether the equations work out differently if you take this premise:

- Since 1A offers a certainty of $24,000, it is deemed to be immediately in your possession. 1B then becomes a 33/34 chance of winning $3,000 and 1/34 chance of losing $24,000.

Can someone tell me how this works out mathematically, and how it then compares to 2B?