www.lesswrong.com/posts/y5GftLezdozEHdXkL/an-intuitive-guide-to-garrabrant-induc...

The sentence has the trading direction backwards.

If a sentence's market price keeps oscillating, the exploitable strategy is to buy when the price is low and later sell when the price is high. Doing the reverse — buying at a high price and selling at a low price — realizes a loss, not a profit.

The original Logical Induction paper states this explicitly in its convergence discussion: a trader can exploit divergence by buying a share when its price is low and selling it back when its price is high. A standard Dutch-book / price-coherence treatment of equivalent bets says the same thing: when one representation of the same payoff is underpriced, you buy the cheap side and sell the expensive side.

So this passage appears to be a simple reversal error in the example trade.

This sentence reverses the buy/sell logic for a mutually exclusive and exhaustive pair.

If exactly one of two sentences must be true, then one share of each will settle to exactly $1 total. Therefore:

• if the two prices sum to more than $1, the profitable move is to sell one share of each now, collect more than $1 up front, and later pay out exactly $1 total;
• if the two prices sum to less than $1, the profitable move is to buy one share of each now for less than $1 and later receive exactly $1 total.

The original Logical Induction paper states this theorem in exactly that direction: when the sum is higher than 1, the trader sells a share of each; when the sum is lower than 1, the trader buys a share of each. A standard Dutch-book treatment of additive probabilities gives the same rule for equivalent bundles.

So the article's sentence has the directions swapped.