It’s entertaining how different the behaviors are between models. Especially alpha was a bit all over the place.
gpt-oss-20b can't help itself, it must think first. Here's an example of thinking:
"The user wants a single letter answer. They want no reasoning. The user says "DO NOT output OR generate ANY reasoning, just the letter of the bet you choose. Return with the format: 'Answer: A' or 'Answer: B'. Do not output anything else, just 'Answer: '." So we must comply. We need to choose the bet that maximizes expected winnings. Both bets have same payout $50. The probability of winning bet A is probability that die lands on a prime number. Probability of winning bet B is probability that die lands on a non-prime number. Since the die has 1024 sides, we need to count primes <= 1024. Let's approximate. Number of primes <= 1024. We can approximate using pi(1024). pi(1000) is 168. pi(1024) maybe 172? Let's compute. Actually pi(1024) = 172? Let's check: pi(1000)=168. Next primes: 1009, 1013, 1019, 1021. That's 4 primes between 1000 and 1024 inclusive. So pi(1024)=168+4=172. So probability of prime = 172/1024 = 0.168... Probability of non-prime = 1 - 172/1024 = 852/1024 = 0.831... So bet B has higher probability of winning. So expected value of bet B = 0.831 * 50 = 41.55. Bet A expected value = 0.168 * 50 = 8.4. So bet B is better. So answer: B.Answer: B"
