i've read Lowenstein's book cover to cover several times. understanding WEB's mind is somewhat difficult but clearly you can see in Byrne's offer the way an insurer thinks. i would assume, using this anectdotal story, that byrne is thinking:

1. how much money can i blow without my wife killing me? (answer: around $30,000 bucks)

2. 30,000 bucks divided by three golf partners is 10,000 bucks.

3. a hole in one on a par three has about 1:1000 probability.

4. 10,000 bucks divided by 1000 is 10 bucks.

5. add my 10% profit for providing this service and the premium becomes 11 bucks.

Buffett, on the other hand is thinking to himself...i've played about 5000 or 6000 par threes in my lifetime, and have never had a hole in one. therefore my chance is probably less than that. so i might be willing to pay, based on my life's empirical evidence, 10,000 divided by 5000 or 6000, or around 2 dollars, hence the premium in his mind being "overvalued". WEB must have assessed his chances of a hole in one at significantly below the 1:1000.

But seriously, the emotional response to pull out the wallet simply because the potential payoff is high, is the reason that lotteries exist and why super-cat can be such a great business for Berkshire.

as far as the premium=insured value*probability of event, you are neglecting the fact that insurers also tend to tack on some service related fee, i.e., they have found that people will consistently pay slightly above that mathematical expectation for the intangible benefit of having the insurance. in the long run, WEB recognizes, as do all smart insurers, that profits in insurance derive primarily from the service premium they can get and from the benefits of float. any profit above that really is gambling in the true sense.

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