Paying for Info

Whether it be actual money or perhaps a normally negative EV play early in a poker hand that will make your opponent give away his hand, you should have an idea of the correct price. It is the weighted average of the various gains you achieve compared to your EV had you not known anything. Including the times it is zero because the info doesn’t change your decision.

 It turns out that information is not worth as much as it appears, at least not when playing poker. Take the hypothetical heads up holdem game where your opponent, every hand, must push in $100 all in before the flop, into an otherwise empty pot. Since you have nothing to lose by folding, your correct strategy would be to only call when you are favored against an unknown hand. Q7 or thereabouts. But suppose you could pay him to turn his hand face up after you saw your own hand. How much would you pay with various hands. Obviously only with AA or 32offsuit would you pay zero. Because your strategy does not have to change with those hands regardless of what he shows. But it would be worth paying a tiny amount with KK or 42 just in case he has AA or 32 and you thus change normal strategy. But the surprising thing is the surprisingly small amount that you would pay with the hands that are helped the most. Such as Q3 or Q8 where it is most likely a fold changes to a call or vice versa, after you see their hand. It’s only about ten dollars. Partly because you gain nothing from the info about half the time and partially because the times you do gain it’s not much. For example, if Q3 sees 89suited, it now calls but only gains about five bucks which is only about half of what it paid. In that case it would have been better off had it not had the option to pay for the disclosure.
Meanwhile the above assumes that the information you pay for is 100% accurate. If there is some doubt about it, it further lowers its value by a significant amount.