Bidding on what the seller knows

Idea. An accepted offer is bad news: the seller accepts exactly when the item is worth less to them than your offer. Taking that into account, every positive offer loses money on average. This is the winner's curse.

Step 1: what acceptance tells you. Take $0\le B\le 100$. The seller accepts with probability $\frac{B}{100}$, and given acceptance, $V$ is uniform on $[0,B]$, with mean $\frac{B}{2}$. So the item is then worth on average $1.5\cdot \frac{B}{2}=0.75B$ to you, and you pay $B$.

Step 2: expected profit. $$\frac{B}{100}\left(0.75B-B\right)=-\frac{B^2}{400}.$$ For $B>100$ the seller always accepts and your profit is $75-B<0$.

Step 3. The expected profit is negative for every positive offer and zero for $B=0$. The best offer is 0: do not bid.

The intuition trap. On average the item is worth 50 dollars to the seller and 75 to you, which suggests a profitable trade. But the seller only sells the items that are worth less to them than your offer, so you only buy the bad ones. An offer can only pay if the item is worth more than twice as much to you as to the seller: with $mV$ in place of $1.5V$, the profit is $\frac{B^2}{100}\left(\frac{m}{2}-1\right)$.