In 1972, Uganda's very large 5-shilling coin was replaced with this smaller (but still large) equilaterally-curved heptagon (7-sided) coin. It was withdrawn from circulation the same year.
Apparently it was withdrawn at the request of the British government (or Bank) because it was the exact same size, shape, and weight as the British (and Irish) 50 p coins -- which had a much higher value -- and the Ugandan coins were showing up in Britain (e.g. in vending machines). This hypothesis makes some sense.
Idi Amin had just taken over Uganda in a coup, and my understanding is that his relations with Great Britain may have been somewhat "friendly" making it believable that he would comply with the request. (It was believed that Britain had actually helped his coup, but that turned out to be probably false, but afterward they did sell arms to Uganda.) But, while the Bank of Uganda would comply and destroy all the coins that came through the bank system, I doubt they would go around the cities and villages and try to round them all up.
Most Ugandan coins that made their way into British vending machines would have ended up in the hands of the banks, and therefore been destroyed. On the other hand, some people would have also just kept them. The ones that survived would probably not be too worn. Look at the example here: It is obviously well-worn. It clearly circulated for years. My guess is it was in use in Uganda for 15 years, until the new shilling was introduced in 1987.
The catalogues say 8 million of these coins were minted. If the Ugandan (and British) governments managed to round up 99% of these coins, that would leave 80,000 in circulation. The only way 80,000 coins could be rare would be if 100,000 or more people wanted one.
All coin images in Daniel's Coin Zoo are from my personal collection. I collect, research, and personally photograph every coin displayed on this site. PLEASE do not take my images without permission. If you would like to use any coin image you see, just ask me. Thank you.