When playing "Monopoly" as part of a chain promotion, the published odds of winning are that of finding the one "rare" piece in every set.

Assuming you have the one "rare" token of a three piece set (of course, there is no way to know that at the time), how many more tokens will you need to acquire before you have a complete set?  To work this I assumed 17 non rare tokens with an 18th being reserved for "instant win" and rare tokens of other sets.

It takes about 22 tokens to get a 50-50 chance of completing a set while over 60 is required to have a 19/20 chance in your favor in the three piece sets.  To complete a two piece set monopoly1.htm or a four piece set (railroads) monopoly3.htm.  Of course, the object is for you to come back often.
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