## Presidential Streaks

Since Ulysses S. Grant, the 18th president of the United States, all U.S. Presidents have been affiliated with either the Republican or Democratic party. Out of the 27 presidents since Grant (inclusive), there have been 17 Republicans and 10 Democrats. Out of 38 elections, Republicans have won 22 and Democrats have won 16.

Presidential Elections, grouped by winning party:

RRRR D R D RRRR DD RRR DDDDD RR DD RR D RRR DD RR DD R

The longest streak, shown above, was a streak of 5 Democratic wins, starting with FDR for 3 terms, followed by Harry S. Truman for 2 terms.

Is that unusual? During elections - specifically this last one… - pundits talk about how hard it is for a particular party to hold on to the presidential seat. Let’s say there were absolutely no connection between one term and the next, *i.e. any sequence of 22 Republican wins and 16 Democratic wins was equally likely*. What’s the probability that the longest streak of consecutive presidential wins for any party would be five or fewer terms long?