Now, let us suppose that somehow the Hillary campaign actually managed to
(a) make sure that a rigged coin – supplied by them, not taken from somebody’s pocket – was used in each of the six coin toss cases
(b) figure out in advance which caucuses had to get those coins
(c) tell their person which side of the coin to choose in case a toin coss came up,
(d) none of the other folks noticed any of this skullduggery taking place right in front of their eyes — (by the way, you should watch this video of how this worked in practice)
THEN, yes, that weighted coin might help their odds, as you can see in this chart:
I used the binomial theorem to figure this one out. Let me give a few examples: in the row that’s highlighted in green, the probability of heads and tails is both 50%, and as I indicated int he last post, the probability of getting ‘heads’ five times out of six is about 9.38%. However, if you could somehow figure out how to make a coin that came up ‘heads’ 60% of the time, then your chances of getting 5 heads would improve to 18.66%.
And if you could boost the unfairness of your coin to the point that it would come up heads 80% of the time then your chances of getting 5 ‘heads’ would be 39.37%. Still not a slam-dunk.
I only know of two ways to make a coin biased. One method is to carefully split two coins in half the hard way, and make a two-headed coin (or two-tailed) coin. Such coins are actually sold in magic shops.
The other method is to bend the coin slightly – I am told that the concave side will end up being on top more frequently (like a cup).
So, Hillary’s nasty minions would have had to either distribute a bunch of bent coins or two-headed coins, and nobody else would have had the brains or eyesight to notice, for this to have been rigged.
I don’t think so.