Yesterday was Father’s Day, and I spent the weekend with family. During the course of the weekend, several friendly disputes came up. One dispute greatly interested me because as a group, we were torn between whether to go see John Wick, while the women of the group wanted to see a comedy called Late Night.

I really wanted to see John Wick, and considering my current busy schedule, this may have been my only chance.

The vote was roughly 50/50. Since the RoadGambler gambles everywhere, not just in the casino, I suggested a coin toss. Every one in the group agreed to a coin toss because everyone knows that it’s 50/50.

Or is it?

IS A COIN FLIP REALLY 50/50?

The short and concise answer to this question is ‘no’.

Perhaps you’ve noticed that when I discuss coin flips, I qualify it with ‘assuming a fair coin flip’. When I say ‘fair’ or ’50/50′, I mean that the probability of heads appearing is the same as tails appearing.

The reality of a coin flip is that it’s not fair in the real world. The side that is facing up will always have an advantage over the side that is facing down.

So if you want an advantage, pick the side that is facing up when the flip starts.

WHY A COIN FLIP IS NOT 50/50

A coin flip is an event where the side up wins.

Then think of a coin toss as a series of events where each side of the coin takes turns being the ‘upside’. This simple illustration will show you why the side that starts facing up will have the advantage.

  • Coin about to be flipped, heads facing up
    • Flip begins, and coin turns, showing each side in turn
      • heads showed first (it was facing up)
      • tails shows (first rotation)
      • heads shows (second rotation)
      • tails shows (thrid rotation)
      • heads shows (fourth rotation)
      • tails turns (fifth rotation)
      • heads turns (sixth rotation)

Notice that in the above flip, the coin rotated six times, meaning that there were 7 ‘showings’ of each side.

Of the 7 shows for each side, there were 4 heads, and only 3 tails. Heads has the advantage over tails because it had more chances to be the final ‘show’.

If this confuses you as to why that would be an advantage for heads, let’s reduce the number of times that the coin rotates in the air to 2.

Think of a poor flip where the coin only rotates twice: heads (start), tails (first rotation), heads (rest). In that case, heads appears two times, while tails only has one appearance. It’s a 2 to 1 edge for heads! That’s why flips that don’t seem spin much in the air are unfair. It’s too blatant of an edge and too big of an edge.

However, even if the coin flipper performs a really good flip of, let’s say, 500 rotations the side that’s ip will always have a +.5 theoretical advantage over the side that’s face down.

The reason why the advantage is roughly theoretically .5+ and not +1 is because 50% of the time, there will be an even number of rotations. In cases where there are an even number of rotations, the upside and downside will have an equal number of ‘shows’. It’s in the odd number of rotations that the upside has the +1 edge over the downside.

On the issue of bounce, it doesn’t matter. The bounce on the ground will randomize the coin somewhat and negate some of the advantage, but the advantage still exists due to the fact that the upside will have more ‘showings’.

HOW TO TAKE ADVANTAGE

How much of a shark do you want to be?

If you really want to win, then give the coin to the most feeble person in the room and let them flip it. As soon as they position the coin in their hand, call the side that’s up. Depending on how poorly they flip the coin, your edge may be huge, maybe so big that the loser will cry foul.

In a non ‘friendly’ type environment, let’s say you’re flipping for money in a bar, give the coin to someone who isn’t the strongest person in the room, and then call the side that’s facing up.

The point is you want to do these things:

  1. give the coin to the person who you think will do the poorest job of flipping the coin because that person will give you a larger edge;
  2. you want to call the side that is facing up;
  3. to reduce the amount that the bounce will negate the edge, make sure the ground is something softer, like wood or carpet; avoid concrete.

DON’T FLIP WITH STRANGERS

Don’t fall victim to the coin flip scam in a bar or at a casino. Just don’t. If some random person at a table wants to flip you for some amount of money, always say no.

I’ve had a group of friends come back from an evening out, and during their drunken evening of revelry and binge drinking, managed to lose all their cash. It started with just flipping for beers. I can almost bet that they were set up.

This is an article that I’ll write in the future…or maybe I won’t so that certain people don’t get ideas.

Just don’t ever flip for money with total strangers.

You’ve been warned.

FINAL WORDS

If you want a fair flip, make your opponent call the side before the flipper takes possession of the the coin.

Of course, if grandpa has read this article and had a favorite grandchild, then he could definitely control who wins. If you don’t believe me, practice controlling the flip. After you practice it enough, you can heavily influence one side of the coin.

Oh, to end the story…I won the flip, but when the audible ‘oooooooooh’ came out from the women in the group, a sense of mercy and family unity came over me and we all decided to see Aladdin. It was a good compromise, and a surprisingly fun movie.

A belated Happy Father’s Day to all!

Posted in: Gambling

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