I’m working through Freddy Bentivegna’s classic bank pool book “Banking with the Beard.” On page 57 Roy “Kilroy” Kosmanski states:
“When flipping for the break, if flipping a penny, call tails. It’s a 10-15% advantage over the normal 50/50… If you are able to make the penny spin on the table, the advantage goes up to at least 60%.”
Huh?! Has this ever been scientifically verified? If this is an actual phenomenon, what on earth would explain it? Why pennies, and not dimes?
Thanks!
p.s.: As a 10-15% advantage over 50/50 (the supposed advantage gained by flipping) would of course be either 60/40 or 65/35, if spinning only increases the flipper’s advantage to “at least 60/40”, why is spinning presented as the optimum alternative??
The idea is that the heads side of the penny is heavier than the other side, because it has the raised image of Lincoln - that means that it will favor having the tails side up, just like a weighted die will favor the lighter sides. No idea how big the actual effect is
I think when he says it’s a 10% advantage over 50/50, he’s talking about 10% of 50, which is 5. So that would make it 55/45.
I doubt the bias could be 10% to 15% in any case. That would surely have been noticed by now. Here’s a paper claiming that biasing a coin isn’t possible through just flipping, but might be through spinning or letting it bounce on the ground: http://www.stat.columbia.edu/~gelman/research/published/diceRev2.pdf
Hadn’t thought of that.
I was thinking tails had a 10% advantage versus heads, which would be more like 52.4% vs 47.6%.
But there’s got to be a legit study on this somewhere.
Wasn’t this on 'Penn and Teller Tell a Lie" a few weeks ago?
Seems like it would be an easy one to verify experimentally on your own:
Even assuming a penny is unbiased, you wouldn’t necessarily expect exactly 500 heads every single time time; if you repeat the 1000-coin-toss experiment, you may get 490 heads one time, 513 heads another time, and so on. Repeating the 1000-coin-toss many times, you’d expect an average of 500 heads, and a histogram of outcomes, with large deviations (like 600 heads) being relatively rare. So if you do your 1000-coin-toss experiment once, and end up with, say 600 heads, you can look to the unbiased-coin histogram see what the probability of that outcome would be if the coin were unbiased. If you find that 600 heads has a 1-in-a-million chance of occurring with a truly unbiased coin, then you can conclude that the coin probably has a bias. But you can’t say so with absolute certainty, because even a truly unbiased coin will come up with 600 heads once in a great while.
This site will do the math for you. Put in 0.5 for “probability of success on a single trial”, enter 1000 trials, and 600 “successes.” Hit “Calculate,” and check the results. Note that the odds of getting exactly 600 heads out of 1000 tosses is about one in 22 billion. But part of the problem here is that we’ve asked about the probability of getting exactly 600 heads. What about if we get 601 heads, or 599 heads? Those might also indicate a biased coin. So let’s check the probability of any number of heads that’s far from 500. Repeat the trial, this time specifying 575 heads. Now look at the results for the probability of any number of heads greater than 575: that outcome is still pretty rare, just one in 3 million.
So do your manual 1000-coin toss, and then go to that calculator to see how your results compare to what you might expect from a theoretical fair coin.
It was indeed and I had heard of the phenomenon even before that. P&T proved it was true, at least for ***spinning ***a penny. I think the author in the OP must have been confused on his facts, there is no such advantage for flipping a coin (or at least a neglibile one). I don’t recall the exact percentage they came up with, but 55/45 in favor of tails sounds about right.
As mentioned upthread, it is indeed due to the weight distribution of a penny. When you spin a coin it’s basically perfectly upright and in the end simply falls to the heavier side. In the case of a standard US penny, there is *slightly *more mass on the Heads side so it falls Tails up slightly more often. When you flip, however, it’s pretty much just dumb luck which side hits the ground first.
There may be a similar advantage with other coins, but it’s probably just not as pronounced as with pennies.
Except that the method I would use to flip a coin (using my thumb) wouldn’t work for tossing 10 coins at once. And you can’t assume a priori that different flipping/tossing methods would produce the same odds.
If two different methods produce different odds, then one (or both) of the methods is introducing a bias not related to the coin itself. A handful of pennies shaken (not stirred) prior to the toss should be sufficiently randomized so as to not introduce any bias into the results. A thumb-flick is not terribly repeatable in force or direction, so it probably also does not introduce a bias.
Years ago I saw a plot that showed the results of a coin toss performed repeatedly by a robotic arm. The coin always started heads-up, and was launched with a specific rotation rate and a specific initial upward velocity. The plot showed the outcome as a function of various rotation rates and launch velocities. For low values of those variables the results were very predictable: the coin would almost always land on either heads or tails, depending on exactly exactly what the rotation/launch speed was, and so large contiguous patches of the results plot were colored to correspond to either heads or tails. But as you moved to higher rotation rates and launch speeds, the results got more “noisy” as the coin tended to bounce more on touchdown, with fuzzier boundaries on the edges of heads/tails regions. Moreover, at high rotation rates/launch speeds, the plot showed smaller and smaller contiguous patches of “heads” or “tails”, i.e. very slight changes in launch speed or rotation rate resulted in a change of outcome.
FWIW, you ought to be able to stack ten pennies on your thumb and flip them. If you’re having trouble getting them to stay put, maybe you could superglue a little flat platform onto your thumbnail. 
As to the spinning thing: I can reliably make a spinning penny land heads or tails, whichever I want. I slightly tilt the coin based on the preferred side and then flick it with a finger.
I saw the Penn and Teller thing and was amazed the P&T let that go. Stuff on how to make spinning come out right has to be right up their alley. The demo proved nothing.
The claim about flipping in the OP is so … wrong it’s … wrong wrong.
That’s the beauty of bullshit. It doesn’t matter which definition someone assumes. 
I don’t think that introducing bias is the issue. It seems to me that a coin tossed onto a table would be more likely to land heavy-side down (if there is indeed a heavy side) than one flicked with a thumb so as to be spinning in the air. Said spinning would essentially eliminate any chance for one side’s weight to play a role.
I doubt it would get to 10% or anything near. I think that much variation would have been noticed long ago.
I once heard a talk by a professional magician turned mathematician on coin flipping. he never mentioned any bias on the coin. His main point was that it is very hard to flip it fairly. If you balance it on a finger, say heads up, and flip it with your thumb, then unless the flipping force is perpendicular to the finger supporting the coin, the coin will come down preferentially heads. (Of course, if you flip tails up, then it will come down preferentially tails. Nothing special about heads.) In fact if the angle between force and finger is less than, IIRC, 22 degrees, the coin will not flip at all and is guaranteed to come down heads. Moreover, he, an experienced magician, cannot detect this failure visually. The coin appears to spin, but does not actually turn over.
He mentioned that had a built a machine to flip coins fairly, but it was too delicate to pack in luggage and since 9/11, TSA would not allow him to bring it as carry-on.
I thought the bias is if you allow the other to call h/t. 70% of the time people call tails, which only come up 50% of the time, swinging the odds in your favor. (no cite - I heard it some time some where)
I might be missing something, but how does that swing the odds in your favor?
The probability of the penny going heads or tails is independent of what the person calls.