**Written by Aeternitas33; PSHG Guest Contributor**

My first visit to a carnival probably took place when I was around 10 or 11. During that visit, I attempted to play a number of carnival games, one of which was a ring toss game, while another was a “knock down the bottle” type game. Now being just a young child, I knew nothing of applied psychology or statistics. However, I did possess a highly developed intuition – which immediately began to set off alarm bells in my head as I attempted to play these games. The one conscious thought which kept repeating itself in my mind was “Something’s not right here.”On my next visit to a carnival, I remember acrobats, and ponies racing around a ring – but I have no memories of attempting to play any games. And as an adult, I would return to carnivals repeatedly to enjoy the rides with whichever girlfriend I was dating at the time – I just never again tried to play any of the games.

Fast forward numerous years, and I found myself doing something I could never have imagined when I was just 10 or 11 – playing carnival games at Mass Media’s Midway in PlayStation Home. It was early 2011, and I was trying to earn my sixth or seventh Midway jacket by playing Fickle Flapper of Fate. I had gotten up to Level 7 without too much difficulty, and then I hit a brick wall.

Try as I might, I just couldn’t seem to land on Bright Green. Instead, I inexplicably found myself continually landing on the colors which were just one space beyond Bright Green. It was the virtual equivalent of flipping a coin and getting “heads” ten times in a row. “Something’s not right here,” I thought, as those long-dormant alarm bells began to sound once more.

I began to reconsider the game’s very premise. Fickle Flapper of Fate has but one instruction: “press X to push the wheel”, with successive presses of the X button during a brief time window resulting in a stronger push to the wheel, the strength of which is supposedly measured by the number of light bulbs which light up along the wheel’s edge from left to right. This didn’t make much sense to me, as Fickle Flapper of Fate allows up to four people to play at once. My reasoning was that if the wheel’s motion is strictly tied to the push it receives, in order to have any chance of trying to control this motion one would have to play alone, because with multiple people playing, each person would obviously be interfering with the efforts of the others, meaning that the outcome would (or should) devolve to pure chance. But surely Mass Media wouldn’t deliberately sabotage Fickle Flapper of Fate by making it a multi-player game?

I decided to experiment. Making sure to only play the game alone, I tried using pushes of different strengths, which I measured by first lighting up one light bulb, then two, then three, etc. But there didn’t seem to be any connection between the wheel’s motion and the “pushes” I gave. I decided to delve deeper.

Upon first approaching Fickle Flapper of Fate, you’ll notice there’s a vertical line running down the center of the game. At the top of this line is the color Yellow, and at the bottom is the color Pink. Through sheer stubbornness I managed to get photos of both the left-hand (pink to yellow) and right-hand (yellow to pink) portions of the wheel, and discovered that, excluding the yellow and pink spaces themselves, the left half of the wheel has 27 color spaces, while the right half only has 26 color spaces, giving 55 color spaces in all.

These 55 spaces are divided among 10 different colors (Burgundy, Blue, Dark Green, Purple, Orange, Aqua, Bright Green, Pink, Dark Pink, and Yellow) in the following manner: Burgundy, the Level 1 color, is the most common, with ten spaces on the wheel. But as one goes up the levels, each succeeding color has one fewer space on the wheel, until we arrive at the Level 10 color, Yellow, which has but one space on the wheel. Of course once the number of spaces for each color is known, it is child’s play to calculate the expected frequency for that color. When this is done, it becomes clear that, on average, one can expect to spin the wheel at least six times to land on Burgundy, while landing on Yellow would usually require no fewer than fifty five spins. Adding up all the spins required to land on all the colors, we learn that clearing all ten levels of Fickle Flapper of Fate should take, on average, about 162 spins; and since each Mass Media Green Ticket costs 99 cents, that means each player would need to spend approximately $4, on average, to complete Fickle Flapper of Fate – at least according to statistical projections. So how much money did I actually spend to complete Fickle Flapper of Fate? At least $6, and this was true for two different accounts which I used to test the game.

There’s that voice again. “Wait a minute… $6? That’s a 50% increase over the expected profit of $4! Something’s not right here…”

The procedure I followed was simplicity itself, the only requirement being infinite patience. Using two different test accounts, I recorded the actual number of times I was required to spin the wheel to land on each color, and then calculated the corresponding percentage for that color as indicated by the actual results. And for both test cases, the actual number of required spins, particularly for Level 10, far exceeded what would have been expected according to pure chance.

On my alternate account, the total number of spins required to complete all ten levels was 283, a 75% increase over the expected 162 spins. On my primary account, I had to spin the wheel 250 times just to complete the last four levels (and this ignores my three previous failed attempts to reach Level 7, for which I didn’t record my results). If one then extrapolates using the data from the second test on my alternate account, the total number of spins on my primary account exceeded 300, which was at least an 86% increase over the expected 162 spins. In both cases, this garnered Mass Media at least $2 in additional profit.

By taking a closer look at the actual frequency for each color, as determined by game play rather than statistical calculations, the reason for these unexpected results becomes clear – in almost every case, the statistical frequencies for the colors which were found through game play did not match the expected frequencies. For example, Burgundy and Pink were both found to be more common than chance would allow, while Orange, Bright Green, Dark Pink, and of course Yellow were all less common than one would have expected. Yellow, in particular, came up less than half as often as it should have according to purely statistical calculations.

Now Fickle Flapper of Fate is of course Mass Media’s game, and they can set the odds for each color to whatever they wish – I’m not disputing that. My objection stems from the fact that because Fickle Flapper of Fate is a “Wheel of Fortune” type game, the average person is going to assume that the frequency for each color is going to match the number of spaces for that color on the wheel, meaning that the average person is going to be misled into thinking that Fickle Flapper of Fate is much easier than it really is.

To put this another way, suppose that instead of 55 color spaces on a wheel we were discussing 52 cards in a playing deck. And suppose that instead of discussing the color Yellow, we were discussing the Ace of Clubs. In a deck of playing cards, each card has approximately a 2% chance of coming up during any game. So suppose it was discovered that in every PlayStation Home card game, all of the Aces had only a 1% chance of coming up during a game, but all of the Twos had a 3% chance. Do you think people might get upset over that?

If one is going to attempt to mimic a real-world game, I believe there’s a reasonable expectation that the virtual game will mathematically conform to the same statistical odds as its real-world counterpart. But with regards to Fickle Flapper of Fate, this appears to not be the case.

……. ……. …….

Notes on images and tables:

Image #1 – The right half of the wheel, from yellow to pink.

Image #2 – The left half of the wheel, from pink to yellow.

Table #1 – Predicted Color Frequency – (reading from left to right) The required color at Level 1 is Burgundy, which has 10 spaces on the wheel. This means it should come up 18.18% of the time, or once in every 6 spins.

Predicted % of Spins = # of Spots on Wheel / 55.

Predicted # of Spins = 55 / # of Spots on Wheel.

Table #2 – Test Cases – (reading from left to right) For Burgundy, the data for my primary account was not recorded. For my secondary account, it took 10 spins of the wheel to land on Burgundy, which correlated to an Actual % of Spins of 10%.

Actual % of Spins = (55 / Actual # of Spins) / 55.

Table #3 – Actual Color Frequency – (reading from left to right) Out of a trial of 533 spins, Burgundy should have come up 97 times. Instead it came up 109 times. The predicted frequency was 18.18%. The actual frequency found over the course of 533 spins was 20.45%.

Actual % of Spins = Actual # of Spins / 533.

“Unknown” in Table #3 refers to errors I made in the record keeping process.

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