Betting on the black swans in the Food Club by neopianbay

Betting on the Food Club is a favorite Neopian past time, and for those who are most fortunate, an easy way to make consistent Neopoints. I, myself, have never participated in Food Club betting but I do have a penchant for statistics. Embarking on a journey to uncover Neopian's food club betting strategies, I read through every PetPage I could find on the subject. I was immediately optimistic about the prospects of Food Club betting. Many Neopians report a great return on investment. They claim that, over time, the Food Club has doubled or even tripled the NeoPoints they have bet. This has an immediate statistical conclusion: The food club's odds are not efficient. Whatever Neopet is in charge of managing the Food Club's bets, they should be fired. If a betting game has an expected return greater than the Neopoints you put in, there is currently an arbitrage opportunity. This means that there is 'riskfree' profit to be gathered. This does not mean every bet will be a win; rather, over time, you should be able to construct a betting strategy that is guaranteed to have a return. With this realization in hand, I decided I wanted to learn more about the betting strategies of other Neopians. There are a few things that Neopians have selected as their 'independent variables'  which is statistics speak for what causes a particular outcome. Here's a comprehensive list of what these bettors look at: 1) The stated odds (e.g. 2:1, 5:1) 2) The allergies of contestants and the contestants preferred foods (which is a factor that is not factored into the stated odds) 3) The strength of the contestants 4) The past win rate of the contestants 5) Whether or not the contestants are on a 'win streak'
These are an interesting set of variables that imply several properties of Food Club betting in general. Here are some immediate implications, 1) The stated odds do not seem to be an accurate representation of the contestants actual odds. 2 to 1 may not represent a true 2 to 1 chance of winning (33.33%, in percentage terms, is 21 odds. There are three reasons this is true, A) The other factors (25) are helpful indicators for profitable bettors. B) Neopians report that the stated odds do not accurately predict food club wins. Most bettors claim that 2:1 odds win about 65% of the time  much greater than the implied odds of 33% of the time. C) The odds often don't add up to 100%, in percentage terms. Statistically, they must, because one of the contestants is going to win no matter what. For example, today's food club had a contest that looked like this: Gooblah the Grarrl, 2:1 Orvinn the first Mate, 13:1 Ol' Stripey, 13:1 Puffo the Waister, 13:1 In percentage terms, each contestants chance of winning looks like this: Gooblah the Grarrl, 2:1 = 1 / (2 + 1) = 33.33% Orvinn the first Mate, 13:1 = 1 / (13 + 1) = 7.14% Ol' Stripey, 13:1 = 1 / (13 + 1) = 7.14% Puffo the Waister, 13:1= 1 / (13 + 1) = 7.14% Obviously, 33.33% + 7.14% + 7.14% + 7.14% does not equal 100%. This implies that there is likely a way for us to profit purely off of the stated odds and the size of our bet. We could construct a portfolio of bets that is guaranteed to either break even or achieve profit. 2) There is a lot of fallacious thinking in the Food Club community. The (5) point on my list of variables that bettors pay attention to proves this. Bettors who look at a win streak or a losing streak are committing the 'hothand' fallacy: they assume that if a contestant has been winning consistently, they will keep winning (and bet with that momentum). Conversely, if a contestant is on a losing streak, they assume that the streak must be beat (and bet on a reversion of the trend). It is likely that trends do not influence the real odds of a contestant winning. Each contest is independent; it does not depend on the outcomes of past contests. It depends on the strength of each opponent. 3) Stated odds may be anticorrelated with actual odds. While 2:1 odds are pretty indicative of performance, Neopians report that contestants with 13:1 odds win more often than contestants with higher odds such as 9:1, 10:1, 11:1, et cetera. So, 13:1 odds seem like a good bet. You get 13x your money and your odds for winning are better than 7.14%~. There is one thing that I am certain about myself: I am incredibly lazy. I don't want to spend a long amount of time tracking contestants performance, calculating the food preferences of opponents, or doing any of the other hard work of other contestants. I don't even want to put a lot of effort into how I think about my bets.
I am also risk averse. I don't want to experience big loosing streaks. I would rather make a consistent profit every time I play. In statistics, we measure risk by standard deviation. Many common strategies have consistent losses every day which is made back by the occasional big win. This is a strategy with a lot of variance; it is high risk. It is also high reward. I would rather pay big a bit of my Return on Investment to expose my bets to a lot less risk. Therefor, I constructed my own strategy: a 'passive betting strategy' for Food Club. Here's the rules of my strategy: A) I don't look at anything other than the stated odds. B) I always make a bet on every single contestant in a particular Arena and I pick the most favorable arenas for my strategy. C) I change my bet amount to guarantee that I always break even.
In order to illustrate these strategies, let's return to the contest I cited earlier with these odds: Gooblah the Grarrl, 2:1 Orvinn the first Mate, 13:1 Ol' Stripey, 13:1 Puffo the Waister, 13:1 This is the ideal contest for me to realize profit. The odds imply that Gooblah the Grarrl is almost certainly going to win. However, there is a risk that one of three 'black swan' contestants will defy the odds and win the contest. If I bet 5,000 neopoints on each contestant, I would profit 5,000 neopoints if Gooblah the Grarrl wins (from a total payoff of 10,000 neopoints). If I bet 5,000 neopoints on any other contestant, I stand to profit 60,000 neopoints.
Lets assume that 2:1 odds candidates win about 65% of the time, as other Neopians have reported. We can calculate an expected return by using these odds. The equation looks like this: (Odds Gooblah wins x Profit from betting on Gooblah) + (3 x Odds any other contestant wins x Profit from betting on any other contestant) Because 3 contestants have the same odds, we can simply multiple their odds together to calculate expected value. The odds that Goobalh wins is about 65%. This means that the other contestants have a 35% chance of winning. Now, let us simulate a simple strategy: 1) Assume we bet 5000 neopoints on each contestant. Your total outlay is 20000 neopoints. 2) The expected return now looks like this (remember, profit equals payoff minus the total amount we bet): (Odds Gooblah Wins x 10000) + (3 x Odds any other contestant wins x 45000) = 65% x 10000 + 45% x 45000 = 6500 + 20250 = 13,750 3) Assuming a contestant with 2:1 odds does have about a 65% chance of winning (as other Neopians have reported), this strategy is profitable on average. However, I don't want to have big losses. I want to profit or break even every time I play. How can I construct a strategy such as this? The key is choosing your bet sizes wisely. This is how we construct our bets, assuming the same Arena that we have been using as an example. 1) Bet the maximum amount on the contestant with the highest odds. Gooblah gets our max bet of 5000 neopoints for an expected payoff of 10000 neopoints. 2) Now, assume Goobalh wins and the payoff is 10000 neopoints. How much can we bet on the other contestants if we want to only break even (profit 0 neopoints, lose 0 neopoints)? The calculation looks like this: (Gooblah Payoff  Gooblah Bet Amount)/(Number of Other Contestants) = Breakeven Bet In our example, our ideal bet on the other contestants would be calculate like this: (10000  5000)/3 = 1666 Now, we bet 1666 neopoints on every other contestant. This gives us two scenarios that could occur. Either A) Gooblah wins, and we profit 0. or B) Any other contestant wins, and we have a total payoff of 21658 with a total bet amount of 10000~ (9998 to be exact), for a total profit of 11658. There, we've done it. We've constructed a strategy that A) Is extremely lazy. No analysis requires. B) Has a downside of 0. We can't lose neopoints. C) Has an upside of more than 100%. We can double on points if it goes well. You can employ this strategy every day and you will never lose neopoints. The key is betting on one arena and sizing your bets appropriately.
