Add prediction market strategy guide (#76)

* Add strategy guide

* Add notes on quality of information

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* Add note about compound bets

* Update docs/learn/betting_strategy.md

Co-authored-by: Chralt <[email protected]>

* Update docs/learn/betting_strategy.md

Co-authored-by: Chralt <[email protected]>

* Update docs/learn/betting_strategy.md

Co-authored-by: Chralt <[email protected]>

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Co-authored-by: Chralt <[email protected]>

docs/learn/betting-strategy.md

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+---
+id: betting-strategy
+title: Betting Strategies
+---
+
+# Betting Strategies
+
+What follows is a short introduction to the basic strategies when dealing with
+prediction markets. It is by no means a complete guide.
+
+Recall that the asset prices in prediction markets are used to form a prediction
+of future events, and the right AMMs are _proper_ in the sense that they
+incentivize the traders (which are in this context often referred to as
+_informants_) to change the prices so that they reflect their beliefs.
+
+Before you become an informant and expose yourself to a prediction market, you
+need a _belief_. This belief could be anything from "$A$ is definitely going to
+occur" or "$A$ is _not_ going to occur with a probability of 80%" to "The
+following probability distribution is correct", etc.
+
+The first example is a bit curious because it is seldom reasonable to assume
+that something will happen almost certainly. In prediction markets, you usually
+don't bet that one particular thing is going to happen, you bet on the
+probability of each of the possible outcomes of an event. This is a common
+misconception regarding prediction markets: They don't predict that an event
+will definitely have a particular outcome, but instead predict a probability
+distribution for the possible outcomes.
+
+For example, you might believe that a particular team will definitely win their
+next game. But maybe the probability of that happening is only 80%. This means
+that buying the corresponding token isn't always a winning move (more details
+below). Just like in Poker, where going all-in with the stronger hand isn't
+necessarily a good move and doesn't guarantee a win, buying the tokens of the
+most likely event isn't always a good idea.
+
+In fact, no matter how good your prediction is, you cannot guarantee a profit.
+For example, if you buy a number of tokens for an outcome $A$ that you believe
+to be 90% certain at the price of 50 cent, that's a good deal (assuming you are
+correct): There's a 90% chance that you will double your money. But according to
+your own beliefs, there's also a 10% chance that your stake will go up in
+flames. Swings like these aren't uncommon in prediction markets.
+
+So, just like in Poker, instead of trying to win every game, we try to trade
+profitably over time by maximizing our _expected value_, which is defined as the
+probability-weighted average over all possible outcomes. For example, in the
+example above, the expected value is
+
+$$
+ p(A) \cdot \$1 + p(\neg A) \cdot \$0 - \$0.5 = \$0.4
+$$
+
+(assuming that our beliefs are correct, the probability of $A$ is $0.9$ and the
+probability of "not $A$" is $p(\neg A) = 0.1$; if $A$ doesn't occur, then we
+lose our stake). Still a good deal (expected profit of 80%), but definitely not
+risk-free (10% chance of total loss).
+
+<!-- prettier-ignore -->
+:::warning
+Prediction markets are high-risk high-reward games. Optimizing your expected
+results does not protect you from massive downswings.
+:::
+
+Note that all our projections about profit are based on the assumption that our
+beliefs are correct (if we didn't assume that, we should probably not betting on
+our beliefs in the first place.). _If your prediction is incorrect, you're
+unlikely to profit._
+
+Of course, we may never know if any prediction was correct. For example, if you
+believe that the probabilities of $A$ and $B$ are 90% and 10%, resp. and then
+$B$ occurs - well, that doesn't mean you were wrong. Your prediction may have
+been spot-on and it just so happened that things played out in an unusual way.
+
+Below are some general notes on how to optimize the standard interactions with
+categorical and scalar markets, especially with regard to providing liquidity.
+The last section is a TL;DR.
+
+<!-- prettier-ignore -->
+:::note
+You can _short_ a token (bet that the event will _not_ occur) by buying the same
+amount of all other tokens. With Zeitgeist's current market maker, this can be
+implemented by first buying $x$ full sets and then selling $x$ units of the
+token you wish to short on the market. In fact, you can create all sorts of
+_compound bets_ by buying full sets and then selling only certain tokens to the
+market maker.
+:::
+
+## Trading Categorical Markets
+
+Suppose there's a categorical market and you believe that a particular outcome
+$A$ has a probability of $p(A)$. Let $q$ be the price of the outcome. Then the
+expected profit of buying one $A$ token
+
+$$
+ p(A) \cdot \$1 - q
+$$
+
+(you pay $q$, and if $A$ occurs, then you receive one dollar; otherwise you go
+broke).
+
+This leads to a very simple strategy: If the price of $A$ is lower than your
+prediction, buy $A$. That way, you're betting that $A$ is more likely to occur
+than predicted by the market. If, on the other hand, the price of $A$ is higher
+than your prediction you short $A$, either by selling $A$ (if you own any) or by
+buying the same amount of all other outcome tokens. This means you're betting
+that $A$ is less likely to occur than currently predicted by the market. In
+particular, it is absolutely a valid strategy to own multiple outcome tokens in
+a market.
+
+The farther off the price is from your prediction, the higher the profit. Note
+that, as discussed above, _we're assuming that your prediction is correct_. The
+more your prediction diverges from the actual probabilities, the higher the risk
+of making a loss.
+
+## Trading Scalar Markets
+
+Suppose there's a scalar market with a range of $[a, b]$. Let $p$ and $q$ be the
+spot prices of SHORT and LONG, resp. Recall that $p + q = 1$. The value
+predicted by the market is $v = pa + qb$. Assume you believe that the market
+will resolve to $w \in [a, b]$. Given the current status $p, q, v$ of the
+market, how should you bet?
+
+The SHORT token takes on more value as the value that the market resolves to is
+closer to the lower bound $a$, and LONG tokens on more value as the value that
+the market resolves to is closer to the upper bound $b$. In fact, suppose that
+your belief is correct and the market resolves to $w$. Then each LONG is worth
+$(w - a) / (b - a)$ and each SHORT is worth $(b - w) / (b - a)$.
+
+Thus, if the market resolves to $w$, then the profit of buying one unit of LONG
+at the price of $q$ and later redeeming it is
+
+$$
+ \frac{w - a}{b - a} - q = \frac{w - v}{b - a}
+$$
+
+(using $v = pa + qb = a + q(b - a)$; a negative profit means a loss, of course).
+Thus, the trade is good whenever $w > v$. In other words, a reasonable informant
+buys LONG if they believe the prediction is too low. Note that the result of
+this buy is that the price of LONG increases, as does the value predicted by the
+scalar market, reflecting that the informant has provided information to the
+market. Since buying LONG is equivalent to selling/shorting SHORT, if you
+already own SHORT tokens, you can sell SHORT tokens in this situation instead of
+buying more LONG tokens.
+
+Similarly, the profit of buying one unit of SHORT at the price of $p$ is
+$(v - w) / (b - a)$, so a reasonable informant buys SHORT if they believe the
+prediction is too high.
+
+If $w$ lies outside of the scalar range $[a, b]$, then just assume that $w = a$
+if $w < a$ or $w = b$ if $w > b$ and apply the system above.
+
+## Providing Liquidity
+
+Trades on prediction markets shift the price of the assets. Buying (resp.
+selling) an outcome asset increases (resp. decreases) its price and decreases
+(resp. increases) the prices of the other outcome assets. By buying (resp.
+selling) you bet that the probability of the outcome is higher (resp. lower)
+than currently predicted by the market. But how can you expose yourself to the
+market if you think that the prices are correct? This is where providing
+liquidity comes into play.
+
+The liquidity of a market is important for creating accurate predictions. When a
+trader buys tokens, they are giving up information in exchange for a potential
+pay-off (if they are correct, they make a profit). The more significant the
+price movement, the more information they are providing. But if prices slip too
+quickly due to a lack of liquidity, their profits are comparatively small to the
+value of their information.
+
+Thus, informants and liquidity providers are taking opposite sides of a bet.
+When liquidity providers sell to the informants, they are hoping that the assets
+are overpriced relative to their likelihood, while the traders assume that the
+asset is underpriced. But when informants buy, the prices go up, which means,
+provided the LPs are correct, that they are overpaying, resulting in a profit
+for the LPs. The same applies to selling.
+
+As an extreme example, imagine the informants are buying out a token which the
+LPs know to be incorrect, even at prices close to 1$. The LPs receive fees and
+keep the profits made from selling the incorrect outcome tokens, which will be
+worthless after the market has resolved. But they also kept the correct outcome
+tokens (their initial investment), giving them a considerable profit.
+Conversely, if there's an information shock and the informants are able to
+conclude which outcome the market will resolve to, they will buy all of these
+tokens from the pool and leave the LPs holding bags of incorrect (this is,
+worthless) outcome tokens.
+
+In particular, providing liquidity is just as risky as trading on a market. In
+case of an _information shock_, you stand to lose your entire position (for
+example, if the outcome of the event is revealed before the market closes). When
+the LPs take a loss to the informants, this may be explained by thinking of the
+liquidity providers' losses as payment for the informants' services.
+
+Increasing the liquidity of a pool by adding tokens does not change any of the
+prices, but it has the effect of making it harder for traders to move the
+prices. This is sometimes described by saying that the market's thickness is
+increased. As a result, traders as able to take greater risks by opening larger
+positions, incentivizing them more to give up what they know about future
+events. But from the LPs perspective, this is also a good thing, as it gives the
+informants more rope. Thus, providing liquidity can be thought of increasing
+your position in your bet against the market.
+
+So, users should provide liquidity when the spot prices are at the level that
+they should be at according to their prediction. The traders then pay money to
+receive outcome tokens and shift the prediction to what they believe to be the
+correct probability distribution. If they get it right, the liquidity provider
+will incur a loss. But if the LPs initial prediction is correct, then their
+expected profit is non-negative (this isn't straightforward to prove); but the
+farther the informants' probability distribution diverges from the LPs
+prediction and the more market noise that occurs while the price moves from the
+initial to the final prediction, the higher the LPs expected profit. Even if the
+final prediction is equal to the initial prediction, the LPs will still have
+collected fees. In particular, when you create a pool, you should always set the
+initial prices according to the probabilities that you predict.
+
+By withdrawing some of their liquidity, on the other hand, an LP removes funds
+from their bet against the market. They might do this to take profits (including
+swap fees) or because they have lost faith in their prediction.
+
+## Minimizing Losses When Gathering Information
+
+Roughly speaking, there are two motivations for creating a market or providing
+liquidity. One is to create a market that allows you to bet against the
+informants that are active on Zeitgeist, as discussed above. This can be
+profitable if the liquidity providers have information which gives them an
+advantage over the traders.
+
+The other motivation is to gather information from the traders. This is the
+exact reversal of the situation above. The liquidity providers start off with as
+good a prediction they can muster (based on whatever they know about the topic),
+which is then corrected by the informants. If the market eventually yields a
+better prediction, this results in a loss for the liquidity providers, but they
+receive a better prediction as compensation.
+
+The question then is how the liquidity providers can minimize losses or maximize
+the quality of information they receive. The liquidity is key. If the pool is
+too shallow, and, thus, the market is too thin, then the potential losses for
+the LPs are quite small, and it is very easy for traders to move the price. But
+this is not a good situation for the traders: Not only do they deal with
+excessive slippage, but they are also forced to give up their information at a
+very low price. For example, if the pool is so shallow that any trader can only
+buy 10 units of a particular outcome token, their profit is limited to \$10.
+Most non-publicly available information is worth more than that, and may very
+well discourage knowledgeable informants from participating in the market, which
+may hurt the quality of the prediction.
+
+On the other hand, if the pool is too deep, and, thus, the market is too thick,
+then the potential losses of the LPs is quite large, and it is very difficult
+for the traders to move the price. This is good for the traders, though, as they
+can buy tokens and lower prices. And just as thin markets can have a negative
+effect on the prediction, so can markets that are too thick. While a
+particularly thick market may incentivize a knowledgeable whale to join the
+market and give up some crucial bit of information in exchange for the chance of
+a particularly big payoff, it can also make it _too_ hard for traders to move
+the price, which may again hurt the quality of the prediction.
+
+In summary, the liquidity providers control both their risk and the quality of
+the prediction by adding or withdrawing liquidity. Thin markets can result in a
+lack of participation, while thick markets can lead to significant losses and
+slow price changes. Manually adjusting the liquidity according to market signals
+is often necessary.
+
+## Summary
+
+- For categorical markets: If you estimate that the probability of a categorical
+ outcome is $p$, then buy the corresponding token if its price is smaller than
+ $p$ and short the token if its price is larger than $p$.
+- For scalar markets: If you estimate that the result of a scalar market will be
+ $w$, then buy LONG if the current estimate is smaller than $w$ and buy SHORT
+ if the current estimate is larger than $w$.
+- Provide liquidity if you believe the current prices are correct. This is a bet
+ against the other informants
+- Withdraw liquidity to take profits or if you believe that a justified market
+ correction is about to happen.

sidebars.js

@@ -22,8 +22,9 @@ const sidebars = {
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- "learn/market-rules",
  "learn/using-zeitgeist-markets",
+ "learn/betting-strategy",
+ "learn/market-rules",
  "learn/governance",
  "learn/court",
  "learn/futarchy",