Top Political Betting Sites

Political betting sites are getting increasingly exciting as the US Election approaches. Lately, online sportsbooks have more accurately predicted election outcomes than political polls and expert opinions. From worldwide elections to Trump conviction odds, recommended political gambling sites are where you’ll want to start.

Top Political Betting Sites

Best Sites For Political Betting

Our expert reviewers checked out the highest-ranked political betting sites by category to help you better understand the pros and cons of each option. We’re confident you’ll find the best online sportsbook from our list:

• Best Overall Political Betting Site: BetOnline
• Top Sportsbook For Worldwide Political Betting: Bovada
• Outstanding Site For US Election Props Betting: SportsBetting.ag
• Best Local & US State Political Betting Markets: BetUS
• First-Rate Futures Odds On The US Presidential Elections: MyBookie
• Best Political Betting Site For Cryptocurrency Users: Everygame

Best Overall Political Betting Site: BetOnline

BetOnline is the best politics betting site around. You can quickly find the odds you’re looking for by clicking the Sports icon at the top of the page and then scrolling to the Politics tab. You can make a moneyline bet on the upcoming election, with competitive odds on Joe Biden and Donald Trump. You’ll also find a wide range of other betting options on US politics, including impeachment specials, Donald Trump jail-time odds, and prop bets for important events like the Republican TV debates. Plus, BetOnline has 24-hour payout speeds and 25 years of experience in the business, making it the ultimate site for political bets.

Top Sportsbook For Worldwide Political Betting: Bovada

Bovada lets you make bets beyond the United States with betting lines on politics in the UK, Europe, Canada, India, New Zealand, and even Russia. Betting on UK politics is the second-most popular option for political bettors around the world, and Bovada provides props on future Prime Ministers, new party elections, and special wagers. You can bet on the hotly-contested Scottish Independence movement, Irish Unification, or whether Vladimir Putin will continue as president. An additional perk is that Bovada’s 50% up to $250 welcome bonus can be used on politics odds.

Outstanding Site For US Election Props Betting: SportsBetting.ag

SportsBetting.ag has fast become the home of US election props betting. The site has expanded to cover many exciting props related to the 2024 election, including former President Donald Trump’s indictment odds, Hunter Biden odds, conviction odds, and more. You can also bet on which Republican candidate will next withdraw from the race, and whether Trump will appear on a TV debate during the primaries. Prop betting is a fun way to bet for casual or beginner political bettors, as they’re an excellent way to get your feet wet, without betting on outright election winners. SportsBetting.ag gives you the freedom to have more fun with political betting compared with other sites.

Best Local & US State Political Betting Markets: BetUS

If you’re interested in local or state-based politics, then you’ll enjoy BetUS’ ability to bet on US Senate, House, and Governor elections. You can wager on the margin of victory with 20 cent lines as standard. For example, the Democrats are the -190 favorites to win Arizona’s Senate race in 2024. In states which are less competitive, you can instead bet on how large the margin of victory will be. For example, in Mississippi, you could bet that the Republican margin of victory will be more than 16.5 percent at -120. BetUS is the best political betting website if you would like to bet on local politics.

First-Rate Futures Odds On US Presidential Elections: MyBookie

MyBookie focuses its odds on the US presidential elections and the primaries, which means that you can enjoy better prices on these markets because there is a smaller range of bets available. In the past, MyBookie has offered odds of +186 for a Democrat to win the election, while other sites like BetUS, BetOnline, and SportsBetting.ag had the same bet at +175. Odds move around depending on the volume bet, however, historically the site has often had significantly better odds than competitors. If the best futures odds are something you’d enjoy wagering on, then MyBookie is the site for you.

Best Political Betting Site For Cryptocurrency Users: Everygame

Everygame’s impressive welcome bonus makes it our top choice for cryptocurrency fans looking to bet on politics. You can claim a boosted welcome bonus of 50% up to $1,000, which comes with a reasonable 8x rollover with minimum odds of -200. This sportsbook often has great betting lines for the US Presidential Election and primaries, and you can use your bonus funds to bet on any of them. To find the political odds, click on the sportsbook section and then scroll down to the left side listing of sports until you see ‘Politics’.

In addition to the bonus, the crypto transactions at Everygame are seamless and fee-free. The site accepts Bitcoin, Litecoin, and BitcoinCash for both deposits and withdrawals. Standard crypto deposits take less than 10 minutes to appear in your account and Everygame is one of the only betting sites to offer Lightning Bitcoin which makes deposits instant and offers a low minimum deposit of $5. This low limit is far more flexible than the $20-25 minimums offered by other bookmakers, and is great if you’re just starting to bet on politics.

How We Select The Top Political Sportsbooks

Our experts review every element of each political betting website to find the very best options for you. Our evaluations focus on user experience, player safety, and a full range of betting opportunities to maximize potential profits.

Here are the main criteria we look for when recommending the best online political betting sites:

Safety & Security

Safe online gambling is paramount, so we look for sites that have SSL encryption for transactions and TLS encryption, where possible. Sites must demonstrate player protection and offer gambling addiction resources.

Payment Options & Withdrawal Speed

We go over all payment processes, expected fees, and transaction speeds. Fast payout speeds rank highly on our list.

Number Of Props To Bet On

We look for sites that have a range of props, so you can bet beyond the usual options. For example, you can bet on the percentage of vote share, state-specific outcomes, or even the color of the winner’s tie.

Customer Service Quality

We test sites for customer service speed, efficiency, and courtesy. The sites we recommend must have a strong customer service reputation and at least two of the following contact options to resolve issues and answer inquiries: live chat, email, postal address, phone, and social media.

Timely Updates & Coverage

A week is a long time in the political world, but some online sportsbooks can neglect their odds for months. We track updates from the leading political gambling sites to ensure timely delivery of odds and coverage from D.C. to Beijing.

Popular US Political Events To Bet On

Betting on politics never stops and there are plenty of events happening year-round to keep it interesting for bettors.  From state caucus results to recall votes, here are some of the most popular upcoming US political events to bet on:

1. 2024 US Election Winner. Betting odds on the winner of the next US presidential election went up as soon as Joe Biden beat Donald Trump in 2020. Now the market is getting hot as we near election day. Political betting sportsbooks are offering a wide range of props and specials on this event. Given the events of January 6th and how narrow many US political races have been since, the election could be a coin toss come fall 2024. MyBookie offers competitive election futures, which means you could lock in significant value if you call the US election winner correctly.
2. 2024 US Presidential Primaries. The US primaries will give us insight into what’s to come during the election. Biden is the heavy favorite to win the Democratic pick as he seeks a second term. Meanwhile, Trump is polling above 50% among Republican voters, but might have to fight the next election from prison. Bettors will want to be aware of what happens in the primaries over the coming months. If you’re looking to bet on the ever-changing primary race, a site like BetOnline constantly updates its odds, which makes it the best option for US Primary betting.
3. Iowa Caucus. Iowa is the first state to hold its primary elections for the Republican and Democrat parties. This means it holds great influence over the eventual party nominees. Bettors can track the odds on our political betting online page and compare them to the presidential moneyline to see if there are discrepancies in prices. As the best betting site for local and state politics, it’s no surprise that BetUS has a top range of Iowa Caucus odds. In addition to the state’s winner, you can bet on the margin of victory and who’ll come in second place.
4. House & Senate Race. The two-year cycle for House and Senate seats is another betting option. You can back individual candidates to win their seats and wager on whether states will flip blue or red. A great prop bet is to wager on the House and Senate results as a whole: Will either party win a majority and how large will it be? Sites like SportsBetting.ag. offer odds on the margin of victory in each state’s Senate race. For example, will Republicans win in Indiana by more or less than 12.5%?
5. Presidential Tickets. You can bet on what the GOP and Democratic tickets will be for the election. Who will earn the favor of Biden and Trump to become their running mates? This is a fiercely-contested betting market since candidates will pander to the big guys during the primaries and align themselves with the popular choice. BetOnline has a tab specifically for the Vice-Presidential race, with top odds for both the GOP and Democratic ticket.
6. State Betting. Place your bets on whether states will vote Republican or Democrat. These moneylines are perfect for bettors who keep up with local politics. In 2020, the swing states of Pennsylvania, Wisconsin, Arizona, and Georgia were won by Democrats by less than 2%, while North Carolina was won by Republicans by a similarly small margin. SportsBetting.ag has the most up-to-date state-specific prop bets available.
7. Trump Conviction Odds. Since Trump is facing upcoming trials across the country for alleged crimes, sites are offering a range of betting lines related to his potential conviction. For example, you can bet on whether or not he’ll be found guilty of felonies in New York, election charges in Georgia, or federal crimes relating to the classified documents case. Bovada has a wide range of conviction odds specials for the former president.

How To Choose A Political Betting Site

Choosing the right political betting site can be tricky with so many factors to consider. To help narrow your search, consider the following aspects:

Updated Odds

Politics can change in an instant, which makes it crucial to find a site that regularly updates its political odds. It’s important to use sites with the latest odds in order to fairly reflect the political landscape and cash in on potential value. For example, if a politician becomes a long-shot because of a viral blunder, you’ll want to stake on the best available lines. For consistently updated political odds, we recommend BetOnline.

Competitive Lines

Betting on politics is highly competitive and you want a site that offers you the best odds. It’s worth comparing what prices sites offer on their core markets, such as the US presidential election, or the next UK election. Sign up at multiple sites on our recommended list and compare prices, so you can better understand which sites offer the best prices across their range of markets.

Quick Payouts

For eWallet and cryptocurrency betting withdrawals, we’d expect to wait no longer than 48 hours. For cards, it should take approximately three days, withdrawals by bank transfer can take 10 days on average, and checks can take 14 days or longer. Sites like Bovada offer fast payouts, including same-day transactions through e-wallets like CashApp and ApplePay (via MatchPay).

Quality Betting Bonuses

Offers at the top bonus betting sites, like the welcome boost found at BetUS, can often be used to stake on political bets. These promotions will provide your bankroll with a significant boost, giving you more chances to strike wins and preserving your bankroll. If a bonus appeals to you, head over to BetUS to claim a 100% up to $2,500. You’ll be able to use the bonus funds to bet on politics and clear the 10x wagering requirement.

Low Juice

Bettors who want to keep more of their profits should look for sites offering low or reduced juice. Juice, or vig, is the amount that the sportsbook adjusts the odds to ensure a profit, regardless of the outcome. The lower the juice and the higher the odds, the better it is for you!

For low vig, we recommend MyBookie since they offer a more condensed range of political bets and they tend to have higher odds than the competitors.

Example of vig/juice:

If the sportsbook calculated that the odds of the Republicans or the Democrats winning were perfectly even, the true odds would be +100 on both sites. However, the sportsbook may post the lines at +105, or even +110. The line hike there is the juice.

Types Of Political Gambling Bets

A top political betting website should provide a range of betting options beyond who will win the US election. Here are the main types of political bets you can expect from a gambling site:

Moneyline Betting. Bet on straight-up moneyline odds for who will win the 2024 US election: Trump or Biden. Each candidate will have their own odds once the primaries take place. The odds could be so close that reduced juice is easily noticeable. Both candidates could be -105 (bet $105 to earn $100) to win.

Futures Betting. Futures bets provide odds on events taking place in the future, usually before we know which candidates will be taking part. This style of bet typically has higher odds because there’s no guarantee that your chosen candidate will be on the ticket. For example, you might find Ron DeSantis is +1400 to be the next US president (bet $100 to win $1,400), even though he might not win the Republican nomination.

Prop Betting. Prop bets allow you to bet on exciting props such as who will be the nominee for both major parties, who will be vice president, and which states will flip blue or red.

Political Betting Tips

Betting on politics can be very profitable if you pick the right candidates at the right time. As political events can change quickly, you can give yourself an edge if you stay on top of both the odds and the daily news to nail bets at the best prices.

Here are a few smart politics betting tips to help you win bigger and enjoy more consistent profits:

1. Understand How To Read Political Betting Odds. Knowing the basics of how betting odds work is important and is an ideal starting point to begin your betting education. In US politics, odds work on the moneyline. The smaller the number, the more likely that bet is to happen. Numbers that drop into the negative show an even greater probability.
   For example, Trump could be -274 to win the Republican nomination in 2024. This means that you would need to bet $274 to win $100. By contrast, Newsom could be +1400 underdog for the Democratic race. This means that a $100 bet would earn you $1,400, although it’s highly unlikely that Newsom would win the candidacy.
2. Keep Track Of Current Political News. It’s vital that you follow political news on a daily basis to understand where the odds might shift. If Biden is having a bad month, his re-election chances could worsen. Likewise, if Trump continues to be charged in criminal investigations, his odds could also worsen. Stay on top of all the updates by checking opinion polls and reading expert political analysis.
   EXPERT TIP: Be sure to look at both sides of the divide.
3. Check Multiple Sites For The Best Odds. Stay on top of which political betting sites offer certain odds. Some sites won’t provide as many props as others, but they might have the best moneyline odds on the 2024 US election. Keep an eye on these sites when considering what you want to bet on.
4. Avoid Political Bias When Betting. Just like in sports betting, it’s a bad idea to wager on your own team to win every week. Try to put aside your own political bias when placing a bet. Consider what the best bet might be and its potential value. Bet with your head, not your heart — this is the first step to a winning political betting strategy.
5. Practice Bankroll Management. We advise all bettors to set a budget and stick to it. Figure out a bet strategy that works for you and never spend more than you can afford to lose. Smart bankroll management can make the difference between profitable experiences and failures.

Downloaded a virus/trojan and they have access to my PC

https://i.redd.it/hrk4iy9k7w2d1.jpeg

Prep for the bull run (pt. 3): How much of your net worth should be on BTC?

TLDR: This very much depends on the person’s risk tolerance. For a typically risk averse person with gamma = 2.0, and assume a return of BTC to be 20% annually and historical volatility of 77%, one should hold 12% of their allocation in BTC. Under-betting might lead to regret, while over-betting can lead to disastrous crash in happiness should the price reduce. Thus, determining your correct risk tolerance (gamma), is crucial to having a healthy investment life. Take the "Find your own gamma quiz" to determine your risk tolerance, and then use it to look up the allocation table at the end of the article.

Introduction📘

How much of your net worth should you bet on Bitcoin? Here in r/cryptocurrency subreddit, we are all firm believers in BTC over the long term. Unsustainable fiscal policy and endless money printing from central banks all around the world have been lasting unabated since 1970, while no attempts at serious reforms are on the horizon. It all points towards the need to keep the fruits of our labors into a decentralized asset that not only is already the hardest to make, but also exponentially getting harder to make over time. And that asset is Bitcoin.

Yet, there has been surprisingly little consensus on how much of our net worth should be invested in Bitcoin. A walk around the subreddit shows all kinds of different numbers: 1%, 5%, 10%, 30% all the way to 100%. Some people suggest a rule of thumb like “only invest money you can afford to lose”, subjecting your allocation to wild swings that would wake you up at night checking Coinbase every minute for price movements.

It turns out, sizing your investment is just as important as deciding what to invest. How should we think about risk and uncertainty? What is the allocation that would allow us to enjoy the returns, while not being bothered by the wild swings of the market? What is the framework that helps us pick the sweet spot between regretting that we don’t invest enough, and regretting that we invest too much? How to truly be happy with our return of crypto assets, knowing that we have decided the best among the “what ifs”?

Why not 100% BTC?🚫

But first, let us ask ourselves a simple question. If we love Bitcoin so much and already believe that Bitcoin will deliver returns superior to all other investments, why don’t all of us invest 100% in BTC? In fact, some people do. To them, Bitcoin is already the last currency, the measuring stick that every single worth of labor and asset should convert to. If you are among this group, this article is not relevant for you.

The reality is that the vast majority of Bitcoin investors do so because they promise high returns relative to the fiat that they use daily for their daily needs. For all its flaws and inflations, the US dollar is still used in everyday life. People still spend 40 hours / week at work, knowing that they will have the same paycheck every 2 weeks for the rest of the year. The price of bananas and bread are stable day after day, even though they keep shrinking 5% every year. This perception of stability and convenience means that imagining wealth as the total amount of fiat remains hard-wired into many people for the time being.

And this means that the wild swing accompanying Bitcoin price is a major psychological baggage to all investors who see their wealth in dollars. A 100% Bitcoin allocation means that on a certain day, they might see a 5% drop or 5% gain in their net worth. They have to maintain their conviction during the long period of 2021 - 2023 where Bitcoin lost 80% from peak value, before finally recovering in late 2023. This can wreak havoc on a person’s psychological well being ranging from constantly being  distracted from work to checking their portfolio to unloading their anger and stress to their wives and kids. Worst of all, the person might be emotionally tempted to panic sell at the worst moment, right before the price recovers, triggering a torrent of regrets.

All this points to the fact that we need a mathematical model to help us reason about not just the expected return, but also the potential loss that we incur so that we can size our bets just enough to both maximize return and minimize regrets. This is a kind of decision that gamblers have to think about on a constant basis, so let’s turn to them to see what we can learn!

Thinking like a gambler🎲

How does a gambler size his bet? I’ll bring up this classic example from the book The Missing Billionaires by Victor Haghani and James White. Suppose you have a starting wealth of $1,000. You are allowed to flip a coin that is loaded with a 60% chance of landing heads, and 40% of landing tails. You can make a bet of any fraction of your wealth from 1% to 100%. What is the optimal fraction of the bet that would allow you to reach as high of a payout as possible after 25 bets?

There are two lenses for looking at this problem. One is through the lens of expected value or average outcome. The expected value is defined as the total of the probability of each outcome times the value of each outcome. The full equation is the following:

https://preview.redd.it/b32r4c3ykr2d1.png?width=1162&format=png&auto=webp&s=6dfe68476998d40723a0a15739f033dcfb6c1657

In which:

• p: probability of winning the coin toss. 0.60 in this case
• a: bet size.
• Wi: is wealth after i bets. W0 would be 1000 in this case.
• n: Number of coin tosses. 25 in this case.

Bet Size (%)	Expected Wealth
5.0	1,282.43
10.0	1,640.61
20.0	2,665.84
50.0	10,834.71
75.0	32,918.95
100.0	95,396.22

From the chart above, it seems that the bet that maximizes the average outcome would be to bet 100% of your money on every bet, yet it should be clear that no sane person in the world would bet like this! You only get your pay out if you win every single bet, and that even if just one bet lands on tail, you risk losing everything!

So perhaps the median outcome would be a better choice here? We are clearly not looking to just maximize the profit, but also maximize the profit gauging the potential loss we can incur when we are unlucky with the coins. Therefore, perhaps we should maximize our money in the event that we are neither lucky or unlucky with the coins?

Using median, 25th percentile and 75th percentile, and now we have a surprisingly complicated picture.

Bet Size (%)	25th Percentile	Median	75th Percentile	Expected Wealth
5.0	1018.93	1244.73	1520.57	1282.43
10.0	975.02	1456.52	2175.78	1640.61
20.0	735.25	1654.32	3722.21	2665.84
38.0	212.39	1052.21	5212.88	6241.76
50.0	47.51	427.63	3848.68	10834.71
75.0	0.09	4.22	206.62	32918.95
100.0	0.00	0.00	0.00	95396.22

The bet size that maximizes the median wealth would be 20% per bet. If you happened to answer 20% when I posed this question to you then congratulations! You truly have the instinct of a gambler, because 20% happens to be the bet size that matches the Kelly Criterion. Kelly Criterion is a strategy that helps gamblers in their game, as well as hedge fund managers and investors world wide in sizing their bets.

But would the optimal bet size for everybody be 20%? Not quite. Looking at the table again, and it would not be surprising to see that some people are uncomfortable with 20%:

• At 20% bet, the median wealth appears to be very high at $1654.32 (a whopping 65.4% return), but the outcome at 25th percentile represents the ending wealth of $735.25 (a 26.5% loss) that can feel really uncomfortable. 
• For those that are risk-averse, perhaps a 10% bet (also known as half-Kelly) could be better here, as they don’t even lose that much in the 25th percentile case (-2.5%), while still having a decent return of 45.6% at median outcome.
• For those that are risk-tolerant, they are ambivalent about the game and don’t care much about the median outcome, but look to have a huge payout. Perhaps a 38% bet would be better here! They will most likely regain the same money that they have before, yet their expected value is much bigger at $6241.5 (+524.1% return) and that their 75th percentile outcome is a whopping $5212.88 (+412.9% return), a massive increase from.

Thus, it is clear that we are still missing a second piece of the puzzle. We need to determine our own level of risk tolerance in order to make a bet effectively. For reference, here is the full spectrum of outcome at each bet size from 1% to 100%.

https://preview.redd.it/buxq90v8kr2d1.png?width=1521&format=png&auto=webp&s=32c4a8808bbf083e32ce6400d9e3523e60f0e7aa

100% BTC example

As a fun exercise, assume that we believe in the power law of Bitcoin, dictating that it would return 33% / year over the next 10 years, while the historical volatility of Bitcoin is 77%. This basically converts a 100% BTC portfolio into a bet size of 84% and a coin toss of 70/30. The median outcome of your portfolio after 25 years (similar to 25 coin tosses) would be the following:

Bet Size (%)	25th Percentile	Median	75th Percentile	Expected Wealth
84.0	1.19 (-99.8%)	156.88 (-84.3%)	1804.09 (+80.4%)	1,396,888.00

This is a disastrous bet. The median case makes you lose 84.3% of your starting wealth, while the 25% percentile you have a potential wipe out. On the other hand, at 75th percentile, you only gain 80.4%, which is even less than had you made a safer 10% or 20% bet. I hope this has convinced you that even if you trust BTC completely and are extremely risk-tolerant, there is still such a thing as an overbet! Learning your own risk tolerance to size your bet appropriately is a crucial exercise that will help you tremendously in your investment journey!

The Utility of Wealth: Losing money hurts much more than gaining money💸

But how do we model different levels of risk-tolerance across different people? For this point, there are some common principles:

• Gaining money generally means more joy, and losing money generally means more pain
• The pain of losing money is often bigger than the joy of gaining the same amount.

Combining these two principles, we can see that the level of happiness does not linearly scale with the level of wealth, but is more like a log curve where gaining wealth has a diminishing return of joy, while losing wealth has an increasing reduction of pain. As Daniel Kahnemann succinctly captured it, "The pain of losing is psychologically about twice as powerful as the pleasure of gaining.

If Loss = Gain, then Pain > Joy

Kahnemann quotes captures the essence of expected utility (happiness), but does not help us determine the level of risk tolerance. The phrase “twice as powerful” does not apply to everyone. What if it is 3 times or 4 times as powerful for risk averse people, while only 1.5 as powerful for risk-tolerant people? For this, we need another variable to determine the level of risk tolerance. Here is the complete formula of the Constant Relative Risk Aversion (CRRA), which represents the amount of utility given wealth relative to the base level

https://preview.redd.it/neb9ib34lr2d1.png?width=334&format=png&auto=webp&s=bae758d70afde07e38f1f3c60b2c474dbd199a4b

In which:

• W represents wealth relative to the base level.
• γ (gamma) is the coefficient of relative risk aversion.

When γ = 1, we have

https://preview.redd.it/t7xmpb68lr2d1.png?width=367&format=png&auto=webp&s=fa0ba76930db0d8684e8e9359de728a7bb880ff9

Let’s visualize our utility functions with different values of gamma

https://preview.redd.it/q8bnbiejlr2d1.png?width=1282&format=png&auto=webp&s=d313de359d0a7db26bf185aaf9d86793f31cfa18

We can see that:

• γ = 0 represents someone who is completely risk-neutral. For someone like this, they don’t care about the risk and simply want to maximize expected value as much as possible. For this person, the optimal strategy for a 60/40 coin would be to bet 100% all the time. We now know that no sane person would actually have a gamma = 0. 
• γ = 1 represents a typical Kelly better, where doubling your money would feel the same joy as the pain they feel from losing half of it. If you have gamma = 2.0, you would have roughly the same risk tolerance as a normal person, characterized by the fact that doubling the money and losing half the money are symmetrical. This person would be ambivalent about two choices between keeping all their current wealth or to either double or half their wealth at equal chance.
• γ = 2 according to White and Haghani, often represents a typical person. For this person, losing half the money would generate twice more pain than doubling the money. (Did this remind you of the saying "The pain of losing is psychologically about twice as powerful as the pleasure of gaining" by Kahnemann?)
• γ = 3 represents someone that is much more risk averse than normal. For this person losing half the money would generate 4 times more pain than doubling the money.

Now that we have a formula for deciding our risk tolerance, let’s instead optimize for expected utility instead of expected wealth. Simply replace W (wealth) with U(W) (utility of wealth), and we have the following formula

https://preview.redd.it/5hmr4dlqlr2d1.png?width=1174&format=png&auto=webp&s=5c2c97d6d9857be4c2e82ca1f6e90557547edd01

Now, let’s visualize the different levels of utility at different bet size to figure out what is the optimal bet size given different risk tolerance.

https://preview.redd.it/q6e05vn5eu2d1.png?width=1533&format=png&auto=webp&s=51b7bb0c957d9c95d8306382dd532818cdcee8e3

Look at this stuff, isn’t it neat? This neatly explains why some people might prefer betting 10%, while others might feel more comfortable with 38%. That is because this level of bet truly optimizes their internal level of happiness based on their own risk tolerance!

We now have a way to determine the optimal allocation based on the the odds and our own gamma. Or more broadly, given an expected risk, expected return and a personal level of tolerance, we have a framework to determine the size of the bet that would maximize our happiness!

A few final notes:

• The level of happiness is very personal and not comparable. We wouldn’t want to say that a risk-taking person is generally more happy than a risk-averse person (though perhaps there is some truth to it?). The CRRA framework helps us determine the optimal bet size for happiness, but it doesn’t tell us how risk-averse we should be.
• Notice that around the optimal point, the expected utility remains largely flat, meaning that you can deviate from the optimal bet size by a little bit and mostly gets near optimal expected utility. But if you get it very wrong, the consequence could be very drastic!
• The lower your risk-tolerance, the more sensitive you are to changes in happiness relative to bet size. Therefore, be very careful and precise about your allocation if you are a risk averse person!

Notice that the level of happiness can be drastically different based on your risk tolerance. A bet of 20% that feels very comfortable for a person with gamma = 1 will feel extremely uncomfortable for someone with gamma = 3. Bitcoin is for everyone, but not of all sizes. Knowing your own gamma is crucial in determining that bet size that is right for you.

100% BTC example

Back to the person who bets 100% on BTC, which is again equivalent to a 84% bet on a 70/30 coin. This is the expected level of happiness of that person.

Gamma	0.5	1.0	2.0	3.0
84.0	-9.68e-01	-9.18e+00	-1.90e+11	-4.64e+29

It is all negative! Even for someone that is unusually risk tolerant like gamma = 0.5, the bet is still a significant overbet compared to their risk tolerance.

You might have noticed that the expected utility framework will produce very negative numbers when the ending wealth is nearing 0. This is a fair criticism of the expected utility framework, especially in the case of near total loss (Is a person who lost 99.9% of their wealth that much more unhappy than someone with 99%?). But given there have been cases of life-threatening circumstances due to near total loss of wealth, we can all agree that sizing our investment based on our risk tolerance to avoid getting near that level of loss is something that we should treat seriously.

Finding your inner gamma🔍

Okay, if you have read until this point and are convinced that determining risk tolerance is important, let’s find our own gamma. Now, the issue with the CRRA framework is that the utility value appears kind of abstract. What does an increase of 0.50 utility actually mean to us? And how does it help us determine our gamma?

Fortunately for us, we can frame our question in a different way to decide our gamma value. Notice that for someone with gamma = 1, their expected utility would be 0 if they bet around 40%, meaning that if they face the problem of picking a bet size for tossing a 60/40 coin 25 times, they are basically ambivalent between not participating in the game at all, and participate the game at bet size of 40%. This number is 20.60% and 13.33% for gamma = 2 and gamma = 3. Thus, we can ask the following questions:

Given that you have $1000 and are invited to place bet on a 60/40 coin 25 times, how much money would make you ambivalent between playing and not playing the game?

But even that is a little bit abstract! Let me place it in a few more realistic scenarios! Assuming that you currently have $100,000 net worth. Please take a moment to answer the following questions honestly and truthfully.

Question 1

You have a choice between a certain amount or a 1% chance to win $100,000 and a 99% chance to win $0. What amount would make you ambivalent between the two options?

• a) $830
• b) $695
• c) $500
• d) $375

Question 2

You have a choice between paying a certain amount for insurance or having a 1% chance of losing $50,000 and a 99% chance of losing $0. What amount would make you ambivalent between paying the premium and not paying it?

• a) $585
• b) $690
• c) $990
• d) $1,450

Question 3

You have a choice between getting paid a guaranteed amount, or performing a coin toss in which there is a 50% chance to win $50,000 and a 50% chance to lose $10,000. What amount would make you ambivalent between the two options?

• a) $18,000
• b) $16,000
• c) $12,500
• d) $9,100

Question 4

You are forced to play a game where there is a 50% chance to win $10,000 and a 50% chance to lose $10,000, unless you pay a fee. What amount of fee would make you ambivalent between paying the fee and playing the game?

• a) $250
• b) $500
• c) $1,000
• d) $1,490

This quiz will work better if you actually put in your real net worth and the answer scales respectively with your net worth. I have prepared a notebook that allows you to type in your net worth and automatically scales up all answers here. Take some time on the quiz to find your true risk tolerance! Feel free to pick a number that is in between as well!

The answer a, b, c, d will match up with γ = 0.5, γ = 1, γ = 2 and γ = 3 respectively.

Putting everything together📊

Okay. Now that I know my own gamma, how much of my money should I put in BTC? Remember that the optimal bet size also depends on the odds too! For a gamma = 1, if the coin is 60/40, then you should bet 20%. If the coin is 70/30, then you should bet 40%. If the coin is 100/0, then you should clearly bet everything!

Thus, one way we can think about the sizing of BTC is to convert its expected return into a coin toss. I think it would be safe to assume a conservative case that BTC has the same amount of volatility that it has previously, which is 77%. Now, depending on how much you believe in BTC, you will have a different notion of expected return. If you believe in the Power Law, then the next 10 years would bring approximately 33% return per annum. I personally used a more conservative 20% annual return for my calculation.

From that point, subtract the return by about 4% (to cancel out the risk-free return of treasury bills), you can use the expected return and volatility to back calculate the coin toss odds and the equivalent bet size. I’ll spare you the math on this one and simply show you the different odd and bet size, given the different levels of expected return as the following. Feel free to visit this public notebook to input your own expected return and volatility and have your calculation of the coin toss.

Expected return	Adjusted expected return (in excess of treasury bonds)	Coin toss probability	Bet size equivalent to 100% BTC allocation
10%	6%	53.88%	77.23%
15%	11%	57.07%	77.78%
20%	16%	60.17%	78.64%
25%	21%	63.16%	79.81%
33%	29%	67.62%	82.28%
40%	36%	71.18%	85.00%
50%	46%	75.64%	89.69%

Now that you have the coin toss odd, you can use our expected utility framework to calculate the optimal bet size, and then scale it with the bet size of 100% BTC allocation equivalent.

Expected return	Adjusted expected return (in excess of treasury bonds)	Optimal allocation (γ = 0.5)	Optimal allocation (γ = 1)	Optimal allocation (γ = 2 - typical person)	Optimal allocation (γ = 3)
10%	6%	15.60%	7.80%	3.90%	2.34%
15%	11%	27.50%	14.14%	7.07%	4.71%
20%	16%	38.93%	20.65%	10.33%	7.15%
25%	21%	49.18%	26.60%	13.71%	8.87%
33%	29%	62.33%	34.91%	18.28%	12.47%
40%	36%	72.12%	42.07%	22.32%	14.60%
50%	46%	81.54%	51.64%	27.18%	19.03%

And that's it! You are done! Congratulations for making it this far🎉. How does it look to you? Was it lower or higher than what you expected?

This is just the beginning🚀

If you make it this far, I hope you are convinced to take the sizing decision seriously. Expected Utility is truly a powerful framework to help you make sizing decisions not just in bitcoin, but also in so many other aspects of life stocks, bonds, mortgages, exiting the IPO, etc. 

And this is just the beginning. How should our BTC be if we now have an additional asset class like stock on the table? What about other cryptos? How much should I keep and how much should I exit if my coins are already 10x? These are all crucial questions that we will have to leave to future additions of the series.

What was your gamma and your optimal allocation? Was it lower or higher than what you expected? Did you feel overexposed or underexposed in your current allocation of BTC? Let me know in the comments below.

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