This allows for bigger wagers, attractive payouts, and exciting action for our players. So why should you invest and be a part of the bankroll? Because you will get positive expected value on your crypto currency holdings!
Imagine if someone asked you to play a coin flipping game. You can bet wether the coin will land heads or tails. If the coin is fair and you wager the same amount over millions of bets you would expect to come out even in the end. However the person flipping the coin has to make a living, so they may declare that if the coin lands on its edge, they win and take your wager. This is essentially a house edge. If the coin lands on its edge 1% of the time, the house edge is 1%. Over millions of bets you would expect to lose 1% of the amount you wagered in total. The coin game now has negative expected value (EV), so mathmatically you should not play. If you started with a bankroll of 100, and wagered 1 for 100 flips, you would expect to have 99 left when you finished. Where did that value go?
The coin flipper took your 1, because he has 1% positive EV, and by the law of large numbers is almost gauranteed to make money in the long term if they can get many people to play. If you can find a game to play that has positive EV, mathmatically you should always play it. However you wouldn’t play it just once due to variance, you would split your bankroll into many pieces and play the game forever because it would be printing coin.
So why do people gamble at all if the games are always negative EV due to the edge which covers house costs? Well in the long run, we are all dead. In the short term, variance causes outcomes that do not fit nicely into a perfect mathmatical vision of the world.
Let’s say you play the coin flipping game, and on your first two flips, you win both. The odds of two wins in a row is around 25%.
The most likely outcome was supposed to be one win and one loss, which has 50% probability. If you stopped after the 2nd round you could walk away with 101 instead of the expected 99 after 100 rounds. Congratulations, you beat math! If you walk away now, variance has allowed you to win instead of lose. Gambling is a financial product where the player trades a small known fee (the house edge) for a chance at positive variance (big win). Over the long term, you will lose a percentage of your total wagers equal to the house edge, but in the short term variance will make your bankroll do a random walk zigzagging up and down straying from that neat mathmatical line.
The house is also a financial product, similar to an insurance company. As long as players keep playing, the edge guarantees a steady stream of profits to the house similar to insurance premiums. However if disaster strikes and a player gets lucky and wins a large amount, the house has to pay out that claim according to the game rules. The house must take measures to reduce variance in order to control their risk.
This comes in the form of maximum limits on bets. In the above example, if the house allowed the player a profit of 10% of the house bankroll per bet and they won twice in a row, the house would be down to 81% after two winning coin flips.
A streak of lucky bets would devestate the house bankroll. So how much should the maximum profit per bet be? Luckily there is a formula in probability theory called the Kelly criterion, which states that if you have a positive edge in a gambling game, you should bet a percentage of your bankroll equal to your edge to achieve maximum returns.
Our coin flipper entrepreneur should therefore allow only a max profit of 1% per bet on his 1% edge game. However full kelly criterion can lead to large drawdowns in the short term, so usually the more conservative half-kelly is used. In order for the house to be profitable, it also should have a statistically large sample size of bets made at all levels, even at the highest max profit limit. If there are one hundred million bets of 1 satoshi, the expected profit of those bets with 1% edge is 1 million satoshi. However if one whale comes and makes a single 1 btc bet, the profit or loss from that bet will completely wipe out the expected edge outcome of the smaller bets.
If there are no players gambling, there is no amount wagered and thus no expected profit. Any investments would be dead coin.
Variance in the short term may cause losses and drawdowns of principal for your investment. You must stay invested for a statistically significant amount of bets to be made in order to achieve positive EV.
If the distribution of bets is skewed, a small number of the largest max profit bets will dominate the outcomes of even hundreds of millions of tiny dust bets. If the max profit is large enough, there is no guarantee the sample size for the largest bets will ever reach statistical size necessary to achieve the house edge’s positive EV.
Unlike the gambler, the house can not choose when to bet or when to stop. The house takes the other side of player bets, which is essentially passive gambling but with +EV. The player can decide to stop and never play again after achieving positive variance, which means the house will never have a chance too recoup the player’s winnings.
If there are no players, that may never happen. As a human being you also measure profits based on calender time, but kelly works on bet time. You can’t expect to login every day and see nice daily profits, as that +EV only comes in blocks of millions of bets which depend on player activity.
Because anyone can invest, your share of the bankroll can be diluted by new large investors. If your principal takes a large hit after a string of lucky player wins and then a new large investment dilutes your share to half of what it was, it will take twice the amount of wagered to claw back to your high water mark. Even worse, the large investor may be the player who just won big at your expense.
Counter party risk exists. The operator and this website are your counter party in any investment.
They may die, be shut down by law enforcement, make errors when transferring investor funds, make errors programming the site or game which cause unexpected losses, you could misplace your login or get hacked giving someone else access to your account’s invested funds, or this could just be a straight up scam and/or ponzi and the operator will run off with your hard earned crypto currency.
These can be mitaged by our safeguards: offering you two factor authentication, properly using a cold wallet for most of the funds, auditing our code and security, offering you an emergency withdrawal address which activates in case of shutdown or death, and offering leveraged kelly options for a reduction in counter party risk.
Due to greed you may use leveraged kelly without having the proper currency reserves which may cause ruin even during normal expected levels of variance.
Dicenow collects 10% commission on every investment’s profits. If you make a profit, we take 10%. If you don’t make a profit, we get nothing. This reduces your +EV to be 90% of house edge.
Commission is collected daily, and your investment’s high water mark is set so you only pay commission on new profits above the highest level of your investment which paid commission. If you divest before the daily period with a profit, commission is calculated at the time of divestment. If you have a loss and divest, only to invest again later, you lose the chance to make commission free profits on those losses, because we calculate profits per investment, not per user account.
Bob is the first investor on the site. He invests 10 btc in bitcoin house 1% edge at full kelly. He now owns 100% of the bankroll of that house, and the max profit per bet is 0.1 btc. Nakowa is the first gambler on the site. He plays bitcoin dice at 1% house edge, wagering 0.1 btc at 49.5% chance to win which has 2x payout. He wins 0.1 btc, which is 100% taken from Bob who now has 9.9 btc in his investment. Sally comes along and invests 90.1 btc in bitcoin 1% house at full kelly.
Bob now owns 9.9% and Sally owns 90.1% of the house. The house bankroll is 100 btc and max profit is 1 btc. Mechs comes along and wagers 1 btc at 49.5% chance to win which has 2x payout. He loses his wager of 1 btc, of which 0.099 btc goes to Bob’s investment, and 0.901 btc goes to Sally’s investment. At midnight Bob’s investment is at 9.999 btc, with a loss of 0.001 so no commission is taken. Sally’s investment is at 91.001 with a profit of 0.901 btc, of which 0.0901 is taken as commission leaving her investment at 90.9109.
TL;DR Just tell me how to invest!
The dice game can be played under three different houses with edges of 1%, 2%, and 3%. Lower edge means higher variance, less expected value, but more wagered because players want to play where their chances are higher. We recommend you use ‘simple invest’ which splits your investment evenly between all three houses to balance your risk.
Choose a Kelly criterion to determine the maximum of how much of your bankroll is risked per bet. Fully kelly is equal to the house’s edge, so the max percentage of your investment risked in the 3% house would be: 3% for full kelly, 1.5% for half kelly, and 0.75% for quarter kelly. Half kelly is recommended as the return is 75% of full, but the volatility is much less.
Warning: Using a kelly greater than 1x gives worse returns in theory. The 2x, 3x, 5x, and 10x kelly options exist only for investors who want to reduce counter party risk. Using 2x kelly, they only need to send us half their coins to achieve the same investment as 1x kelly. However you must rebalance your investment constantly, or the large moves from normal variance due to leverage will cause your investment to stray from the expected path. DO NOT use leveraged kelly unless you actually have coins to back it up!