The advent of provably fair gambling on the blockchain has the potential to be a paradigm shift for the whole gambling industry. What started with simple dice games has already grown to include Roulette, Blackjack, and many others. While this brave new world undoubtedly offers a great opportunity for enterprising would be casino operators, there are a few fundamentals of gambling that cannot be ignored. In this post, I will discuss a very important one — why the house must have an edge.

By Colin McCrae

It can be demonstrated that anyone with a finite bankroll offering unlimited zero edge fixed odds bets has a non-zero risk of ruin. Indeed, if an attacker has a larger bankroll than the house, the risk of ruin for the house is greater than 50%. The only way to offer zero edge bets with no risk of ruin is to have an infinite bankroll. This can be achieved on the blockchain using native tokens, but creates a token with undesirable economic value incentives. Therefore, offering zero edge bets on the blockchain is not a feasible long term possibility.

If this result doesn’t sound intuitive, then consider it from another perspective. Imagine two people choose to bet $10 against each other on the flip of a fair coin. After each flip, the losing player must pay the winning player $10 from his personal bankroll. Now, if both players start with $100, it is just a matter of time before a long enough run of ‘bad luck’ strikes one player he is bankrupted by the other player. Since they both start with $100, the set-up is symmetrical, and they both have a 50% risk of ruin if they continue this series of bets until one of them has $200 and the other has $0 and is bankrupt.

In the case above, you can see that both players have a long run risk of ruin of 50%, even though they both are betting at fair odds (there is no house edge). This would still hold true even if their bankrolls were much larger, although the average number of bets until bankruptcy would increase.

Now imagine the same scenario, except this time one player only starts with $10, and the other player starts with the usual $100. Now both payers are still betting at fair odds and there is no house edge. It turns out there are still plenty of scenarios where the short-stacked player wins and the wealthier player goes bankrupt. In fact, this happens more than 10% of the time.

As you can see by this scenario, even having a substantially larger bankroll does not completely protect you from risk of ruin. It simply makes it less likely that it will be you who goes bankrupt. You still have a non-zero risk of ruin.

The only scenario where a zero house edge can truly be offered ad infinitum where the house has no risk of ruin, is where the house has an infinite bankroll.

Anyone offering a zero house edge who does not have access to an infinite bankroll must place restrictions on the betting to reduce their risk of ruin. They could reduce or eliminate their risk of ruin by doing one or several of the following:

Limiting bet size, payout odds and/or payout size Limiting total number of bets Only offering zero edge occasionally with house ‘profits’ Designing games such that obtaining the zero edge is nearly impossible Minting new chips to payout winners

None of these is particularly desirable, and does not allow the operator to state truly that they are offering unlimited zero edge bets.

The final point (minting new chips to payout winners) does mean that the house effectively has an infinite bankroll. However, this is at the expense of chip holders, and depending what the chips represent could be potentially fraudulent. If the chips are redeemable for a local fiat currency, then this method would not work, since the house does only have finite real value (the fiat currency).

In the blockchain world, it is possible to deploy a smart contract that has access to an infinite bankroll of its own native tokens. Any bet that cannot be paid out from the initial bankroll (or previous winnings), can be paid out by simply minting new tokens as required.

A fixed odds platform built on this basis has fatal economic incentives. Allowing the contract to mint new tokens on demand means the token supply cannot be fixed, and indeed must be able to increase infinitely as required in an unpredictable way. The token value will therefore be unstable, and follow an inflationary long-term trend. Token holders and users alike are discouraged from holding these tokens, and the platform is unlikely to succeed.

It is therefore a requirement that the native token used for a fixed odds platform must be of fixed total supply, and this must be provable and transparent. Given that the total token supply is fixed, an infinite bankroll is not possible, and zero edge bets cannot be accepted against the core bankroll.

It is established then, that the house needs an edge. The next question, is how much of an edge? But for now, it is enough to say that with EdgeFund we are delivering a platform for fixed odds gaming that will take bets at the lowest possible mathematical odds that still protect the bankroll.

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I am currently working on EdgeFund, an open-source platform which offers a decentralized shared bankroll on the Blockchain. To learn more about EdgeFund, please visit our website. Join our Telegram group to chat to the team and follow us on Twitter!