A pool where everyone has the same chance to win

There’s been a lot of talk about creating a “fair” pool lately. Most proposals say that the current pool is unfair to participants with fewer tickets and that whales have an advantage by being more likely to win.

The proposals I’ve seen so far
A) Want to cap the number of tickets per address or
B) Want to skew probabilites in favor of small holders.

A) can easily be circumvented by creating multiple addresses.
I would argue that B) is actually more unfair than the current model, as it lowers the expected profit for anyone that holds more than a single ticket. It incentivizes playing with as many addresses as possible in order to take the most advantage of the unfair probabilities.

Effectively, A) and B) just multiply gas costs and don’t actually achieve the desired outcome of increasing the probability to win with few coins.

So here’s my alternative: A prize pool where everyone has an equal probability of winning, regardless of how many tickets they have. What changes is how big the prize is if you win. This means the expected value stays the same for everyone, making it a fair game for all participants.
If you are a small fish and you win, you get a prize that’s big compared to how much you have, but not to the total prize pool. If you are a whale and win, you get almost the whole prize pool.
Basically, by having twice as many tickets, the prize you can win is now twice as large as it was before, instead of the probability of winning doubling.

I’d have to think some more about how to actually do the math for this in a way that is technically implementable, but I’m fairly certain it could be done.

Let me know what you think!


We analyzed this approach when developing V3, in fact. The ‘fair’ prize distribution would be that if they win their share of the prize is the fraction of tickets they hold. For many users, this makes the prize marginal.

For example:

Assume a prize of $1000

User A has 1 ticket out of a total supply of 1m tickets. 1000 unique users have deposited.

Chance to win: 1/1000
Prize: (1/1m) * $1000 = $0.001

They have good odds of winning, but their prize is only a tenth of a cent.

This changes the game into a chance to win your own interest. That’s not very interesting!

Additionally, if the winner is only taking a fraction of the prize, then the prize will grow indefinitely and no-one will be able to capture it all.

All that being said, I don’t think it’s a compelling approach to fairness.


Good point. The key is that there would still need to be a majority of players that don’t win anything. A prize can only be substantial if there are some people that don’t win.

I’m not quite sure on the specifics on how to make that work while keeping the expected value fair, but it could be worth investigating.


When I saw the headline for this post I thought “that wont work” but reading your ideas on how to make it possible seems to make sense. Seems like a smart idea.


The biggest problem about skewing the odds towards smaller users is the disincentive it organically creates for the whale users to leave their liquidity there.

Whales winning most of the time isn’t really an issue as far as I can see; they could afterall just put it in compound and it would average out more or less the same.

I don’t think there is necessarily a problem to fix either. If someone has $100 and have long odds to win 100k each week then that’s the protocol working perfectly. I’m sure there are some innovative ideas to make it more attractive for smaller users all the same, but I think we should be careful to take incentive away from the biggest liquidity providers because they will likely bail.


I do like this idea, but I can see where it gets tricky. My thoughts around PT is this is mainly a saving opportunity with a potential gain attached to it. What if you chopped it into deciles. If the amount of tickets you hold is in the 3rd decile you win 30% of the prize, the rest rolls over, so on and so forth. It’s not the prettiest or most elegant but it would encourage further deposits for saving and still allow for potentially sizeable prizes.

What about the idea of betting on other accounts to win?
For example,
Player A has 1 / 100 tickets.
Player B has 99/100 tickets.

Player A can place a bet (with his 1 ticket) that Player B will win since he has a 99% chance to.
Player B also bets that he’ll win.

Assuming a 1000 prize If Player B wins, Player B will get .99 * 1000 = 990 - and Player A will get .01 * 1000 = $10
If Player A actually wins, no one wins the prize pool and it carries over to the next drawing.

Same scenario but Player B puts a bet of 1 token on Player A’s address.
If Player B wins, Player B will get .989898 * 1000 = 989$ - and Player A will get .010101 * 1000 = $10.10
If Player A actually wins, Player B would get (player b is the only one with a token on the winning address) 1 * 1000 = $1000.

Hi guess, we can propose a limit wins to same wallet… today same wallet win 3 times on one week PoolTogether App i don´t know really if whales go to create a lot of wallet for pooltogether prizes… i imagine a lot of whales not.
I prefer not see same wallet win 3 times on 1 lottery :T
Maybe reserve 1 prize to low wallet, not bigone prize (chest), normal.