Topic: bustabit – The original crash game - page 103. (Read 61394 times)

Not quite. 1 - 0.99 / m is the probability of losing a bet at m. So 0.01 is actually the probability of losing a bet at 1.00x if such a bet were possible.

This might seem impossible since 1.00x is the lowest multiplier you can roll, so you would expect the probability of losing that bet to be 0%. But if we look at the formula we can see that it's actually possible to "roll" a 0.99 before a floor of 1.00x is applied:

I see, I didn't think about that, it makes sense to keep them separate then.

Is this correct? Assuming players were hitting the maximum bet per round every round (we wish), we'd get 0 expected bankroll growth with a "leverage" of (2*0.75)/1.125=4/3

I understand the use case, but I don't think it's worth providing. In order to safely risk the optimal amount, bets against the bankroll need to be processed sequentially. Synchronizing bets across both games isn't feasible, e.g. you wouldn't want to wait for the round on bustabit to end before you're able to place a bet on bustadice. bustabit could pessimistically reserve part of the bankroll while bets on bustadice continue, but then bustadice investors would no longer be risking the optimal amount.

Regardless, the solution is overly complex without providing any benefit to either casino. At more than 4,000 BTC each, both bustabit and bustadice already have the largest bankrolls of any Bitcoin casinos that I'm aware of.

You can still invest in both bankrolls at the same time by using the offsite investment feature. Of course that means you'll need to be slightly more active in managing your investment than if you had only invested in one bankroll.

I see. Wouldn’t the probability of 1 be 1% then?
1-0.99/1=0.01

I meant offering that option, not that by default investing in one place entails investing in both. I’d personally prefer that my bankroll was used in both places, so I’d have bigger expected returns. If others prefer just one of the sites, they could choose that option too.

Well bustabit has a 1% house edge, so the chance of getting to >= X is simply 0.99/X.


 And the chance of not getting to X, would be 1 minus that.



1x bust is kind of a special case. You can't bet at 1x, because there's a 1% house edge it means that 99% of the time you win (nothing) and 1% you lose (everything). This is a bit retarded, so it doesn't even make sense to let people bet at 1x.

So any time a result that comes up that would cause someone betting >= 1.01x  ... it is called a 1x. So to figure out the probability of that, would be:

chance of >= 1.01   is ....   0.99/1.01   ...  or 98.02%
so the chance of not getting it is  1-that. Or 1.98%



...i think

I don't think this is a good idea. Bustadice uses a pretty unique provably fair system that gives investors and Daniel himself much better assurances than any normal provably fair site (including bustabit). Even should the bustadice server and database get hacked, the hacker would still not be able to predict rolls. This means that if a whale comes on bustadice and wins a lot of money, Daniel has very strong assurances the wins are legitimate (or me being also hacked or the hacker). Likewise this ends up extending considerable protections to investors (assuming they believe me and Daniel to be independent).

 And unfortunately these same guarantees can't be extended to bustabit itself, due to the real-time nature of bustabit. And you can't really combine the bankrolls without inheriting the security aspect of the weakest. And I think in practice these are extremely useful guarantees, and should not dismissed lightly. But also taking a step backward, the bustabit/bustadice bankroll both already allow >30 BTC wins which is already higher than any non-busta casino out there. My intuition is that there's probably not much advantage for having a much bigger bankroll anyway, and Daniel's time would be a lot better spent on improving player-facing issues.

Some more questions:

1. What's the probability of bust at 1?
2. What's the formula to know the probability of bust before a round reaches X?


3. So, if I understand it correctly, assuming players were hitting the maximum bet per round every round (we wish), we'd get 0 expected bankroll growth with a "leverage" of (2*0.75)/1.125=4/3

Is that true?

4. I insist on please checking a way to share Bustadice and Bustabit bankrolls for those of us interested, it would in practice make both bankrolls bigger, maximum bets bigger, and expected returns from investing higher. Good for everyone.

As both sites are yours now, you could offer some way to invest in both places at the same time (shared bankroll). I'd prefer that way more than the "offsite" option, as I may not notice that a casino is losing money (I don't want to have to monitor it constantly), and it's possible that both casinos go bad, which would mean increasing the leverage on both of them, something very risky.

Ryan already made some good points, so I'll just add a few things


Of course there is no way for me to tell with any certainty whether investors actually have the the funds they claim to have offsite or are just abusing the offsite system to leverage. But based on their behavior when high rollers won a lot, I do think that the offsite system is largely being used as intended.

Besides reducing your counterparty risk, freeing up liquidity is the other big advantage the offsite investment offers you as an investor. You could expose the same sum of money to both bankrolls of bustabit and bustadice at the same time for instance.


If you've set a recovery email address we'll send you an email when you are margin-called. Currently investors aren't notified when they are close to being margin-called, however.


Without leverage, the maximum risk per player and round is 0.75% of the bankroll (1x Kelly). If a player were to exceed that he is forced to cash out, but other players aren't. The maximum risk for the entire round is 1.125% (at worst 1.5x Kelly).

If you don't leverage, you will always be guaranteed a positive expected bankroll growth. But if you leverage by 2x you are risking 3x Kelly in the worst case scenario of a super whale use multiple accounts, so your expected bankroll growth may be negative in the worst case scenario.

I understand the purpose of allowing offsite investments, but I bet it's mostly used as a proxy to use a higher Kelly multiple (leverage). I doubt people investing are worried about counterparty risk. If we didn't trust Devans, we just wouldn't invest at all. If I'm willing to invest say 2 BTC, because I like the investment and I trust Devans, why would I invest just 1 and have to spend all day watching for whales and be ready to deposit the other BTC if things go wrong (and still trust Devans at that point, which some investors wouldn't as they may be suspicious)?

Even considering that some leverage was optimal, having to manually adjust it and monitor the investment makes it way less attractive than if it was automatic. Allowing investors to choose to risk up to 0.5, 1, 2, etc. Kelly (as you explained in a previous post) would be way better and we could stop that "offsite" farce. I think there was already a casino using that method, Safedice if I remind correctly.

Right now, using 1:2 leverage would mean that a max bet would be 2 times the Kelly criterion? I read mentions to people multiaccounting involving a higher risk for the casino, but I didn't understand that part well.

At the moment, probably the max offsite if I had to guess. But keep two things in mind:

a) It's very explicitly not a leverage system, it's an offsite system. It's designed to allow you to keep money in your own cold storage, while "risking" it. If you use it as a leverage system, you're probably going to have a bad time.

b) What is "ideal" based on the recent betting, might not be ideal going forward. The last time there was some serious whale action on bustabit, the site profit was 747 BTC and then got totally smashed and finally recovered to 613 BTC. Which makes it look like investors were hurt a bit. But in reality I was invested in that time period, and made a profit. The reason? Some of the overly leveraged investors got margin called on the way down, and the remaining investors made a profit on the up.

Really the entire purpose of offsite investing is to reduce your counter-party risk. But it doesn't do a super great job against maliciousness (e.g. if the house was intentionally draining the bankroll) as to use the offsite system properly you should be topping up your investment. But it provides very strong protection if the site were to suddenly vanish, or something of that nature.

Considering the distribution of bets, what would be the optimal leverage ratio? If people were constantly max betting, then no leverage should be used, but the fact that most bets are smaller (safer for investors), should make some degree of leverage optimal.

I think. That is the statistics are clearer.

Yeah, that's correct

So about 211000 BTC have been wagered just since February?

Exactly. In practice it’s mostly used to leverage, so you are forced to do it too. At least here it is “just” 3, not like in other casinos...

Users' stats such as net profit and total wagered include version 1. The figures you see on our statistics page also include version 1 unless it says version 2 only.

That’s interesting, I didn’t know there was a game with positive EV around. Are there any other games with positive EV (other than potentially poker)?

Are all the statistics shown on the website from Version 2, or just some of them?