Topic: bustabit – The original crash game - page 111. (Read 61394 times)

Well yes, but as B moves coins from his offsite to his onsite then his L (as per post above) changes. Let's consider the simplified situation where A and B have the same investment (say 50 btc onsite and 50 btc offsite), A is lying and B isn't, and B will move his offsite to his onsite when he gets margin called (ie when his onsite reaches 0) and not before. While it is true that B will be able to recover whereas A won't, the probability of their onsite going to 0 is the same since they have the same investment, up until the point where B actually starts moving his offsite to his onsite both A and B will evolve in tandem. So if A has the expectation of negative bankroll growth and going bust then B has the same expectation of his onsite going down too.

Sure, the moment B actually moves some coins from his offsite to his onsite the analysis changes since A and B won't have the same investment anymore, but as long as that doesn't happen B has the same (short-term) expectation of losing his onsite as A does. If A can expect to go bust then B can expect to lose his onsite as well, irrespective of whether B will be able to recover again afterwards or not.

The assumption that B will replenish his onsite with his offsite as he takes losses doesn't hold in real life, there will be a delay before B logs in and makes those changes, and the bankroll can change by a lot very fast - before B might be able to react by moving coins from offsite to onsite. My argument above applies to a constant offsite.

This does not excuse the past dishonest and shameful behavior, but this is a good move and one of the right steps towards helping protect investors.

While they didn't come right out and admit to their mistakes, at least they're acknowledging the fact that it wasn't right the first time around by doing this.

Great question.

These are the situations of your two investors:

 * A has 50 BTC in total, it's all on-site, but he lies about having another 50 BTC offsite just to get more exposure to the action. He is willing to risk 2% of his 50 BTC on every bet. He's risking 1 BTC per bet of his 50 BTC.

 * B has 100 BTC in total, He is willing to risk 1% of his 100 BTC on every bet. He's risking 1 BTC per bet of his 100 BTC.

Immediately it should be obvious that A's position is riskier than B's. A is risking 2% of his bankroll on the first bet, whereas B is only risking 1% of his bankroll.


But we're not concerned with whether our "onsite" grows. We only care about our net worth. (EBG = expected *bankroll* growth, where "bankroll" means "coins you actually own"). In A's case his onsite is the same as his net worth, whereas in B's case his net worth is the sum of his onsite and offsite. I think that's the point you're missing. As A loses his onsite he risks an ever increasing percentage of his net worth until he ends up being margin called. As B loses his onsite he tops it up with the coins which were offsite until now, and avoids the margin call. A goes bust, B doesn't.

Let L = (onsite + offsite) / onsite. Then, given a certain bet distribution D, whether an investor (or the house as a whole for that matter) is +EBG or -EBG is solely determined by L. Specifically, there will be an L* such that for all L < L* the investor is +EBG and for all L > L* the investor is -EBG. Whether the offsite is real or not has nothing to do with this. Furthermore, given the current structure of the bankroll on BaB, there exists a legal (ie in conformance with the rules/limits) bet distribution D such that a player using D will be at +EBG.

The "realness" of your offsite has nothing whatsoever to do with whether your onsite will go up (+EBG) or down (-EBG). If two people have the exact same investment (say 50 btc onsite + 50 btc offsite) then that investment (specifically their onsite) will take the exact same trajectory. Obviously...

Do take that mail I sent you seriously Ryan, because this isn't just wrong but (as BaB currently stands) exploitably wrong.

I'm sorry, haven't both A and B lost 50 BTC here? So aren't both -EBG? And hence it doesn't matter whether your offsite is real as to whether you'll be +EBG or -EBG? And hence, like I said, Daniel's and DarkStar's claims are simply false?

Maybe let's try this another way: Suppose I invest 50 BTC onsite and 50 BTC offsite. Will I be +EBG or -EBG? And if your response is to ask me "Are you lying about your offsite" then my answer is "I'm not telling you." So go on, will my investment go up (+EBG) or go down (-EBG)?

I don't think so. DarkStar's reply makes perfect sense, maybe re-read it again =)

Taking your example: "Suppose there are two investors, A and B, and each have 50 btc onsite and 50 btc offsite. A is lying about it but B isn't."

A 50 BTC loss to A is 100% loss of their bankroll, but a 50 BTC loss to B is only a 50% loss. This drastically changes things as a margin call to A is fatal, while B would just be looking at replenishing their onsite investment.

Again, this is false, obviously so.


And a 50 BTC + 50 BTC real off-site doesn't?

When you leverage, the expectation is that you are willing to move those off-site coins on site as you lose, so that you do not get margin called. You are at a 2x Kelly maximum (current bustabit rules), which allows for +EBG. That person can expect their bankroll to increase.

A 50 BTC + 50 BTC fake off-site gives a 4x Kelly, assuming no off-site is 2x Kelly. Once your investment loses 50 BTC, you are left with nothing. It doesn't matter what the site thinks about your investment. By treating 1 coin as 2 coins, you are increasing your exposure. If everything invested with 2x leverage on bustabit, the max win would technically be 2.5% of the actual investment.

This statement is false, just think about it. Suppose there are two investors, A and B, and each have 50 btc onsite and 50 btc offsite. A is lying about it but B isn't. Why would A have -EBG but B have +EBG? Whether they are lying about it is only "revealed" when their onsite gets to 0, so why would A's onsite go to 0 whereas B's onsite doesn't - even before it is known whether they are lying or not? Surely the site can not predict the future of whether A or B will turn out to have been lying, and then set A to -EBG and B to +EBG based on predicting the future. Whether they are at +EBG or -EBG depends solely on their onsite and offsite, obviously...

inb4 "dishonest and shameful"...

Now that investors are comfortably back in profit at approximately 324 BTC, I have reinstated the wager commission of 0.25 %.

Consequently, the bet limit and the maximum profit per player have been lowered to 0.75 % of the bankroll again and the maximum profit per game has been lowered to 1.125 % of the bankroll.

I think you shouldn't pay attention to this. 0-EBG point moves from 2xKelly very slow and only in extreme cases.
max profit = 1xKelly or 2xKelly minus HE looks good solution for me.

In fact, it does not matter whether the maximum profit, kelly criterion, fees and others things was set correctly or not.

What if some lucky player won a lot at casino? Investors lost money.
Investor can not prove that a lucky player is a casino. And that is not just luck, but scam.
Casino can not prove that a lucky player is not casino. And that is not scam.
So such investment is entirely based on trust to the owner.

Touché, I checked again and you do indeed seem right. I'm both pretty embarrassed about my math and impressed by yours. Well done

Rechecked again. Sure.
Player: low-value high-multiplier low-win-probability
Casino: high-value low-multiplier high-win-probability
0-EBG at <2 Kelly

Maybe, it's really counterintuitive.
But, for example, casino (HE=1%) may lose 5% of bankroll per bet with high probability (slightly less than 99%). But player's bet is much higher than the whole bankroll. And that's is EBG+ for casino.

I'm happy with the solution that bustadice uses, but I'm still in search for the pot of gold at the end of the rainbow that would be a fully trustless zero-knowledge on-demand RNG. Something where nobody has to trust any number of people and could be used to make games fair for both players and investors.

You sure about that? It looks to me that the worst case is for the casino is low-value betting on high multipliers from the casinos perspective, but this is generated by a player betting a large amount on a low multiplier. (i.e. if a player is betting 1 BTC to try win 10 BTC,  from the casinos perspective this is a 10 BTC bet trying to win 1 BTC)

Vice versa. The worst case for casino is low-value-betting on high multipliers, until forced cashout. According to my calculations, max-profit = bankroll * house_edge * (2-house-edge) would be EBG 0+ for any cases.

For dice games, bustadice goes pretty far. I've seen some interesting ideas to make it entirely provably fair for investors, but unfortunately none of them were really feasible.