Topic: [POLL] Just-Dice INVESTORS: Do you agree with lowering the max bet? - page 2. (Read 7080 times)

Yes - with a minor caveat. 

Whether it ACTUALLY improves or reduces profits depends on what specific bets everyone makes that are different to what would have happened had the max bet not changed.  But it reduces expected profits (unless someone has a reason why they think betting volume would INCREASE).

Correct.

affirmative

Yeah, I really like VTC's line of reasoning too.  Let me try to take this a bit further:

At a given level of aggregate profits, decreasing max bet from 1.0% to 0.25% increases investor exposure to counter-party risk (as they need to deposit 4X as much to earn the same profits).

The profits that JD earns depends on bet-volume x house-edge.  And while bet volume depends on many things, I can't see how it depends on the total amount invested.  

So, does this mean that decreasing the max bet below the optimal value increases our aggregate exposure to a counter-party failure but does nothing to improve total profits?

While the expected profit amount would be the same, the 8,000 and 1% would be higher in percentage terms (what actually matters). This, of course, comes with higher risk due to variance. I am intentionally ignoring counter party risk since it is hard to quantify and may differ for each investor.

It really comes down to what kind risk/reward investors are looking to achieve.

Perfectly valid points - and ones which were belaboured at length the first time nakowa had big wins.  Unfortunately some invesotrs *cough* mechs) seem to have some reason to want as much capital as possible left with dooglus rather than manage their own bankrolls, risk and variance.  It's not so much that THEY want low variance (but high CP-risk compared to likely profits) but that they want to insist on everyone else doing the same - despite 1% being optimal Kelly and thus giving investors the most ability to adjust.

Those figures are clearly wrong.
Did you happen to forget to reduce max bet when the whale wins?

+1

In my opinion VTC nailed it in all the points. JD is not a bank, it's an unregulated BTC CASINO, so you obviously want a high return on what you invest, expecting high variance especially in the very short term. And you definitely need whales for that.

I think there may be some deeper insight in what VTC is saying above.  

He says investors invested at 32,000 BTC and 0.25% max bet is the same as investors at 8,000 BTC and 1.0% max bet: in both cases the max bet is 80 BTC.  In both cases the investors, in aggregate, earn the same profits, no?  But in the 0.25% case the investors risk a larger amount due to counter-party risk.  

Did I understand you correctly, VTC?

I don't think this is right. Even if the gambler has infinite capital the probability I get is 2.8% to take 25k out of 30k.
With a max bet of 0.5% I get 0.08%.

If your assumptions are not realistic the rest is not either.

What if you take a more realistic assumption and for example say that the whale has double the stack of the house?

What if you consider the bankroll ruined when it's ruined?

How high is the risk for ruin then?

This would actually be pretty easy to calculate using the simulator and excel, but I'm feeling pretty lazy now to verify. The one thing I will note is that I think that your assumption about the size of Nakowa's bankroll is likely flawed, and the probability of the house bankrupting should go down significantly if say he only starts with a bankroll of half the size of the house.

Lowering the max bet to 0.25% is not the same as divesting 75%, except in the face of bets >0.25% of the roll, which are only one user. This max bet system is a cool idea, I think that doog will definitely implement it as quickly as he can.

Some simple risk of ruin math introduced here.

Assumptions:
- The whales have enough capital to try and break the bank without going broke.
- JD is considered "ruined" when the bankroll drops from 30,000 BTC to 5,000 BTC.  Considering the panic already seen among investors, this is a very conservative estimate.

With a 1% max bet the risk of ruin is surprisingly high:  18.2%

With a 0.5% max bet it drops drastically to: 3.3%

With a 0.25% max bet it is miniscule: 0.11%

Also, Kelly criterion does apply for the best long-term ROI, but with kelly betting you can never go broke.  Just eventually the max bet would get into the satoshis and nobody would play.

If any investors wanted a max bet .25% of their roll they could have divested 3/4ths of their investment.

If all investors wanted this than the investors bankroll would be about 8,000 with 1% max bet , which is the same thing as 32,000 invested at .25%.  Both give a max bet of 80 BTC.

Why couldn't Doog just divest all accounts by 75% if he was scared of whales placing too big of bets. 

It would be less risky for investors to keep 8,000 with the site at 1% max bet than 32,000 at .25% max.  Now we have to trust Doog with 4x the amount in cold storage.

Now with a .25% max bet as soon as the steady profits start new investors will come which will further dilute all the current investors making it harder to recoop loses.

Whales should be treated like VIP, regardless of how they act, as long as they continue betting.  Each 300 btc bet was an expected gain of $360 to investors.

And then you have investors who thought JD was a, quote unquote, "long term stable investment"

I believe there are two factors we should consider when discussing this matter:

MATHS:

Kelly Criterion works just fine, but the fact is that Nakowa's bankroll is many orders of magnitude bigger than the average player's, and so is his average bet. He is virtually the only one going nowhere near the "max bet". This just means that himself alone can provoke huge variance - but if he plays long enough, it will even out.

PSYCHOLOGY:

From one side, its definitely the casino's ally. If you understand this business, you simply know that Nakowa is either a) a cheater or b) the absolute best customer you can probably EVER have. Let's remember that there's absolute no evidence for a), and that:

Nakowa is the kind of guy willing to gamble $40k every 5 seconds during 3/4 hours

From the other side, you have a mob of whiners or angry "investors" who treat JD as a bank, and these guys are obviously ready to spread FUD about JD and Dooglus if they see their investment shrink by %25 in a few days due to variance. Some of this "investors" are ready to crap their pants by disinvesting probably because they do not understand in what they were investing in the first place, and this could create a "bank run" effect if the whale has another lucky strike.

The latter is something difficult to factor when calculating the probability of "bankruptcy of the house", but anyhow I'm sure Doog took his decision considering also this difficult to weight but very real "bank run" scenario.

IMO, a "market for risk" is a brilliant concept. I also hope more investors understand now what does it means to invest in a gambling site: who is your average customer, who is your STAR customer, and how your expected result can fluctuate wildly.

I think you guys are missing the point. We're talking about the max risk, which, assuming a fixed payout of 1:1 (which is how Nakowa always gambles), is essentially the same as a max bet size. If you have your risk tolerance set to 0.25%, you will be invested in all bets below 0.25%. Increasing this to 2% when there is no one betting > 0.25% of the roll will not give you increased returns. So the max bet would actually be a weighted average of people's investment and tolerance, but everyone would get equal returns on all bets, with the return being capped on large bets to the level of their risk tolerance; i.e. every bet on the site other than Nakowa's.

This actually wouldn't be that difficult to implement mathematically, only slightly more so than the current investment math. You could even set it up with two or more baskets of risk like the design of Betterment: one basket where you're willing to risk say 0.25% and another where you're willing to risk maybe 10%.

Two more points of emphasis:
1. In gambling, specifically poker, a whale is a "big fish." This is not the same as a "shark," who eats fish and whales. <-- Point being they're both prey animals
2. You guys are all barking about how we've chased Nakowa away, yet most of these posts came after he shipped 3k back today at the lower levels; there was only one post in the whole thread that acknowledged this. Now, the losing might scare him off, but if he's as addicted as we all believe he is he'll be back, he has nowhere else to go. Where else will he be able to get such high max bets with such low edge.

P.S. For the record, I voted "No" to the thread poll, I don't think the size should have changed
P.P.S. Kupsi made this point as well before I published, but I'd already type it up so maybe some people will benefit from my explanation vs his.

It can be done this way...

Let's say you invest 100 BTC and I 200 BTC. You have 0.25% risk and I 1% risk. Maximum profit will then be 2.25 BTC.

When someone makes a bet with a potential profit of 0.3 BTC. We both risk 0.1%.
When someone makes a bet with a potential profit of 0.6 BTC. We both risk 0.2%.
When someone makes a bet with a potential profit of 1 BTC. You risk 0.25% and I risk 0.375%.
When someone makes a bet with a potential profit of 2.25 BTC. You risk 0.25% and I risk 1%.

Everybody will benefit from the small players, and investors with big risk will benefit extra from the big players. Big investors have no reason to increase the risk only when small fish play because it don't increase their profit.