Topic: Just-Dice.com : now with added CLAMs : Play or Invest - page 166. (Read 454769 times)

Dooglus' irresponsible advertising has ruined my life. J-D used to be a nice family place where we all just talked smacked about eachothers mothers and occasionally someone stuck a sparkler up their butt.  But then he permitted a webcam whore to advertise on the site.  I clicked the alluring banner ad but Ravin was not doing it for me, but then I found Brina: http://www.myfreecams.com/?baf=11771344#Brina_

Next thing I know I lost an hour of productivity watching her take a bath.  

Thank you Dooglus - now I am addicted to webcam whores:(  

What's next, linking us to Silk Road and getting me hooked on the crack?!

Then why, if you run those numbers as you have, and then change the drop down from "win prob" to "edge" does it show an edge of 1.54% and not 1%?

OK, I think I see why your numbers don't agree with mine.  I think it's optimal for the house to risk 1% of bankroll whatever the odds.

I think the calculator disagrees because you're telling it the edge is 1% for the house, but it's 1% for the player.  ie. the player loses 1% of everything they risk.  The house doesn't.

Consider the 1% chance-to-win game that pays out 99x to the player.

If the player plays 100 times, he expects to win once and lose 99 times.  When he wins, he wins 98 units, when he loses, he loses 1 unit.  Over the 100 trials he risks 100 units, wins 98 and loses 99, for a net loss of 1 unit, or 1%.  The player loses 1% of the total he risked.

From the house point of view, the house risks 98 units per trial, and wins 1 when they win.  In 100 trials they expect to win 99 times and lose once.  In total they risk 9800 units, loses 98 and wins 99 for a net profit of 1 unit, or just 0.0102% of risked amount.

Here's how I would use the tool for the 60% game:

Payout to the player is 1.65x, and he has a 60% chance to win.
From the house point of view, the house has a 40% chance to win, and wins 1.65/0.65 = 2.53846x.
Putting those numbers into the tool:



The tool tells the house to risk 1% of its bankroll on such a bet.

I think the numbers you're seeing are how much the player should risk of his bankroll *if* the edge was 1% in *his* favour.

I used a kelly criterion calculator here http://www.sbrforum.com/betting-tools/kelly-calculator/

If you want to play with it you can change the odds setting to decimal and it should be fine. So at 2.0 (ie 50%) you would put edge at 1% and then your total bankroll and it will tell you your max risk. I am not a math guy, but you can wikipedia kelly criterion for the greek letter explanation that you can probably understand better than I.

Here's an example of having 60% win odds with 1% edge.




edit

detailed explanation

http://forum.sbrforum.com/handicapper-think-tank/29009-expected-value-vs-expected-growth-kelly-criterion-part-i.html

A) Suppose you have a bankroll of 10, and equal chances of turning it into 1 or 100.
The expected value of the bankroll is (1+100)/2 = 50.5
The expected value of the log of the bankroll is (log(1)+log(100))/2 = (0+2)/2 = 1

B) Suppose instead you have equal chances of turning it into 0.1 or 500.
The expected value of the bankroll is now (0.1+500)/2 = 250.05
The expected value of the log of the bankroll is (log(0.1)+log(500))/2 = 0.849485

So A has a lower expected value, but a higher expected log(value).

B might look attractive (we're winning 490 or losing 9.9, compared to winning 90 or losing 9) but it's risky because losing 9.9 means losing 99% of the bankroll (dividing it by 100) while only possibly multiplying it by 50.  A on the other hand has equal chances of dividing by 10 or multiplying by 10.

I'm still confused. Is there a difference between maximizing the expected value of the logarithm of the bankroll, and maximizing the expected value of the bankroll If x>y, log(x)>log(y) for all positive x and y, right?

I thought I could get away with sloppy writing by appending "or some such"...  Apparently not.

What I am attempting to do is to maximize the expected value of the logarithm of the bankroll.

You're right; that isn't what I wrote.

Can you explain how you got those numbers please?

If you want to maximize log(expected bankroll growth), you better maximize expected bankroll growth.
If you want to maximize log(expected bankroll) growth, you better maximize expected bankroll growth.
If you want to maximize log(expected) bankroll growth, you better lie down.

Why is the log necessary?

On a 50/50 chance with 1% edge it is correct, but if you have 60/40 in you favor then 1.5 % is actually optimal with 0.5% for 40/60. But 1% is probably a good average max bet size, I assume most bets center around 50/50.

It's unlikely, but by no means impossible.  I don't want to be in the position where I have to say "sorry, I can't pay your interest because I risked more than I could afford to risk".

1% is apparently the optimal amount to risk per event when the house edge is 1% (if you want to maximize the log of expected bankroll growth - or some such).  That's how I chose it.  It turns out that it's pretty rare for people to bet more than 1 BTC per roll, let alone 500 BTC, so it's pretty much academic at this point.

If I was just in this for the money, the rational move would be to hike commission rates drastically.  The site doesn't need anywhere near as much investment as it currently has.  But I enjoy having lots of small investors, and giving lots of people somewhere fun to invest.

Isn't losing 40% of your roll with max bet adjustments anything but totally unlikely? But I understand your position and congratulate you on limiting your investors' exposure to a very conservative 1%.

If I was to borrow 50,000 BTC and guarantee to pay interest on the loan, I am at great risk of defaulting.  The site risks up to 1% of the whole bankroll on every dice roll.  That means that a lucky player can do massive damage to the bankroll pretty quickly.  I don't want to wake up one morning and find that I only have 30k left of the 50k I borrowed, and have to come up with the extra 20k from somewhere, plus interest.  I don't have that kind of money.  If I did, I wouldn't need investors at all.

So instead I ask the investors to assume all the risk, in exchange for 90% of the net profits the site makes on their coins.  That way I don't have to worry about losing to big players.

There's a single bankroll, which grows and shrinks as players gamble.  So in a sense investor profits are compounded, but they're all compounded together, so each investor's share of the bankroll stays the same (until the next invest/divest action).  The maximum profit per roll is calculated per roll, as 1% of the current bankroll, so you only notice the "compounding" effect when a player is placing max bets (which almost never happens).

I meant more from the creator's perspective, in business terms.

Because its a gamble! Users make money off of investments as people lose, lose as people win.

Cool site and idea regarding the investing. Why not borrow coins and pay an interest rate over letting users assume risk as you have it now? What is the effective implied interest rate as it stands now? Is one's investment compounded? So if the site wins and an investors account grows is this added to the investment account or is it held in a separate "dividend" account?

The site regularly checks for new bitcoin deposits.  Overnight the job that does the checking locked up, so deposits weren't being credited to user accounts.

When I woke up I saw the problem, restarted the job and all the pending deposits were processed.

Sorry for the inconvenience.

I lol'd.

DEPOSITS WORKING AGAIN. GOGOGOGOG

If you don't ask the answer is always no