Topic: Just-Dice.com : Invest in 1% House Edge Dice Game - page 29. (Read 435353 times)

f = (bp - q) / b

where f is the fraction to risk,
b is the payout multiplier minus 1
p is the probability of the house winning
q is the probability of the house losing

So in the 49.5% bet, where the payout is 2x,
b = 2-1 = 1
p = 0.505
q = 0.495
f = (1*0.505 - 0.495) / 1 = 0.505 - 0.495 = 0.01 = 1%

And in the 33% bet, where the payout (for the house) is 1.5x,
b = 1.5-1 = 0.5
p = 0.67
q = 0.33
f = (0.5*0.67 - 0.33) / 0.5 = (0.335 - 0.33) * 2 = 0.01 = 1%

And it's the same for every other bet:

If the player has probability q of winning, the payout to the player is 0.99/q
When the player risks 1 unit, the house risks 0.99/q - 1 unit
That's a payout multiplier for the house of 1 / (0.99/q - 1) + 1

b = 1 / (0.99/q - 1) + 1 - 1
f = (b*p - q) / b
  = (p/(0.99/q - 1) - q) * (0.99/q - 1)
  = (p*q/(0.99 - q) - q) * (0.99 - q)/q
  = (p/(p - 0.01) - 1) * (p - 0.01)
  = p - (p - 0.01)
  = 0.01
  = 1%

So is he a lemming? Is he Icarus?

He won 12 times, came back the next day and 7 even bigger bets, then the next morning 7 more times. Then he waited 2 hours and played and lost it all. What was he thinking about in those 2 hours?

I'm pretty sure it applies for all odds.  You need to look at the payout that the house is getting.  When a player risks 1 unit at 33% for a 3x payout for example, the house is risking 2 units for a 1.5x payout with a 67% chance of winning. If you apply the Kelly Criterion on those numbers you'll see that it's still optimal to risk 1% of the bank.  And the same applies no matter what odds the player is getting.


I don't think it does.  It changes for the player, but not for the house.  Of course the player has a negative expectation and so shouldn't be playing anyway.

John Larry Kelly, Jr. was a mathematician from Bell Labs. He is most famous for using a voice synthesizer in the early 1960's to have a computer sing "Daisy, Daisy, give me...". Arthur Clarke was visiting a friend at Bell Labs at the time and worked the song into 2001, A Space Odyssey".

But he also developed the Kelly Criterion. One of the results of the Kelly Criterion which dooglus used is that for a bet with 1% house edge for even money bets only the optimal amount for the investors to bet is 1% of the house bank.

It should be noted that the Kelly Criterion changes for different payouts. For instance if the player selects a profit of 50%, Kelly Criterion says he should be allowed to bet up to 2% of the bankroll. Presumably dooglus thought that would complicate the rules and he assumed that the majority bets would be 1:1 return.

Even Kelly supporters usually argue for fractional Kelly (betting a fixed fraction of the amount recommended by Kelly) for a variety of practical reasons, such as wishing to reduce volatility. Hence the phrase "half Kelly".

Kelly died of a stroke on a Manhattan sidewalk at the young age of 41 in 1965. It is reported that he never used his own criterion to make money.


Technically it recommends you do that only if betting a profit of 100% (i.e. 50%-HE/2 probability of winning). It changes if you select another profit.

He's referring to the Kelly criterion which tells you the optimal amount to risk when you have a positive expectation.

It turns out that Kelly recommends you risk the same amount of your bankroll as the house edge percentage.  Since JD has a 1% house edge, "full Kelly" means 1%.

There's a tradeoff to be made between volatility and expected profit.  We're conservative in only risking 0.5%.

This article is a good introduction to the concept, and includes this image which shows how volatility and profit trade off against each other:



See this, too:

http://compoundingmyinterests.com/compounding-the-blog/2012/10/12/how-did-ed-thorp-win-in-blackjack-and-the-stock-market.html

It's not clear what he was trying to do, but 7000 wasn't his goal, since he reached that and kept playing.

While he was playing I got the impression that he had resolved to play until he lost. I think he said several times for investors not to worry about his wins because they would get their coins back in the end, or words to that effect.

I see JD as a platform I provide where anyone who wants to can provide the bankroll, or the action.

If you provide a lot of the bankroll, you stand to profit from advertising the platform to people who will provide the action.

I'm happy to let things play out and see what happens.

If people stop playing so profits stagnate and the bankroll gets divested, that's fine with me too.

Use it however you see fit, and I'll keep it up and running, and look after the coins.

I assume Doog hasn't changed anything because it is not really worth the effort and makes investing more complicated. The current max payout is so high that your first example would be rather pointless. The second example would just force everyone to go to full Kelly, if they want the same profits. The second example is also why allowing leverage could be problematic. Since there are rarely "large" bets, it would be relatively safe using high leverage. I could easily see the max payout inflate due to more and more leverage being used.

When you use the word "Kelly" here, is that just meaning 1%, or is there some other meaning for the word?

I assume that no one filtered the bets to look for trials where the profit was higher than 0.5% Bank and also where the payout was 1:X where X=1 or  less.

It sounds as if Nakowa was upset about the 0.25% restriction, that he actually almost never went much above 0.5%.

If the data does nothing else it may show another whale that the win was done by only breaking .5% a relatively small number of times. It could encourage another whale to begin playing under the current rules.

It seems like one whale encourages another one. The story was 'mechs/fuckit', one of the largest just-dice investors lost about 500BTC of his 2,200BTC to Nakowa. As a result it encouraged him to try a risky strategy. He tried to turn the 1700 into 7000 and lost it all. He won back the lost investment in 5 plays, but he lost on his 27th play.

There was a pretty lengthy debate a after max winning was reduced to 0.25% of bankroll (i.e. quarter Kelly) and they increased up to 0.5% (half Kelly). It seems that some do want it back at full Kelly, but there wasn't a clear way of how to implement it in a way that everyone thought was fair. Some wanted two pools: one pool for small bets less half kelly and and another pool for bets greater than half kelly. This way people that only wanted to risk 1/2 Kelly would only do that, while others would be free to risk more. Doog thought such a set up was unfair to the people who wanted to invest more. They were taking the increase in risk/variance for the site while everyone was benefiting. The counter was that this system would basically limit losses to what a person was comfortable with per bet. people in the 0.5% pool would never loose more than 0.5% per bet.

Example of system:
Player A invests 100BTC in 0.5% pool
Player B invests 100BTC in 1% pool
Total pool is 200BTC
The max winning is thus 1.5 BTC (0.5% of 100BTC+1% of 100 BTC)
The total amount of BTC invested by people ok with 1/2 Kelly (0.5%) = 200 BTC
Total amount of BTC invested by people ok with full Kelly (1%) = 100 BTC

The first 1BTC (0.5%) of losses and winnings is shared amongst everyone that is OK with half Kelly (200 BTC). The second 0.5% of losses and winnings are assigned to those that are OK with full Kelly.

gains/losses per person is:

Player_Total = player_sum_of_amount_invested_in_either_pool
House_Total = total invested in all pools by all players
Payout_HK = the loss or winnings of a single bet capped at half Kelly
Player_FK = player amount invested in full kelly pool
House_FK = total invested in full Kelly pool by all players
Payout_FK = the loss or winnings of a single bet that is in excess of half Kelly but less than full kelly

Player_Totall/House_Total*Payout_HK + Player_FK/House_FK*Payout_FK

Case 1:
Someone bets wins/loses 1BTC (so it is entirely 1/2 kelly). Losses/gains are assigned as follows:
Player A: 100/200*1 BTC= 0.5 BTC
Player B: 100/200*1BTC=0.5 BTC

Case 2:
Someone bets wins/loses 1.5BTC (maximum allowed). Losses/gains are assigned as follows:
Player A: 100/200*1 BTC= 0.5 BTC
Player B: 100/200*1BTC + 100/100*0.5BTC=1 BTC

The alternative was to have and "adjustable" risk factor - either as two separate pools (half kelly and full kelly) where earnings/winnings are assigned proportionally. It was pointed out that that would be identical to having house edge be 1% for everyone, but everyone have an adjustable slider as to what they wanted their "kelly" to be, and thus invest accordingly. Since that was identical to the original situation that led to high variance, it too didn't get much traction

Example:
Same investments as above, but there is only one pool
Player A effectively contributed 50 BTC to the pool
Player B contributed 100 BTC to the pool
Total pool size = 150BTC
Max winnings/losses = 1.5 BTC (same as above)

Case 1:
Someone bets wins/loses 1BTC (so it is entirely 1/2 kelly). Losses/gains are assigned as follows:
Player A: 50/150*1 BTC= 0.33 BTC
Player B: 100/150*1BTC=0.67 BTC

Case 2:
Someone bets wins/loses 1.5BTC (maximum allowed). Losses/gains are assigned as follows:
Player A: 50/150*1.5 BTC= 0.5 BTC
Player B: 100/150*1.5BTC=1.0 BTC

As you can see, max bet sizes end up the same, but the player that chooses 1/2 kelly earns more money in the first system (which is where nearly EVERY bet occurs on just dice) than they do in the second. That's why it appears unfair: maximum jackpot increases which benefits everyone and increases site traffic and potentially profits for the people that did not "do the work" in order to increase traffic. The counter argument to that is that it actually does help those that assume more risk: they still get the exact same return as they currently do at the current site, and they get to take advantage (and attract) play by whales that the lower kelly players do not get to do.

Expected return for investors (considering that it will stay as the last months) is going so low that I'm thinking about divesting. I really love Dooglus' idea, but I don't get why the website isn't advertised much more (to players, of course, he doesn't need nor want more money invested).



Yes, of course, as 1% still isn't risky for investors, while we could encourage more betting.

well, if you invested back in the days when the whale was feeding, you'd know what I mean. Even Doog divested. I don't think he cares if it's 1% or 0.5%, as long as he can pound those 300 each, he will never leave his prime.

20,651 average BTC wagered per day previous (June 20, 2013 - Feb 17,2014)
 2,386 average BTC wagered per day last 4 months (Feb 18, 2014 - Jun 17, 2014)

In the last 120 days the total amount wagered is 18.43% of the amount wagered in a single day on Sep 29,2013.

So we've established that Nakowa didn't actually go about 302BTC profit per bet, but that he liked the idea of raising his bets to a profit of 1% of Bank.

So am I correct in understanding that if it was your website you would favor raising the max profit back to 1% in order to attract someone like Nakowa again (or Nakowa himself). You would like the possibility of cashing in big as an investor vs another big loss.


And you are clearly worried that he will come back.


Are you guys investors or are you just looking on?

I want him to come back because I don't care about variance but I do about profit.

I'll let my FR code go for 0.01 BTC if anyone wants it. Otherwise I'll likely just be playing, .

Are any of the FR codes for the VIP?  If so I'd really like one so please pm me.  @MilkyLep sent u a pm bro.

You don't hope that he will come back because you are afraid of variance? You must hope the max bet would be less than 0.5% of the bankroll then?

I think 0.5% is good as it is not too conservative but gives better expected winnings to those invested than a lower max bet

I hope he comes back.

i'm a little worried that max bet is approaching 300 territory where Nak was fully employed.