Topic: Just-Dice.com : Invest in 1% House Edge Dice Game - page 57. (Read 435357 times)

The latest whale used a unusual martingale strategy where the betting probability he used went as low as 6.33%. I think that this is the reason he managed to profit so much from his luck.

Looking at the kelly criterion again, I realized that it depends on the probability chosen by the player. This means that the optimum maximum winnings are only 1% of wagered amount if the player uses a 49.5% bet. For bets with lower chances of success the kelly bet is much lower.

The kelly criterion states that optimal bet size is (1-p)/a-p = (1-p)/(0.99/p-1)-p = 0.01p/(0.99-p) where a is the payout for probability p.

When p=49.5% then kelly=1%, as we know. But when for example p=33%, kelly=0.5%, and when p=9% kelly=0.1% i.e. five times smaller that what is allowed today.

As we know, going well above kelly is risky and lowers the long term profit. I suggest that we let the maximum profit depend on probability. Alternatively, the edge could be increased for low probability bets.

Note also that the "lottery" function, where a player can win 10,000x his bet is extremely unprofitable.


Edit: fixed numbers

^This! Custom investor risk adjustment please

Thanks for the calculations. But i meant it more from the view from a individual investor.

For example. If the house is 10k and 1% kelly then max profit is 100. If each bet is targetting max profit then the optimum really would be 1% kelly. But thats not the reality since most bets are way way smaller than that.

That wouldnt change anything for the whole house but if an individual investor could set his kelly value then he could take advantage from that. For example raising the kelly value to 2% for this single investor would probably be a more profitable investment strategy since the invested money can take part with the double amount with each bet. So this single investor would prozentually grow faster in profit than the other investors with 1% kelly. At least as long as no max profit bets happen. Because max profit bets would have a higher risk then. But the max risk at 2% would be to not make a profit at all. No negative profit. So all bets lower than max profit will yield a higher return for that individual investor.
Of course that wouldnt work anymore when all investors set it to 2%. But i doubt that since it seems that many like half kelly in exchange for one quarter of the profits that users with 1% kelly would get.

I only mean the 1% kelly is only correct if all bets are for max profit. Though its not the only param that makes it wrong.

We can't make investors go up to 10x kelly on small bets because we we can't force users (players) to increase their bets if they bet small. A small bet is a small bet: every investor takes a share of the gains proportional to their investment; no bets are allowed which will exceed the 1% maximum optimum bet since any bets that exceed it will reduce long term gain.

No need to simulate, the math isn't that bad:
when you win, you win:
(1+f*b)*current_bankroll
where f is your kelly percentage, b is how much you win when you win (minus original bet, e.g., "1" for a 50:50 roll)
when you lose, you lose:
(1-f*a)*current_bankroll
where a is your wager.
is if you win p*N times, and lose q*N times (where p is the probability you win, q is the probability you lose, and N is the total number of games played), your ending money is:

endbankroll=(1+f*b)^(p*N) * (1-f*a)^(q*N) * starting bankroll
your percentage profit is then:
C=(1+f*b)^(p*N) * (1-f*a)^(q*N)

you can plug in any numbers you want for any type of roll, house edge, or kelly fraction and you will see what you get

the optimum f to maximize C is simply the derivative of C (or log of C since log is a monotonic function) respect to f set to 0.
optimum f = p/a-q/b

C is negative (that is, a losing strategy when)
p*log(1+f*b)+q*log(1-f*a) is negative, even if you have a positive house edge.

Wouldnt kelly be 0.010101 period then? I mean 0.01 / (2*0.495) = 0.010101010...

Youre right... but this max win on changed chance has to be changed automatically to still meet kelly. Thats something hopefully will be set up for obvious reasons.

But what i mean is... lets assume all bets are 50%. Kelly 1% would only be the optimum for an investor when a player plays to full max profit. But most of the bids are way way lower than the amount needed for max profit. So the risks that 1% involves are never met for the single investor. He could easily use 10x kelly and still remain way under the 1% of his personal investment used in each bet since only a small portion of the house is used in each bet. The individual investor would have to set a way higher kelly to rally maximize his profits. Though of course he has to hope that its not often happening that someone really plays 1% max profit of the house since then 10% of his investment would be involved. Which is a high risk. I mean there should be a sweat spot for the real kelly value for an individual investor. And thats not 1% kelly. Its higher. I guess im not smart enough for calculating...

the formula is (house edge / bet variance)
house edge = 0,01
variance depends on bet type, with standard 2x (0,495 chance to win) bets you have variance = 1

so thats where the 1% as ideal number for max win comes from, now not all bets are made as standard 2x (the lowest variance bets) so depending on what percentage of bets are made with higher variance, the more we should lower the optimal max win number.

TLDR: optimal max win for just dice is not 1% but <1%

He claims that at 2% no growth will happen... really didnt thought that and its still hard to believe... maybe i should run some script to test this out. Anyway... this would only apply if someone plays really the max profit. If he plays half max profit then 2% kelly would be 1% kelly in reality...

I cant find out the formula values to get to 1% as ideal kelly value for just-dice. What are the values for the formula?

I guess he cought it in a Pokèball™...

read:
http://wizardofodds.com/gambling/kelly-criterion/

(it's great site by the way, in general)

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

and
http://www.bjmath.com/bjmath/kelly/kellyfaq.htm
(see Q5)

If edge is 1%, and you wager 2% every time, the house bankroll won't grow. Wager >2%, and it will actually shrink over time.

you have to train an AI, see http://en.wikipedia.org/wiki/Training_set

"I trained software"

What does that even mean? He found a wild software in the jungles of the Amazon and tamed it? It takes artificial intelligence / machine learning to break HMAC-SHA512?

I guess he wants a couple of bitcoins because otherwise he is taking the 35000BTC from the house... isnt that nice?

Fixed your post

That's amazing.

Btw: I don't say betting system doesn't work!!! Actually they all work!!!

Problem is that usuall noobs(I'm not saying I wasn't one too ) think that "working system" let them beat casino with much more coins than they have - but actually it just distributes probability of one roll among many rolls

oh god :D:D I hope he is not lying about him coding bot and sells his bot to as many people as possible as "sure win bot" before losing all his own coins == learning what probability, luck and especially "betting systems"(trololol) stands for :D

looking forward

Ha, ha, ha! I hope he tries that bot

Hahahahah 

*lol*