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Topic: Just-Dice.com : Invest in 1% House Edge Dice Game - page 56. (Read 435458 times)

sr. member
Activity: 470
Merit: 250
I don't really see the benefit in creating an investor risk adjustment option. The site already has a fairly large bankroll, do we really need to accommodate larger bets? Why create a confusing and hard to implement (from my understanding) system that isn't really needed?
legendary
Activity: 2674
Merit: 1083
Legendary Escrow Service - Tip Jar in Profile
Thanks for explaining maqifrnswa!

You haven't answered my question, you keep explaining that 1% Kelly is better than 0.5% Kelly. Let me rephrase it: Suppose my investment setting is 0.5% Kelly, and yours is 1% Kelly, and we have invested the equal amount of BTC. The bettor bets 1BTC and looses. Does that mean that you get 2X the profit from that bet than I get? Or are you proposing something much more complicated? Once again - please give us one good example, it's far from obvious what exactly is your idea.

For a house advantage of 1% it would mean that 0.5% of your complete investment is taken and 1% of my full investment is taken and added to the max profit value. Thats the maximum a gambler can play for then. In case he plays for full profit as target and he wins i lose 1% of my investment and you 0.5%. If he loses we win proportionally to the risk played. It all boils down to the amount of bitcoins put into the jar that contains the winable amount of bitcoins.

1a doesn't seem fair because it looks like some investors would artificially increase their bankroll percentage without actually taking any more risk, because we all cover those smaller bets with ease.

1b looks OK. If someone wants to go into higher risk bin and take on themselves percentage of all bets above current Max Profit it's fine with me.

I think 1a and 1b are practically the same. I believe you misread UserBankroll as Bankroll. I would be fine with 1b if its the better solution. Too much finetuning isnt needed anyway i think.



In my estimation Doog is going to make 25 - 40 BTC this week on commission here in a few hours.  

So why would he change anything, it ain't broke, its not losing market share to others, in fact the amount of USD being wagered there appears to be increasing.  

Doog just needs to keep doing what he is doing, keeping his coins uninvested as he does not like the varience, and live off the future commission until he gets bored with it, then when he does send all the BTC back to the investors and sell the site and script for $1 Million USD in BTC, and call it a LIFE.

Why so conservative? If things run why change? What about making things better?

Might be that doog is set and dont need to change the website but still we can ask if he would do it. I await he would develop and test things on a clone website so there is no downside i see.
hero member
Activity: 609
Merit: 506

Quote
1b) An improved idea (and the one Doog was favoring) was to ask users to select one of a few options for maximum bet. For example, you would chose if you want 0.5% maximum wagered per bet or 1%. The site then just has to calculate the percentage of the bank roll owned collectively by those two bins after every roll since the percentage a single investor owns of either bins remains a constant unless there is an invest or divest event. This, for now, seems to be the way it may be implemented.

1b looks OK. If someone wants to go into higher risk bin and take on themselves percentage of all bets above current Max Profit it's fine with me.

This has all been hashed over before. Max profit should be returned to the kelly optimum of 1%, and investors should be encouraged to reduce their investment size until they no longer have hernias when a whale wins big. There is no need for an additional risk limit knob -- that's what your investment amount is for.

Not quite; there are a couple scenarios in which a higher "leverage" on Just-Dice is advantageous over a higher investment amount. There are more, but three spring to mind:

  • A lack of perfect trust in dooglus, dooglus' computer skills, etc
  • A lack of bitcoins
  • Having taken out a loan to invest in Just-Dice (not that I condone this one)

Um. Leverage is a Very Bad Idea. If the investors don't have the full amount of bitcoins to back their position, then who's going to pay out if a whale were to win it all? Who would bet on a platform when you know they might not actually be able to pay out?

If you want to borrow bitcoins to invest on just-dice, that's fine, so long as you aren't implicitly borrowing them from other just-dice investors who never consented.

Upon rereading I think maybe what you are suggesting by "leverage" would be raising your individual kelly percent above 1%. In other words, saying you're willing to bet bigger than the optimal amount  (because you like to gamble with a positive edge). I can sorta see some validity to that.
hero member
Activity: 609
Merit: 506

Quote
1b) An improved idea (and the one Doog was favoring) was to ask users to select one of a few options for maximum bet. For example, you would chose if you want 0.5% maximum wagered per bet or 1%. The site then just has to calculate the percentage of the bank roll owned collectively by those two bins after every roll since the percentage a single investor owns of either bins remains a constant unless there is an invest or divest event. This, for now, seems to be the way it may be implemented.

1b looks OK. If someone wants to go into higher risk bin and take on themselves percentage of all bets above current Max Profit it's fine with me.

This has all been hashed over before. Max profit should be returned to the kelly optimum of 1%, and investors should be encouraged to reduce their investment size until they no longer have hernias when a whale wins big. There is no need for an additional risk limit knob -- that's what your investment amount is for.

Not quite; there are a couple scenarios in which a higher "leverage" on Just-Dice is advantageous over a higher investment amount. There are more, but three spring to mind:

  • A lack of perfect trust in dooglus, dooglus' computer skills, etc
  • A lack of bitcoins
  • Having taken out a loan to invest in Just-Dice (not that I condone this one)

Um. Leverage is a Very Bad Idea. If the investors don't have the full amount of bitcoins to back their position, then who's going to pay out if a whale were to win it all? Who would bet on a platform when you know they might not actually be able to pay out?

If you want to borrow bitcoins to invest on just-dice, that's fine, so long as you aren't implicitly borrowing them from other just-dice investors who never consented.
member
Activity: 63
Merit: 14
Why would we need to plan around irrational behavior?

They'll learn quickly enough whether they can handle the swings with their invested amount. If they can't, they'll have learned to invest less.
member
Activity: 99
Merit: 10

Quote
1b) An improved idea (and the one Doog was favoring) was to ask users to select one of a few options for maximum bet. For example, you would chose if you want 0.5% maximum wagered per bet or 1%. The site then just has to calculate the percentage of the bank roll owned collectively by those two bins after every roll since the percentage a single investor owns of either bins remains a constant unless there is an invest or divest event. This, for now, seems to be the way it may be implemented.

1b looks OK. If someone wants to go into higher risk bin and take on themselves percentage of all bets above current Max Profit it's fine with me.

This has all been hashed over before. Max profit should be returned to the kelly optimum of 1%, and investors should be encouraged to reduce their investment size until they no longer have hernias when a whale wins big. There is no need for an additional risk limit knob -- that's what your investment amount is for.

You know that it is impossible to enforce such a rational behavior.
hero member
Activity: 487
Merit: 500
Made $600. Now I'm done.
hero member
Activity: 487
Merit: 500
Made $20.
hero member
Activity: 784
Merit: 1000
0xFB0D8D1534241423

Quote
1b) An improved idea (and the one Doog was favoring) was to ask users to select one of a few options for maximum bet. For example, you would chose if you want 0.5% maximum wagered per bet or 1%. The site then just has to calculate the percentage of the bank roll owned collectively by those two bins after every roll since the percentage a single investor owns of either bins remains a constant unless there is an invest or divest event. This, for now, seems to be the way it may be implemented.

1b looks OK. If someone wants to go into higher risk bin and take on themselves percentage of all bets above current Max Profit it's fine with me.

This has all been hashed over before. Max profit should be returned to the kelly optimum of 1%, and investors should be encouraged to reduce their investment size until they no longer have hernias when a whale wins big. There is no need for an additional risk limit knob -- that's what your investment amount is for.

Not quite; there are a couple scenarios in which a higher "leverage" on Just-Dice is advantageous over a higher investment amount. There are more, but three spring to mind:

  • A lack of perfect trust in dooglus, dooglus' computer skills, etc
  • A lack of bitcoins
  • Having taken out a loan to invest in Just-Dice (not that I condone this one)
hero member
Activity: 609
Merit: 506

Quote
1b) An improved idea (and the one Doog was favoring) was to ask users to select one of a few options for maximum bet. For example, you would chose if you want 0.5% maximum wagered per bet or 1%. The site then just has to calculate the percentage of the bank roll owned collectively by those two bins after every roll since the percentage a single investor owns of either bins remains a constant unless there is an invest or divest event. This, for now, seems to be the way it may be implemented.

1b looks OK. If someone wants to go into higher risk bin and take on themselves percentage of all bets above current Max Profit it's fine with me.

This has all been hashed over before. Max profit should be returned to the kelly optimum of 1%, and investors should be encouraged to reduce their investment size until they no longer have hernias when a whale wins big. There is no need for an additional risk limit knob -- that's what your investment amount is for.
legendary
Activity: 1974
Merit: 1077
Honey badger just does not care
Thanks for the summary.

1a doesn't seem fair because it looks like some investors would artificially increase their bankroll percentage without actually taking any more risk, because we all cover those smaller bets with ease.

1b looks OK. If someone wants to go into higher risk bin and take on themselves percentage of all bets above current Max Profit it's fine with me.
sr. member
Activity: 454
Merit: 252
You haven't answered my question, you keep explaining that 1% Kelly is better than 0.5% Kelly. Let me rephrase it: Suppose my investment setting is 0.5% Kelly, and yours is 1% Kelly, and we have invested the equal amount of BTC. The bettor bets 1BTC and looses. Does that mean that you get 2X the profit from that bet than I get? Or are you proposing something much more complicated? Once again - please give us one good example, it's far from obvious what exactly is your idea.

This has been discussed, with much detail, a few months ago over several pages of this thread. Here's a summary.

There are two competing philosophies: 1) distribution proportional to risk, and 2) classify bets into tiers and only expose those that volunteered for that level of risk.

Here are two implementations of (1)

1a) The most straight forward system is that every user contributes to the overall bank roll, UserContribution = UserBankroll*K, where K is the percentage a user sets as the maximum they can lose and can be set to any value. The overall bankroll is the sum of UserContributions, and each user then gets UserContribution/Bankroll times the amount won or loss per bet. This approach, however, has been shown to be too computationally difficult as it requires constant calculation of every user's contribution. Right now the site only calculates it when money is invested or divested.

1b) An improved idea (and the one Doog was favoring) was to ask users to select one of a few options for maximum bet. For example, you would chose if you want 0.5% maximum wagered per bet or 1%. The site then just has to calculate the percentage of the bank roll owned collectively by those two bins after every roll since the percentage a single investor owns of either bins remains a constant unless there is an invest or divest event. You get a return proportional to what you choose for maximum wager (1% gets 2x the losses and gains as 0.5%). This, for now, seems to be the way it may be implemented.

Here is the implementation of (2)
The argument for (2) above is that some people that wanted lower variance felt like they would get a much lower return than they are currently getting if distribution is proportional to risk since max bets are placed very rarely. They proposed a system where people choose their risk and are placed in bins like 1b. However, they want to implement betting "tiers." In this example, the two bins are 0.5% and 1%. If a bet would win <=0.5% of the bankroll, then everyone shares the winnings just like it is now, which is proportional to the bank roll. If a bet is placed that would win > 0.5% of the bankroll, everyone shares like they currently do for the first 0.5%, but all winnings/losses between 0.5% and 1% are only shared amongst those that are are in the 1% bin. They want effectively 2 bankrolls: one that covers from 0-0.5% of the bankroll and the other that covers 0.5-1%.
sr. member
Activity: 353
Merit: 251
^This! Custom investor risk adjustment please Smiley

I second this.  Please allow investor with higher risk appetite to increase our risk and possible return.

-J

I would donate for that possibility if dooglus would be willing to implement it. Perfectly would be a kelly percent you can chose freely, not even fixed values to chose from. For gamblers it wouldnt change anything than most probably the max profit. For investors wouldnt change anything either except they want to. And the calculation behind would be done automatically by the site.
To be on the sure side there should be a warning so that noobs dont complain later when the risk didnt work out.
At the end i believe anyone can only win with it. Gambler can play higher, investors can play riskier or play safe and the attracted gamblers would lead to dooglus getting more profit. Win-Win-Win.

I don't quite get what do you guys mean by "Custom investor risk adjustment" in practice. Do you mean some investors can arbitrarily raise max profit? How can this be calculated? Please give us one example of the parameters you propose to be investor-adjustable and how this should be calculated on average bet and high-volume bets.

To be honest this looks to me of much less importance to majority of investors than, for instance, API. Good API can lead to high-quality bots, which means higher betting volume - higher profit. All current bots are just quick hacks packed in the browser plugins. API and quality bots could also probably significantly reduce the load on the site, again leading to more satisfied users, higher volume, etc. I don't see why dooglus should devote his development resources to some esoteric ideas which are not described and documented well, when he can make something that we could be positive would make more profit for the investors.

It means adjusting the kelly percent. First just-dice ran with 1% kelly with is the optimum to get the most profits with the least risk. Now just-dice runs with 0.5% kelly which means 3/4 profit with much less variance. And the kelly value determines what amount of the house can be taken to play by gamblers. Since we only have a house advantage of 1% and 0.5% kelly that means 0.5% of the house can be won in one game. But some would like to risk more of their investment. That works like dicenow shows. Players that play a bigger investment then risk more of their investment and have the chance to lose more of course. At 2% kelly an investor should make no profit anymore when gamblers play full profit. Its not growing or shrinking in average.

At the end the only effekt of different kelly values would be the playable money is raised or lowered depending on the risk level the investors use.

Im not sure about API. Is there really such a demand for players that want to use a bot? I mean at the end they need bitcoins first to gamble with. I doubt a bit that this will lead to a significant more bitcoins gamed but of course it would be a feature.

Its nothing esoteric. Its already done at dicenow, only with fixed values to chose from. And its not really much to code in my eyes. Of course i dont know the website code here.

It could lead to more players when investors raise their kelly percent. Because then the max profit is rising and you could advertise with higher max wins.

You haven't answered my question, you keep explaining that 1% Kelly is better than 0.5% Kelly. Let me rephrase it: Suppose my investment setting is 0.5% Kelly, and yours is 1% Kelly, and we have invested the equal amount of BTC. The bettor bets 1BTC and looses. Does that mean that you get 2X the profit from that bet than I get? Or are you proposing something much more complicated? Once again - please give us one good example, it's far from obvious what exactly is your idea.

I would be interested in a more detailed explanation aswell, and also why the same thing you propose can not be achieved by individual investors changing their invested amounts to fit their preferences Smiley
legendary
Activity: 1974
Merit: 1077
Honey badger just does not care
^This! Custom investor risk adjustment please Smiley

I second this.  Please allow investor with higher risk appetite to increase our risk and possible return.

-J

I would donate for that possibility if dooglus would be willing to implement it. Perfectly would be a kelly percent you can chose freely, not even fixed values to chose from. For gamblers it wouldnt change anything than most probably the max profit. For investors wouldnt change anything either except they want to. And the calculation behind would be done automatically by the site.
To be on the sure side there should be a warning so that noobs dont complain later when the risk didnt work out.
At the end i believe anyone can only win with it. Gambler can play higher, investors can play riskier or play safe and the attracted gamblers would lead to dooglus getting more profit. Win-Win-Win.

I don't quite get what do you guys mean by "Custom investor risk adjustment" in practice. Do you mean some investors can arbitrarily raise max profit? How can this be calculated? Please give us one example of the parameters you propose to be investor-adjustable and how this should be calculated on average bet and high-volume bets.

To be honest this looks to me of much less importance to majority of investors than, for instance, API. Good API can lead to high-quality bots, which means higher betting volume - higher profit. All current bots are just quick hacks packed in the browser plugins. API and quality bots could also probably significantly reduce the load on the site, again leading to more satisfied users, higher volume, etc. I don't see why dooglus should devote his development resources to some esoteric ideas which are not described and documented well, when he can make something that we could be positive would make more profit for the investors.

It means adjusting the kelly percent. First just-dice ran with 1% kelly with is the optimum to get the most profits with the least risk. Now just-dice runs with 0.5% kelly which means 3/4 profit with much less variance. And the kelly value determines what amount of the house can be taken to play by gamblers. Since we only have a house advantage of 1% and 0.5% kelly that means 0.5% of the house can be won in one game. But some would like to risk more of their investment. That works like dicenow shows. Players that play a bigger investment then risk more of their investment and have the chance to lose more of course. At 2% kelly an investor should make no profit anymore when gamblers play full profit. Its not growing or shrinking in average.

At the end the only effekt of different kelly values would be the playable money is raised or lowered depending on the risk level the investors use.

Im not sure about API. Is there really such a demand for players that want to use a bot? I mean at the end they need bitcoins first to gamble with. I doubt a bit that this will lead to a significant more bitcoins gamed but of course it would be a feature.

Its nothing esoteric. Its already done at dicenow, only with fixed values to chose from. And its not really much to code in my eyes. Of course i dont know the website code here.

It could lead to more players when investors raise their kelly percent. Because then the max profit is rising and you could advertise with higher max wins.

You haven't answered my question, you keep explaining that 1% Kelly is better than 0.5% Kelly. Let me rephrase it: Suppose my investment setting is 0.5% Kelly, and yours is 1% Kelly, and we have invested the equal amount of BTC. The bettor bets 1BTC and looses. Does that mean that you get 2X the profit from that bet than I get? Or are you proposing something much more complicated? Once again - please give us one good example, it's far from obvious what exactly is your idea.
legendary
Activity: 2674
Merit: 1083
Legendary Escrow Service - Tip Jar in Profile
^This! Custom investor risk adjustment please Smiley

I second this.  Please allow investor with higher risk appetite to increase our risk and possible return.

-J

I would donate for that possibility if dooglus would be willing to implement it. Perfectly would be a kelly percent you can chose freely, not even fixed values to chose from. For gamblers it wouldnt change anything than most probably the max profit. For investors wouldnt change anything either except they want to. And the calculation behind would be done automatically by the site.
To be on the sure side there should be a warning so that noobs dont complain later when the risk didnt work out.
At the end i believe anyone can only win with it. Gambler can play higher, investors can play riskier or play safe and the attracted gamblers would lead to dooglus getting more profit. Win-Win-Win.

I don't quite get what do you guys mean by "Custom investor risk adjustment" in practice. Do you mean some investors can arbitrarily raise max profit? How can this be calculated? Please give us one example of the parameters you propose to be investor-adjustable and how this should be calculated on average bet and high-volume bets.

To be honest this looks to me of much less importance to majority of investors than, for instance, API. Good API can lead to high-quality bots, which means higher betting volume - higher profit. All current bots are just quick hacks packed in the browser plugins. API and quality bots could also probably significantly reduce the load on the site, again leading to more satisfied users, higher volume, etc. I don't see why dooglus should devote his development resources to some esoteric ideas which are not described and documented well, when he can make something that we could be positive would make more profit for the investors.

It means adjusting the kelly percent. First just-dice ran with 1% kelly with is the optimum to get the most profits with the least risk. Now just-dice runs with 0.5% kelly which means 3/4 profit with much less variance. And the kelly value determines what amount of the house can be taken to play by gamblers. Since we only have a house advantage of 1% and 0.5% kelly that means 0.5% of the house can be won in one game. But some would like to risk more of their investment. That works like dicenow shows. Players that play a bigger investment then risk more of their investment and have the chance to lose more of course. At 2% kelly an investor should make no profit anymore when gamblers play full profit. Its not growing or shrinking in average.

At the end the only effekt of different kelly values would be the playable money is raised or lowered depending on the risk level the investors use.

Im not sure about API. Is there really such a demand for players that want to use a bot? I mean at the end they need bitcoins first to gamble with. I doubt a bit that this will lead to a significant more bitcoins gamed but of course it would be a feature.

Its nothing esoteric. Its already done at dicenow, only with fixed values to chose from. And its not really much to code in my eyes. Of course i dont know the website code here.

It could lead to more players when investors raise their kelly percent. Because then the max profit is rising and you could advertise with higher max wins.
legendary
Activity: 1974
Merit: 1077
Honey badger just does not care
^This! Custom investor risk adjustment please Smiley

I second this.  Please allow investor with higher risk appetite to increase our risk and possible return.

-J

I would donate for that possibility if dooglus would be willing to implement it. Perfectly would be a kelly percent you can chose freely, not even fixed values to chose from. For gamblers it wouldnt change anything than most probably the max profit. For investors wouldnt change anything either except they want to. And the calculation behind would be done automatically by the site.
To be on the sure side there should be a warning so that noobs dont complain later when the risk didnt work out.
At the end i believe anyone can only win with it. Gambler can play higher, investors can play riskier or play safe and the attracted gamblers would lead to dooglus getting more profit. Win-Win-Win.

I don't quite get what do you guys mean by "Custom investor risk adjustment" in practice. Do you mean some investors can arbitrarily raise max profit? How can this be calculated? Please give us one example of the parameters you propose to be investor-adjustable and how this should be calculated on average bet and high-volume bets.

To be honest this looks to me of much less importance to majority of investors than, for instance, API. Good API can lead to high-quality bots, which means higher betting volume - higher profit. All current bots are just quick hacks packed in the browser plugins. API and quality bots could also probably significantly reduce the load on the site, again leading to more satisfied users, higher volume, etc. I don't see why dooglus should devote his development resources to some esoteric ideas which are not described and documented well, when he can make something that we could be positive would make more profit for the investors.
legendary
Activity: 2674
Merit: 1083
Legendary Escrow Service - Tip Jar in Profile
^This! Custom investor risk adjustment please Smiley

I second this.  Please allow investor with higher risk appetite to increase our risk and possible return.

-J

I would donate for that possibility if dooglus would be willing to implement it. Perfectly would be a kelly percent you can chose freely, not even fixed values to chose from. For gamblers it wouldnt change anything than most probably the max profit. For investors wouldnt change anything either except they want to. And the calculation behind would be done automatically by the site.
To be on the sure side there should be a warning so that noobs dont complain later when the risk didnt work out.
At the end i believe anyone can only win with it. Gambler can play higher, investors can play riskier or play safe and the attracted gamblers would lead to dooglus getting more profit. Win-Win-Win.
sr. member
Activity: 303
Merit: 250
^This! Custom investor risk adjustment please Smiley

I second this.  Please allow investor with higher risk appetite to increase our risk and possible return.

-J
sr. member
Activity: 337
Merit: 252
Quote
from the house (investor) point of view:
probability is 1-p
payout b= 1/(.99/p-1)
kelly = (p*(b+1)-1)/b =
((1-p)*(1/(.99/p-1)+1)-1)/(1/(.99/p-1)) = 1-.99=0.01


I may very well be wrong, that wouldn't be the first time Wink but I don't follow you. Your formula for kelly is different from mine, but I still can't see my error.

Yes, now I finally see it.
E[log(1+sX)] = (1-p) log(1+s) + p log(1-(0.99/p-1)s)  (1-p) log(1+s/(0.99/p-1)) + p log(1-s)
sr. member
Activity: 454
Merit: 252
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 is not true: I think you're mixing up player edge and house edge, using the player payout formula for computing the house expected value.

from the house (investor) point of view:
probability is 1-p
payout b= 1/(.99/p-1)
kelly = (p*(b+1)-1)/b =
((1-p)*(1/(.99/p-1)+1)-1)/(1/(.99/p-1)) = 1-.99=0.01

Here's some matlab/octave code that computes ideal kelly fraction as a function of player chosen percentage (it's always 1%, or the house edge)

Code:
clear all
close all
edge=0.99;

for kk=2:98
player_percent=.01*kk;
house_percent=1-player_percent

house_odds=1/((edge/player_percent)-1)
kelly2(kk)=(house_percent*(house_odds+1)-1)/house_odds
 
end

plot(kelly2)

Here is some matlab/octave code that demonstrates the same concept. It finds the final bankroll as a function of whatever probability the player chooses. No matter what probability they choose, 1% (i.e., the house edge) is always the correct play.

Code:
clear all;

percent=.98;
edge=0.99;
payout=1/percent*edge;


number_of_rolls_per_trial=100000;
bankroll=zeros(1,number_of_rolls_per_trial);
bankroll(1)=1;

bankroll(number_of_rolls_per_trial)=0;
number_of_trials=1;

for test=1:100
    kelly=0.001*test;
    for yy=1:number_of_trials
        for kk=1:number_of_rolls_per_trial
            maxwin=kelly*bankroll(kk);
            wagered=maxwin/(payout-1);
            roll=rand;
            if roll > percent
                bankroll(kk+1)=bankroll(kk)+wagered;
            else
                bankroll(kk+1)=bankroll(kk)-maxwin;
            end
        end
        last(yy)=bankroll(end);
    end
    out(test)=(sum(last)/number_of_trials-bankroll(1))/bankroll(1);
end
semilogy([0.001:.001:.1],out)
xlabel('MaxWin as Ratio of Bankroll')
ylabel('Ratio of ending to Initial Bankroll')
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