Just-Dice.com : Invest in 1% House Edge Dice Game

[Dabs]

A uniformly distributed random number is still a random number, Dabs. You're saying here that the results aren't random because they're random?

I'm challenged because I don't know how to explain it. I'm trying to say that while the pattern fits and looks random, it is predictably random.

The fact is that both you and nakowa speak about "spotting a pattern" (gambler's phallacy in its purest form), but neither of you cannot clearly explain a) how do you find the pattern and b) why this pattern (and thus flaw) exists.

This is a problem. Maybe I'm a savant or something. I don't think so. I just can't explain it.

I'm not very firm with math-stuff, just wanted to assure Dabs he's not alone in his suspicion.

@molecular, it's called Gambler's Fallacy. A lot of gamblers and non-gamblers (I never was a gambler until this year) think, some things must be "due".

I completely understand it is a fallacy. I also completely understand why so many chose to believe it. I've seen gambler's lose big time.

I have a limit, so that's why I'm not losing my shirt. And why millions of people around the world continue to bet one dollar on a state run lottery ticket with a 50% house edge.

if You found a pattern to Your advantage, You should know how to explain it, IMHO. I believe in patterns in connection with RNG games.

@elm, that's a problem. I can't explain it any better than I've written. The pattern is seen as a whole, not a specific win loss sequence.

dooglus should put out a bounty to prove the RNG is flawed. allow people to benefit financially without losing their soul...

The bounty is already there. To play and bet against the house that you will win with what you believe or think is the exploit. That's what I've been doing until I went bust. Doog could show my chart, it has a nice graph to it until I busted.

I'm wondering why Nakowa is only going after just-dice and not any other dice sites.
If it all was about math and 1% house edge, he should be able to win big at prime dice as well.

PD uses a completely different method to compute it's rolls. Coinroll would most likely be the next victim if it only had a bigger bankroll or investors to win money from. However, it has a minimum bet (bad for me) but that shouldn't affect Nakowa with his style of play.

However PD is constantly being accused of rigging the site and not being totally provably fair. It is, losing players just can't accept it.

[🏰 TradeFortress 🏰]

A uniformly distributed random number is still a random number, Dabs. You're saying here that the results aren't random because they're random?

I'm challenged because I don't know how to explain it. I'm trying to say that while the pattern fits and looks random, it is predictably random.

Please investigate this more and claim a few millions when you find a flaw in SHA256.

[Deprived]

Doog could show my chart, it has a nice graph to it until I busted.

Same for everyone else with a system - their graphs look good until they bust.  There's a reason for that.

Just the rest of them don't then try to beg other people to fund the next bet in return for SOME of the profit (when of course any investor could make the bet themself and get ALL the profit and none of the CP risk).

[mechs]

A uniformly distributed random number is still a random number, Dabs. You're saying here that the results aren't random because they're random?

I'm challenged because I don't know how to explain it. I'm trying to say that while the pattern fits and looks random, it is predictably random.

Please investigate this more and claim a few millions when you find a flaw in SHA256.

Maybe nakowa is the NSA and broke SHA

[chriswen]

this can be done without tiers, the only change to the ui is a "max % loss per single bet" field. the example you presented fits this model:
https://bitcointalk.org/index.php?topic=242962.msg3234742#msg3234742

Okay, everyone is mentioning doing something more complicated than tiers.  The thing is that would complicate matters a lot matter.  As doog mentioned before, the invested amount for each player is really easy to calculate, a recalculation needs to be done only when players invest or divest.  The thing with a non-tier system is that there will be a hell lot more calculating that needs to be done.  And taking the sum of all the invest amount times risk is really hard to do.  It will need to be updated after each bet as each bet loses and gains differently.

That's why tiers is better as it helps simplifies calculations.

I have a compromise to offer.  Maybe you could have 3 tiers (or more).  And players can invest in a combination of tiers.  0.25%, 1%, 5%.  Something like that.  The highest one could be really high.

This is because you can invest in a combination of tiers.  And the calculations wouldn't be extremely difficult as the server can bunch all the low risk accounts together, med, high etc.

I don't have the data, dooglus has, but I would be very interested in the daily wagered amount if we took out all bets over 80BTC.  I would guess it would match those days that nakowa or some of the other high rollers aren't betting - so that's maybe around 5k a day?

To me - 5k a day which works out as around 35% annual return is fine for me.  I don't want more than that and a corresponding higher variance.

The thing is why would it be a 35% annual return?  The return is tied to the amount invested in total.

You could be screwing old investors even more.  So, now you'll be making steady profits but less, so it'll take a while to get return.  But, wait there's more.  Since there is "easy" profit, the amount invested will increase.  And your annual return might go down.  Especially since, this is very liquid investment, if it was very liquid and quite safe then this means that annual return does not need to be very high.

And what happens when investment increases.  Well, the max bet increases too.  So, if having a high max bet means gamblers can profit a lot, and if the invested amount increases.  This means that its almost the same as before.  So, the only solution would be to cap investments.  But that is totally against the idea of just-dice.

[Oleander]

I'm challenged because I don't know how to explain it. I'm trying to say that while the pattern fits and looks random, it is predictably random.

Here's an example of "predictably random":  the decimal expansion of Pi is statistically random (the digits pass every known test for randomness), but Pi is obviously not random.

[willphase]

I'm challenged because I don't know how to explain it. I'm trying to say that while the pattern fits and looks random, it is predictably random.

HMAC is predictable - that's the whole point of a message authentication code, if it was truly random it wouldn't be much use!

However, it appears random (and for all extends and purposes is random) if you don't know the secret and the input changes each time, even by 1 bit.

Will

[geofflosophy]

Okay, everyone is mentioning doing something more complicated than tiers.  The thing is that would complicate matters a lot matter.  As doog mentioned before, the invested amount for each player is really easy to calculate, a recalculation needs to be done only when players invest or divest.  The thing with a non-tier system is that there will be a hell lot more calculating that needs to be done.  And taking the sum of all the invest amount times risk is really hard to do.  It will need to be updated after each bet as each bet loses and gains differently.

That's why tiers is better as it helps simplifies calculations.

I have a compromise to offer.  Maybe you could have 3 tiers (or more).  And players can invest in a combination of tiers.  0.25%, 1%, 5%.  Something like that.  The highest one could be really high.

This is because you can invest in a combination of tiers.  And the calculations wouldn't be extremely difficult as the server can bunch all the low risk accounts together, med, high etc.

I think this would actually be really dope, and very easy to implement. With that said, I'm not convinced that letting users input their own risk level, while more complicated to code, represents that much of an increase in computational difficulty for a computer. But I've mentioned a few times that I'm in favor of multiple investment buckets, if tiers are the difference between a single number denoting acceptable risk on the entire investment and being able to split your investment into higher and lower levels of risk without creating a new account, I would be very happy with that solution.

[chriswen]

Comment on variable house edge.

I think this is a great idea.  Well, considering the current outlook of things (Capped max bet), it seems like we must reach a compromise.  By increasing the max bet you lower variance and at the same time allowing whales to bet more.  As other sites don't offer such high bets, a premium is no big deal.

I'm not sure how you'll be implementing it but I have something in mind.

A tiered system will not be the best as there will be significant changes between tiers.  Its not really the best solution.

A better solution would be doing something like a tiered tax system.  Higher tiers have a higher tax rate but they only need to pay the higher tax rate on the earnings in that tier.  This way, if you bet 0.000001 more btc the house edge isn't doubled.

And if this was implemented in a thoughtful way to decrease variance I think we could be seeing 2% house max bet (well at least 1%).

Also, how are the tiers being decided.  Is it hard tiers (50 btc) or soft tiers (0.25% of house edge).  Or it might be a mixture of both.

Yeah, so I offer some suggestions and I was just wondering how variable house edge would be implemented.  I think it's a great idea to offer investors higher return with not a lot more variance.  And it'll also attract whales with their high roller strategies.  They can't bet this much anywhere else so asking for a premium is okay.

[allover]

I once was an investor of JD (several thousands). When I realized that investing JD is also gambling (with an EV of +1%, yet the variance would hit hard, and turns that 1% into minus, which I proved by actions), I was hesitate about whether I should invest further.

Doog took things a little bit personal. Hunting whales by changing rules (without warning all players and during they are playing) rather than by the result of mathematics is absurd. This is not a protection for investors, rather, it's protection for winning whales from losing back. Thank you Doog.

BTW: As the one who was targeted, I think Doog owes me an apology, directly. A casino shouldn't change the rule without warning players.

However,  I understand. Were I him, I'd be pretty tired.

[chriswen]

I'm challenged because I don't know how to explain it. I'm trying to say that while the pattern fits and looks random, it is predictably random.

HMAC is predictable - that's the whole point of a message authentication code, if it was truly random it wouldn't be much use!

However, it appears random (and for all extends and purposes is random) if you don't know the secret and the input changes each time, even by 1 bit.

Will

Disclaimer: cryptography is not my strong point

So, I don't exactly understand what you're saying.  HMAC is based on hashing.  What you're saying is that all cryptographic hashing just 'appears random', which sounds very low to me.  I thought the randomness of cryptography hashes was quite strong.

Also, isn't the HMAC just doing something to a hash?  So the underlying security of the hash is still there.

[GOB]

A better solution would be doing something like a tiered tax system.  Higher tiers have a higher tax rate but they only need to pay the higher tax rate on the earnings in that tier.  This way, if you bet 0.000001 more btc the house edge isn't doubled.

I have a compromise to offer.  Maybe you could have 3 tiers (or more).  And players can invest in a combination of tiers.  0.25%, 1%, 5%.  Something like that.  The highest one could be really high.

But I've mentioned a few times that I'm in favor of multiple investment buckets, if tiers are the difference between a single number denoting acceptable risk on the entire investment and being able to split your investment into higher and lower levels of risk without creating a new account, I would be very happy with that solution.

Guys, all this talk about tiers and buckets is entirely missing the point, simplicity and beauty of what Dooglus is going to implement.

It's two parts:

A) Having the choice to reduce your Max Profit percentage below the Kelly Criterion optimum of 1% (if you are risk averse and want less variance), or above 1% (to, say, 1.25% or 1.5%) if you are more risk-seeking (you'd be increasing your profits from whales and increasing your chance of busting). Although it'll be tedious to make the changes, this isn't a complicated system to implement. As someone mentioned before in one of the recent posts, he'll have to change from storing your percentage of the invested total on each bet to your percentage of the invested total AND your risk %. Then divide wins/losses accordingly.

B) Allow you to set your total invested amount, but only deposit a fraction of it in Just-Dice, so long as it is more than the max profit you are risking. This sounds risky, but understand that at no point would it be possible to "owe" just-dice money. You'd simply choose an investment of, say, 100 BTC at 1.5% max profit and deposit, say, 10 BTC. Now, for calculations your investment is 100 and your max profit risk on the first roll is 1.5 BTC. If your investment increases, great! no problem. If it drops, also, no problem, because as soon as your coins on deposit aren't enough to cover your max profit risk, you are auto-divested. A HUGE benefit to this is that this reduces CP risk for investors. You could invest 10K btc at 0.5% (max profit = 50 btc), yet only have to trust Doog with a fraction of them (say 500 btc).



tl;dr forget buckets, and tiers. User-selectable risk is what Doog is implementing and it's going to be siiiiiiiiick. Honestly, it will improve the site, not just settle this discussion.

EDIT: Changed percentages above kelly in part A from "2% or 5%" to "1.25% or 1.5%". Apparently, just as kelly maximizes bankroll growth, 2x kelly results in zero expected growth and >2x kelly results in negative bankroll growth. So it probably wouldn't be wise to even have 2% or more as an option.

[Peter R]

A better solution would be doing something like a tiered tax system.  Higher tiers have a higher tax rate but they only need to pay the higher tax rate on the earnings in that tier.  This way, if you bet 0.000001 more btc the house edge isn't doubled.

I have a compromise to offer.  Maybe you could have 3 tiers (or more).  And players can invest in a combination of tiers.  0.25%, 1%, 5%.  Something like that.  The highest one could be really high.

But I've mentioned a few times that I'm in favor of multiple investment buckets, if tiers are the difference between a single number denoting acceptable risk on the entire investment and being able to split your investment into higher and lower levels of risk without creating a new account, I would be very happy with that solution.

Guys, all this talk about tiers and buckets is entirely missing the point, simplicity and beauty of what Dooglus is going to implement.

It's two parts:

A) Having the choice to reduce your Max Profit percentage below the Kelly Criterion optimum of 1% (if you are risk averse and want less variance), or above 1% (to, say, 2% or 5%) if you are more risk-seeking (you'd be increasing your profits from whales and increasing your chance of busting). Although it'll be tedious to make the changes, this isn't a complicated system to implement. As someone mentioned before in one of the recent posts, he'll have to change from storing your percentage of the invested total on each bet to your percentage of the invested total AND your risk %. Then divide wins/losses accordingly.

B) Allow you to set your total invested amount, but only deposit a fraction of it in Just-Dice, so long as it is more than the max profit you are risking. This sounds risky, but understand that at no point would it be possible to "owe" just-dice money. You'd simply choose an investment of, say, 100 BTC at 1.5% max profit and deposit, say, 10 BTC. Now, for calculations your investment is 100 and your max profit risk on the first roll is 1.5 BTC. If your investment increases, great! no problem. If it drops, also, no problem, because as soon as your coins on deposit aren't enough to cover your max profit risk, you are auto-divested. A HUGE benefit to this is that this reduces CP risk for investors. You could invest 10K btc at 0.5% (max profit = 50 btc), yet only have to trust Doog with a fraction of them (say 500 btc).



tl;dr forget buckets, and tiers. User-selectable risk is what Doog is implementing and it's going to be siiiiiiiiick. Honestly, it will improve the site, not just settle this discussion.

+1 GOB

And then dooglus, as site operator, doesn't even have to care what the "optimal % max bet" is.  All he has to worry about is the *user* experience (the gambler not the investor ).  He may want to limit leverage if he finds the max bet in BTC bounces around too violently during whale attacks.

[Peter R]

Thinking more about the two "tuning parameters" GOB just described: deposit reserve ratio, and max profit %.  I am wondering how many degrees of freedom this system actually has.


inputs: (D) deposit amount, (R) deposit reserve ratio, (M) max profit %

outputs: (P) profit, (V) variance of profit, (C) counter-party risk

If I increase D, holding R and M fixed, then P, V and C go up, I think.

If I decrease R, holding D and M fixed, then P and V go up, but C stays fixed.

If I increase M, holding D and R fixed, then P and V go up, but C stays fixed.

How exactly is decreasing R different than increasing M?

[chriswen]

A better solution would be doing something like a tiered tax system.  Higher tiers have a higher tax rate but they only need to pay the higher tax rate on the earnings in that tier.  This way, if you bet 0.000001 more btc the house edge isn't doubled.

I have a compromise to offer.  Maybe you could have 3 tiers (or more).  And players can invest in a combination of tiers.  0.25%, 1%, 5%.  Something like that.  The highest one could be really high.

But I've mentioned a few times that I'm in favor of multiple investment buckets, if tiers are the difference between a single number denoting acceptable risk on the entire investment and being able to split your investment into higher and lower levels of risk without creating a new account, I would be very happy with that solution.

Guys, all this talk about tiers and buckets is entirely missing the point, simplicity and beauty of what Dooglus is going to implement.

It's two parts:

A) Having the choice to reduce your Max Profit percentage below the Kelly Criterion optimum of 1% (if you are risk averse and want less variance), or above 1% (to, say, 2% or 5%) if you are more risk-seeking (you'd be increasing your profits from whales and increasing your chance of busting). Although it'll be tedious to make the changes, this isn't a complicated system to implement. As someone mentioned before in one of the recent posts, he'll have to change from storing your percentage of the invested total on each bet to your percentage of the invested total AND your risk %. Then divide wins/losses accordingly.

B) Allow you to set your total invested amount, but only deposit a fraction of it in Just-Dice, so long as it is more than the max profit you are risking. This sounds risky, but understand that at no point would it be possible to "owe" just-dice money. You'd simply choose an investment of, say, 100 BTC at 1.5% max profit and deposit, say, 10 BTC. Now, for calculations your investment is 100 and your max profit risk on the first roll is 1.5 BTC. If your investment increases, great! no problem. If it drops, also, no problem, because as soon as your coins on deposit aren't enough to cover your max profit risk, you are auto-divested. A HUGE benefit to this is that this reduces CP risk for investors. You could invest 10K btc at 0.5% (max profit = 50 btc), yet only have to trust Doog with a fraction of them (say 500 btc).



tl;dr forget buckets, and tiers. User-selectable risk is what Doog is implementing and it's going to be siiiiiiiiick. Honestly, it will improve the site, not just settle this discussion.

Okay, I see dooglus is planning on implementing some great stuff.

But, I think some thought should be put into part b.  To think about the consequences.  Part b doesn't only reduce cp risk.  It also acts as a stop loss.  But I can see bad things happening with it.  First, there should be a mandated down payment, maybe 20% for now.

So, this is like day trading but on drugs.  Lets say the site starts losing money, some people get auto divested.  The house bet might decrease significantly.  So, the people who are still invested gets a bigger portion of the pot.  It just matters what the down payment percentage is and what percent of people have 100% down payment.  I can just see the site investment vaporizing.

You're really deceiving yourself when you call this for reducing cp risk.  It's actually for leverage.  It's okay but make it clear, that the huge benefit is that people can leverage there bitcoins.  (But, its gonna be weird when the site goes on a losing streak)

[chriswen]

Thinking more about the two "tuning parameters" GOB just described: deposit reserve ratio, and max profit %.  I am wondering how many degrees of freedom this system actually has.


inputs: (D) deposit amount, (R) deposit reserve ratio, (M) max profit %

outputs: (P) profit, (V) variance of profit, (C) counter-party risk

If I increase D, holding R and M fixed, then P, V and C go up, I think.

If I decrease R, holding D and M fixed, then P and V go up, but C stays fixed.

If I increase M, holding D and R fixed, then P and V go up, but C stays fixed.

How exactly is decreasing R different than increasing M?

What are you defining D as?  Deposit reserve or deposit amount?

[GOB]

Guys, all this talk about tiers and buckets is entirely missing the point, simplicity and beauty of what Dooglus is going to implement.

It's two parts:

A) Having the choice to reduce your Max Profit percentage below the Kelly Criterion optimum of 1% (if you are risk averse and want less variance), or above 1% (to, say, 2% or 5%) if you are more risk-seeking (you'd be increasing your profits from whales and increasing your chance of busting). Although it'll be tedious to make the changes, this isn't a complicated system to implement. As someone mentioned before in one of the recent posts, he'll have to change from storing your percentage of the invested total on each bet to your percentage of the invested total AND your risk %. Then divide wins/losses accordingly.

B) Allow you to set your total invested amount, but only deposit a fraction of it in Just-Dice, so long as it is more than the max profit you are risking. This sounds risky, but understand that at no point would it be possible to "owe" just-dice money. You'd simply choose an investment of, say, 100 BTC at 1.5% max profit and deposit, say, 10 BTC. Now, for calculations your investment is 100 and your max profit risk on the first roll is 1.5 BTC. If your investment increases, great! no problem. If it drops, also, no problem, because as soon as your coins on deposit aren't enough to cover your max profit risk, you are auto-divested. A HUGE benefit to this is that this reduces CP risk for investors. You could invest 10K btc at 0.5% (max profit = 50 btc), yet only have to trust Doog with a fraction of them (say 500 btc).



tl;dr forget buckets, and tiers. User-selectable risk is what Doog is implementing and it's going to be siiiiiiiiick. Honestly, it will improve the site, not just settle this discussion.

I need to make a correction: In part A, I said you could set your max profit % to "say, 2% or 5%". However, after reading more about the kelly criterion, just as kelly maximizes bankroll growth, 2x kelly results in zero expected growth and >2x kelly results in negative bankroll growth. So it probably wouldn't be wise to even have 2% or more as an option.

[GOB]

tl;dr forget buckets, and tiers. User-selectable risk is what Doog is implementing and it's going to be siiiiiiiiick. Honestly, it will improve the site, not just settle this discussion.

+1 GOB

And then dooglus, as site operator, doesn't even have to care what the "optimal % max bet" is.  All he has to worry about is the *user* experience (the gambler not the investor ). 

Thanks.

As for Doog, it's more complicated than that! He both has to worry about the user experience for both user and investor. Assuming he stays divested, his income depends on his commissions on investor earnings. That requires both more investment and more gamblers. Plus the huge max profits and crazy whale stories are what will keep driving traffic to the site.

[GOB]

A better solution would be doing something like a tiered tax system.  Higher tiers have a higher tax rate but they only need to pay the higher tax rate on the earnings in that tier.  This way, if you bet 0.000001 more btc the house edge isn't doubled.

I have a compromise to offer.  Maybe you could have 3 tiers (or more).  And players can invest in a combination of tiers.  0.25%, 1%, 5%.  Something like that.  The highest one could be really high.

But I've mentioned a few times that I'm in favor of multiple investment buckets, if tiers are the difference between a single number denoting acceptable risk on the entire investment and being able to split your investment into higher and lower levels of risk without creating a new account, I would be very happy with that solution.

Guys, all this talk about tiers and buckets is entirely missing the point, simplicity and beauty of what Dooglus is going to implement.

It's two parts:

A) Having the choice to reduce your Max Profit percentage below the Kelly Criterion optimum of 1% (if you are risk averse and want less variance), or above 1% (to, say, 2% or 5%) if you are more risk-seeking (you'd be increasing your profits from whales and increasing your chance of busting). Although it'll be tedious to make the changes, this isn't a complicated system to implement. As someone mentioned before in one of the recent posts, he'll have to change from storing your percentage of the invested total on each bet to your percentage of the invested total AND your risk %. Then divide wins/losses accordingly.

B) Allow you to set your total invested amount, but only deposit a fraction of it in Just-Dice, so long as it is more than the max profit you are risking. This sounds risky, but understand that at no point would it be possible to "owe" just-dice money. You'd simply choose an investment of, say, 100 BTC at 1.5% max profit and deposit, say, 10 BTC. Now, for calculations your investment is 100 and your max profit risk on the first roll is 1.5 BTC. If your investment increases, great! no problem. If it drops, also, no problem, because as soon as your coins on deposit aren't enough to cover your max profit risk, you are auto-divested. A HUGE benefit to this is that this reduces CP risk for investors. You could invest 10K btc at 0.5% (max profit = 50 btc), yet only have to trust Doog with a fraction of them (say 500 btc).



tl;dr forget buckets, and tiers. User-selectable risk is what Doog is implementing and it's going to be siiiiiiiiick. Honestly, it will improve the site, not just settle this discussion.

Okay, I see dooglus is planning on implementing some great stuff.

But, I think some thought should be put into part b.  To think about the consequences.  Part b doesn't only reduce cp risk.  It also acts as a stop loss.  But I can see bad things happening with it.  First, there should be a mandated down payment, maybe 20% for now.

So, this is like day trading but on drugs.  Lets say the site starts losing money, some people get auto divested.  The house bet might decrease significantly.  So, the people who are still invested gets a bigger portion of the pot.  It just matters what the down payment percentage is and what percent of people have 100% down payment.  I can just see the site investment vaporizing.

You're really deceiving yourself when you call this for reducing cp risk.  It's actually for leverage.  It's okay but make it clear, that the huge benefit is that people can leverage there bitcoins.  (But, its gonna be weird when the site goes on a losing streak)

Yeah he is!

Part b doesn't only reduce cp risk.  It also acts as a stop loss.

That is a great way to put it! It is a stop-loss. This makes me think it's a feature not a bug

But I do understand your concern that if a whale were to suddenly go on a win streak, a bunch of divestors could suddenly be auto divested and investment could fall dramatically and quickly. Though when that happens, that provides an opportunity for other investors to up their stakes or jump in to get a higher percentage of the investment pot. That will be a tremendous opportunity. There is a lot of spectating here, so I suspect people will be ready to jump in. Also, after a couple times of getting auto-divested, people will tend to want to leave enough to not have to deal with it all the time, if they plan on investing long term.

However, I don't disagree that Doog could set a minimum down payment of 10% or 20% to start (or a maximum leverage, if you will). It could be gradually reduced if warranted, or increased it necessary.

[Peter R]

Thinking more about the two "tuning parameters" GOB just described: deposit reserve ratio, and max profit %.  I am wondering how many degrees of freedom this system actually has.


inputs: (D) deposit amount, (R) deposit reserve ratio, (M) max profit %

outputs: (P) profit, (V) variance of profit, (C) counter-party risk

If I increase D, holding R and M fixed, then P, V and C go up, I think.

If I decrease R, holding D and M fixed, then P and V go up, but C stays fixed.

If I increase M, holding D and R fixed, then P and V go up, but C stays fixed.

How exactly is decreasing R different than increasing M?

What are you defining D as?  Deposit reserve or deposit amount?

I was defining D as the bitcoins you sign over to JD.  I think this is opposite to how Doog was looking at the problem.