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Author Topic: Just-Dice.com : Invest in 1% House Edge Dice Game  (Read 435290 times)
Eric Muyser
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June 27, 2013, 05:51:02 PM
 #101

I'd also recommend increasing your cut - somewhere between 5% and 25% seems the right sort of area to me.  As someone likely to use it I WANT you to be making significant profit.  An operator/issuer making significant profit is one of the single biggest factors reducing likelihood of scamming - if you can clearly make decent profit running it then there's a lot less reason for you to even consider stealing the bank.  Personally I stay well away from anything where I can't see how the operator is making a good return.
+1


+1

As for increasing my cut, I made it low to attract investors.  If you think it's too low, such that it scares investors (he's not making enough so the business model must be "steal all the coins") then I can increase it (with 7 days' notice, as promised on the site).  I'm currently around 18% of the site's bankroll, and that's making me more than enough.

If lots of you would rather see me take a bigger percentage, then I'm game.  Smiley  I don't doing so makes me any more or less likely to "steal all the coins", but if it makes things look better to new investors then I'll do it.

I'm down for at least 5-10%. I think very few wouldn't be OK with 5% and they're probably scrubs. I think 10% is a good spot, but up to 20% is fine for me personally.

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dooglus (OP)
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June 27, 2013, 05:57:17 PM
 #102

Planning on a GPG-signed investor contract ?
That would be nice, you're on OTC, you have a key, use it, that's what it's for.

I was just going to point you to my previous answer to that question, but I can't find it!

I'm sure I replied to you asking on the other thread, saying that I'm happy to sign a reasonable contract, but don't have the skills required to draft it, or the time to contract someone qualified to do so.  But I don't see the post anywhere, so I guess I clicked 'Post', it timed out, and I didn't notice.

Can you (or anyone) suggest something simple and reasonable that you would like me to GPG sign?

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   1% House Edge
trout
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June 27, 2013, 06:23:27 PM
 #103


Good points, and I will get to implementing those features, but I don't think they're necessary before I allow >1% risk.
Sure. At 1% those features are totally unnecessary.


It's possible for the house to have long losing runs, especially when most players make tiny bets.  The few who make the big bets pretty much affect the house's profitability.  In a long enough period I would expect the house to profit.  Wouldn't you?

I would not,  at >2% investment.  Small bets are not what I was having in mind.
If you only consider *largest* bets, you, as a house, will be losing money in the long run
if you allow bets over 2%.

This may seem paradoxical - the odds are in your favour;  your expected return grows exponentially, yet your actual capital decreases with certainty.
The effect is obvious if you consider a simple game: 75% chance to double your stake,  and you stake
all capital every time (corresponding to 100% investment, the largest bet every time, 50% house edge).  After N plays, your expected capital is skyrocketing: (3/2)^N  (assuming you start with 1), yet
with overwhelming probability (1- (3/4)^N) you are ruined- your capital is 0.

And this is not an artefact of 100% investment.  Consider 50% investment, largest bets: when you lose your
capital is divided by 2, but you win it's multiplied by 1.5.  Make some imaginary plays (at a small, ~1% house edge) and you see how fast it decreases. But it does increase at 50% house edge.

The optimal investment percentage on largest bets, at house edge 1%,  is 1%.  You are not losing (as a house) when investing at under 2%.  The optimal overall (all size bets) of course depends on the distribution of the bets. Speaking of which, it'd be interesting to look at the empirical distribution of bet size so far.

I can explain how I got 2% and 1%, but I better say where I got them from: from this paper.
Yes, this is a mathematical paper, but  it's very readable (and you can ignore the information-theoretic interpretations if they don't make sense to you).

Edit: as has been pointed out by others before, this does not make the feature of higher investments percents useless. You can use it but you have to manage your investment manually, alimenting and withdrawing in order to maintain a safe percent overall. Hence my request for those features.
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June 27, 2013, 06:44:28 PM
 #104

I'm by no means convinced allowing investors to take on more than 1% risk is a good thing.

The problem I see is that if they can take on significant risk per bet then it removes all incentive for anyone to actually play the game.  Why would someone take on the role of player (with the odds against them) if they can expose their capital rapidly but with the odds in their favour?

Investment MUST be slow and steady profit - to force gamblers into taking on the player role and accepting the bad odds.
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June 27, 2013, 07:33:35 PM
Last edit: June 27, 2013, 07:57:02 PM by Entropy-uc
 #105


(like how AM IPO holders have an enormous advantage due to 35x rise in share price making a larger barrier to entry for new investors on an absolute basis)

This statement is just another way to say "AM is a bubble and the shares aren't worth what they go for". That this realization is slowly percolating even through the investors that'd be much better served thus should be perhaps a little worrying

You ought to create a new thread and back up that story.

The reality is:
Friedcat offered a fair deal in his IPO, worked extremely hard, and through a combination of good fortune, incompetence on the part of his competition, and shrewd decision making has increased the valuation of his company.

Just mining income alone supports a 35% yield at current prices.  That's not a bubble.

Will he hold his market share in the long term?  That is hard to say.  But I'd give it better odds than seeing any of the Keystone cops competing with him take the lead.

And just to be on topic:

Dooglus good luck to you with this venture!  I hope it works out, and I think 1% is far to low a commission for operation costs.
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June 27, 2013, 07:35:50 PM
 #106

I'm by no means convinced allowing investors to take on more than 1% risk is a good thing.

The problem I see is that if they can take on significant risk per bet then it removes all incentive for anyone to actually play the game.  Why would someone take on the role of player (with the odds against them) if they can expose their capital rapidly but with the odds in their favour?

Investment MUST be slow and steady profit - to force gamblers into taking on the player role and accepting the bad odds.
I agree almost completely. I was kinda on the fence about increasing risk on investing, and in any case my thoughts were that 5% was a rather high ceiling, but I think you just clarified my gut instinct rather well. There is necessarily a distinction between investors and bettors, and I think 5% is too much. What is the actual delineating line? I dunno. Perhaps more than 1%, I'm open to that. But too much may encourage losing the bankroll.

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June 27, 2013, 07:42:23 PM
 #107

(like how AM IPO holders have an enormous advantage due to 35x rise in share price making a larger barrier to entry for new investors on an absolute basis)

This statement is just another way to say "AM is a bubble and the shares aren't worth what they go for". That this realization is slowly percolating even through the investors that'd be much better served thus should be perhaps a little worrying
What the hell are you talking about? This is a clear-cut, textbook example of a strawman failure of logic. I in no way implied anything of the sort. The fact that you think it's even remotely logical to infer what you did would frankly be hilarious if it weren't so abjectly sad.

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June 27, 2013, 07:59:03 PM
 #108

I'm by no means convinced allowing investors to take on more than 1% risk is a good thing.

The problem I see is that if they can take on significant risk per bet then it removes all incentive for anyone to actually play the game.  Why would someone take on the role of player (with the odds against them) if they can expose their capital rapidly but with the odds in their favour?

Investment MUST be slow and steady profit - to force gamblers into taking on the player role and accepting the bad odds.

This was discussed in the local chat. The situation where MP risks 1k BTC confronting the players + 99k BTC on CP for a total of 100k at 1% is overall worse (for everyone) than the situation where MP risks 1k BTC confronting the players at 100% while holding on to the rest in safety.

The alternative implementation where this is only allowed to large investors is probably safer for the minnows, but it will probably be strongly protested as "unfair" and "fiat-like". The implementation where any minnow is allowed to act as a big fish with a stern warning is probably more in the spirit of Bitcoin. There will certainly be nuts risking 100% of their balance at 100%, but they won't likely last.

In general "forcing" and derived arguments don't mix with Bitcoin. For that matter, investment will be profit no matter what, but it won't be steady. The site went from 250 to 80 to 330 back down to 200 within the space of about a day, putting plenty of investors at least temporarily in the red at least twice in that time. It will probably continue going under and over its EV back and forth forever.

If you only consider *largest* bets, you, as a house, will be losing money in the long run
if you allow bets over 2%.

Your modeling is completely broken in that it imagines capital available as a fixed numeric value. This is now how it works (but your edit saved you from much stronger words).

Capital availability is limited by the cost of opportunity and the profile of risks involved. With the current arrangement the dampening derived from dooglus' own CP risk is the largest factor in that equation. This has to be diminished so as to allow the site to grow. In another perspective, the site is only realizing a fraction of the investment it could be realizing currently, which is not so different from an engine only burning part of the fuel it's being fed: it won't go quite as far.

In any case removing the arbitrary limit actually protects the house, in that it allows it to raise maximums past where even the larger whales can afford to play down towards the maximum. Currently the house is running with a 1/100 dampener, and MP (among others) leeched it pretty seriously - it's easy to do if you can afford to risk the sort of BTC it takes to hammer the max out of it.

Planning on a GPG-signed investor contract ?
That would be nice, you're on OTC, you have a key, use it, that's what it's for.

I was just going to point you to my previous answer to that question, but I can't find it!

I'm sure I replied to you asking on the other thread, saying that I'm happy to sign a reasonable contract, but don't have the skills required to draft it, or the time to contract someone qualified to do so.  But I don't see the post anywhere, so I guess I clicked 'Post', it timed out, and I didn't notice.

Can you (or anyone) suggest something simple and reasonable that you would like me to GPG sign?

A strange case of feedback at work here: once you implement the variable %s this isn't particularly needed as the investors hold most of their balance in their own hands anyway, and the economic interests are so aligned to keep everyone honest, much in the way the cold war didn't culminate in a nuclear winter for other reasons than because all parties gpg-signed contracts. For the interim until you implement variable %s it doesn't seem this will help enough to justify the hassle.

That aside, once you have it pretty clear in your head enough to be able to make absolute, definitive statements as to your projected handling of the site it's probably a good idea to draft, review and sign a declaratory statement of some sort.

(like how AM IPO holders have an enormous advantage due to 35x rise in share price making a larger barrier to entry for new investors on an absolute basis)

This statement is just another way to say "AM is a bubble and the shares aren't worth what they go for". That this realization is slowly percolating even through the investors that'd be much better served thus should be perhaps a little worrying
What the hell are you talking about? This is a clear-cut, textbook example of a strawman failure of logic. I in no way implied anything of the sort. The fact that you think it's even remotely logical to infer what you did would frankly be hilarious if it weren't so abjectly sad.

Let's try and think together.

If the actual value of AM is above its trading price, then the original buyers hold no advantage over later buyers. Stating that the price going up constitutes a "barrier to entry" is exactly equivalent to stating that the current price exceeds the fair value, as that excess and that excess only could in fact be constituting a barrier to entry. This is all.

Perhaps a revisiting of what "strawman fallacy" means is in order, seeing how you fail to correctly identify it in the field.

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June 27, 2013, 08:05:03 PM
 #109

I'm probably not 100% understanding how this works, but is it true that if the rate of people investing outpaces the amount gambled, the returns will dilute? If so, would it make sense to have some sort of on-the-fly tracking/scaling of a total allowable house investment base on a windowed rate of house gain? Something to keep a fix on the estimated rate of return. Just like there's a max-bet determined by the pool size, this would be keeping the other side of the coin intact.
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June 27, 2013, 08:06:43 PM
 #110

I'm by no means convinced allowing investors to take on more than 1% risk is a good thing.

The problem I see is that if they can take on significant risk per bet then it removes all incentive for anyone to actually play the game.  Why would someone take on the role of player (with the odds against them) if they can expose their capital rapidly but with the odds in their favour?

Investment MUST be slow and steady profit - to force gamblers into taking on the player role and accepting the bad odds.

This was discussed in the local chat. The situation where MP risks 1k BTC confronting the players + 99k BTC on CP for a total of 100k at 1% is overall worse (for everyone) than the situation where MP risks 1k BTC confronting the players at 100% while holding on to the rest in safety.

The alternative implementation where this is only allowed to large investors is probably safer for the minnows, but it will probably be strongly protested as "unfair" and "fiat-like". The implementation where any minnow is allowed to act as a big fish with a stern warning is probably more in the spirit of Bitcoin. There will certainly be nuts risking 100% of their balance at 100%, but they won't likely last.

I considered the other implementation but rejected it as you'd end up with the perverse situation of players running martingales on the investment side where they actually work.  That's the problem with allowing minnows to act like big fish - you can't allow them to risk ANY portion of their balance without also allowing them to change it frequently to make it +EV.

I can't see a 'fair' way to allow different degrees of risk whilst preventing people using it to gamble (and in the process removing benefit from all other investors as well as allowing them to sit at the wrong side of the table for what they're doing).
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June 27, 2013, 08:14:01 PM
 #111

I'm probably not 100% understanding how this works, but is it true that if the rate of people investing outpaces the amount gambled, the returns will dilute? If so, would it make sense to have some sort of on-the-fly tracking/scaling of a total allowable house investment base on a windowed rate of house gain? Something to keep a fix on the estimated rate of return. Just like there's a max-bet determined by the pool size, this would be keeping the other side of the coin intact.

The market sorts that itself.  If ROI falls then at some point it'll drop below some people's threshold and they'll pull out their cash.  Maximising capital is in dooglus' best interest - as it also maximises possible revenue.  What you propose also potentially loses gambling customers - as when they finish a session of play and want to sling their BR into investment mode until the next day they sometimes won't be able to.  And that then encourages them to withdraw - adding a delay/barrier against them resuming play later.

dooglus should just focus on getting as many people gambling as possible - and let investment sort itself out.  If capital becomes too excessive then the easiest way to handle it is increase his own cut - if he's getting far more capital than he needs then clearly he isn't taking enough.
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June 27, 2013, 08:18:31 PM
 #112

I considered the other implementation but rejected it as you'd end up with the perverse situation of players running martingales on the investment side where they actually work.  That's the problem with allowing minnows to act like big fish - you can't allow them to risk ANY portion of their balance without also allowing them to change it frequently to make it +EV.

I can't see a 'fair' way to allow different degrees of risk whilst preventing people using it to gamble (and in the process removing benefit from all other investors as well as allowing them to sit at the wrong side of the table for what they're doing).

Do go into detail as to this actually working Martingale, as I suspect it's based on a broken model.

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June 27, 2013, 08:25:02 PM
 #113

(like how AM IPO holders have an enormous advantage due to 35x rise in share price making a larger barrier to entry for new investors on an absolute basis)

This statement is just another way to say "AM is a bubble and the shares aren't worth what they go for". That this realization is slowly percolating even through the investors that'd be much better served thus should be perhaps a little worrying
What the hell are you talking about? This is a clear-cut, textbook example of a strawman failure of logic. I in no way implied anything of the sort. The fact that you think it's even remotely logical to infer what you did would frankly be hilarious if it weren't so abjectly sad.
Let's try and think together.

If the actual value of AM is above its trading price, then the original buyers hold no advantage over later buyers. Stating that the price going up constitutes a "barrier to entry" is exactly equivalent to stating that the current price exceeds the fair value, as that excess and that excess only could in fact be constituting a barrier to entry. This is all.

Perhaps a revisiting of what "strawman fallacy" means is in order, seeing how you fail to correctly identify it in the field.
Clearly, you don't understand simple logical constructs. Well, I'll give you (another) benefit of the doubt, and limit that to the possibility that you simply don't understand the idea that arguing against a statement not actually made is a fundamental failure of logic. I made a statement, you incorrectly pretended it was a different statement, then you made an improper argument based on your inference (and I'm being generous here by calling it an inference. Seeing a small portion of your posting history, it was likely an outright but indefensible attempt to appear clever while also trying to direct attention to your alter ego dear leader.) Repeating the argument which was based on the failure of logic, such as in the quote above, could be taken as an indication that you concede the failure of logic but are trying to divert attention again from the failure by simply repeating the same failed argument again (which is, in itself, an informal fallacy.)

The "bubble argument" you are improperly making may even be defensible (although I don't at all think it's true), but the method you're using here to try and make it is laughably bad. Use real logic, you might even win an argument from time to time.

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June 27, 2013, 08:32:25 PM
 #114

I considered the other implementation but rejected it as you'd end up with the perverse situation of players running martingales on the investment side where they actually work.  That's the problem with allowing minnows to act like big fish - you can't allow them to risk ANY portion of their balance without also allowing them to change it frequently to make it +EV.

I can't see a 'fair' way to allow different degrees of risk whilst preventing people using it to gamble (and in the process removing benefit from all other investors as well as allowing them to sit at the wrong side of the table for what they're doing).

Do go into detail as to this actually working Martingale, as I suspect it's based on a broken model.

The idea probably goes like this :

Hold the majority of coins in balance.  Invest epsilon at 100% risk, then 2 epsilon, 4 e, etc if you lose.

HOWEVER, >99.999% of bets on the site are not Max Profit bets.  Thus, your investment would not be getting fully at risk each time.  Rather, some very small fraction of your epsilon would, except in very rare max bet events.  Thus, it would not function as a 'house-advantaged martingale'.  Rather it would function as you investing epsilon, and getting 100x * 1% edge * epsilon / house capital = epsilon / house capital returns, rather than 1% * your capitial / house capital = 1% your capital returns.

I am 90% confident that just investing your whole stack at some capital at risk multiplier of say 5x will outperform any house-edge martingale strat.

-Bug
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June 27, 2013, 08:44:07 PM
 #115

stuff

The only way out for you is to show how you construct that mental "barrier to entry" so that it's not what I say it is. Go ahead. All the rest is really a waste of my time, which is valuable.

Your time is NOT comparably valuable, for the record, so before you shit all over your april2013noobface again, read a lot more of my posting history than what you've tried so far. Starting perhaps with April 2012.

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June 27, 2013, 09:02:58 PM
 #116

I considered the other implementation but rejected it as you'd end up with the perverse situation of players running martingales on the investment side where they actually work.  That's the problem with allowing minnows to act like big fish - you can't allow them to risk ANY portion of their balance without also allowing them to change it frequently to make it +EV.

I can't see a 'fair' way to allow different degrees of risk whilst preventing people using it to gamble (and in the process removing benefit from all other investors as well as allowing them to sit at the wrong side of the table for what they're doing).

Do go into detail as to this actually working Martingale, as I suspect it's based on a broken model.

The idea probably goes like this :

Hold the majority of coins in balance.  Invest epsilon at 100% risk, then 2 epsilon, 4 e, etc if you lose.

HOWEVER, >99.999% of bets on the site are not Max Profit bets.  Thus, your investment would not be getting fully at risk each time.  Rather, some very small fraction of your epsilon would, except in very rare max bet events.  Thus, it would not function as a 'house-advantaged martingale'.  Rather it would function as you investing epsilon, and getting 100x * 1% edge * epsilon / house capital = epsilon / house capital returns, rather than 1% * your capitial / house capital = 1% your capital returns.

I am 90% confident that just investing your whole stack at some capital at risk multiplier of say 5x will outperform any house-edge martingale strat.

-Bug

There's two basic models to use for allowing increased risk:

1.  The one you describe - where those willing to risk over 1% only get 'extra' action on bets exceeding 1% of all capital.
2.  Allocating ALL bets based on ALL risked capital - so those who risk more get a bigger slice all the time.

You MAY be correct about risking all at 5x outperforming a martingale but it IS the case that there's differences between risking 100% of BR at 5x and risking 5% of BR at 100x.  The detail of the difference varies depending on which model you use - certainly in case 1. my instinct is that risking 100% at 5x is far superior due to picking up 20x as much of smaller bets - though you do then stand the risk of losing the lot over a fairly short series of max bets (though for that to be a real risk it involves an idiot gambling on the horribly priced bets where they're odds-on to win but pay through the nose for the privilege - at the 98% level the house edge is effectively 50% : you only make half the profit on winning bets that you would on a fair bet).
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June 27, 2013, 09:03:37 PM
 #117

stuff

The only way out for you is to show how you construct that mental "barrier to entry" so that it's not what I say it is. Go ahead. All the rest is really a waste of my time, which is valuable.

Your time is NOT comparably valuable, for the record, so before you shit all over your april2013noobface again, read a lot more of my posting history than what you've tried so far. Starting perhaps with April 2012.
Barrier to entry... Barrier to Entry... Im getting hypnotised?


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June 27, 2013, 10:13:22 PM
 #118

I considered the other implementation but rejected it as you'd end up with the perverse situation of players running martingales on the investment side where they actually work.  That's the problem with allowing minnows to act like big fish - you can't allow them to risk ANY portion of their balance without also allowing them to change it frequently to make it +EV.

I can't see a 'fair' way to allow different degrees of risk whilst preventing people using it to gamble (and in the process removing benefit from all other investors as well as allowing them to sit at the wrong side of the table for what they're doing).

Do go into detail as to this actually working Martingale, as I suspect it's based on a broken model.

The idea probably goes like this :

Hold the majority of coins in balance.  Invest epsilon at 100% risk, then 2 epsilon, 4 e, etc if you lose.

HOWEVER, >99.999% of bets on the site are not Max Profit bets.  Thus, your investment would not be getting fully at risk each time.  Rather, some very small fraction of your epsilon would, except in very rare max bet events.  Thus, it would not function as a 'house-advantaged martingale'.  Rather it would function as you investing epsilon, and getting 100x * 1% edge * epsilon / house capital = epsilon / house capital returns, rather than 1% * your capitial / house capital = 1% your capital returns.

I am 90% confident that just investing your whole stack at some capital at risk multiplier of say 5x will outperform any house-edge martingale strat.

-Bug

There's two basic models to use for allowing increased risk:

1.  The one you describe - where those willing to risk over 1% only get 'extra' action on bets exceeding 1% of all capital.
2.  Allocating ALL bets based on ALL risked capital - so those who risk more get a bigger slice all the time.



Perhaps I was not clear. I am assuming model 2. 

Quote
You MAY be correct about risking all at 5x outperforming a martingale but it IS the case that there's differences between risking 100% of BR at 5x and risking 5% of BR at 100x.  The detail of the difference varies depending on which model you use - certainly in case 1. my instinct is that risking 100% at 5x is far superior due to picking up 20x as much of smaller bets - though you do then stand the risk of losing the lot over a fairly short series of max bets (though for that to be a real risk it involves an idiot gambling on the horribly priced bets where they're odds-on to win but pay through the nose for the privilege - at the 98% level the house edge is effectively 50% : you only make half the profit on winning bets that you would on a fair bet).


The issue here is that you will rarely get close to even 10% action on your invested coins, even at 100% risk level.  If selectable risk % is implemented, max bet will go to 1,000BTC.  Mean bet size is currently .0035 BTC. So even at 100% risk, only a miniscule amount of your investment will be at risk.

The goal is to maximize TOTAL exposure relative to TOTAL house BR on each bet with minimal risk of ruin. For the first bet, 100% of BR at 5% risk gets you the exact same amount of action as 5% of BR at 100% risk using model 2.  There are some interesting differences in variance after bet #1 though.  One problem I see is that 5% BR at 100% risk will likely blow that investment portion in a large fraction of max bet events, forcing a manual reinvestment at stochastically determined timepoints. Which would be a PITA.

I'd be happy to continue this discussion in a more private venue.  Tipping off people to superior risk and coin-management approaches seems self-defeating.


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June 27, 2013, 10:34:28 PM
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The issue here is that you will rarely get close to even 10% action on your invested coins, even at 100% risk level.  If selectable risk % is implemented, max bet will go to 1,000BTC.  Mean bet size is currently .0035 BTC. So even at 100% risk, only a miniscule amount of your investment will be at risk.

The goal is to maximize TOTAL exposure relative to TOTAL house BR on each bet with minimal risk of ruin. For the first bet, 100% of BR at 5% risk gets you the exact same amount of action as 5% of BR at 100% risk using model 2.  There are some interesting differences in variance after bet #1 though.  One problem I see is that 5% BR at 100% risk will likely blow that investment portion in a large fraction of max bet events, forcing a manual reinvestment at stochastically determined timepoints. Which would be a PITA.

I'd be happy to continue this discussion in a more private venue.  Tipping off people to superior risk and coin-management approaches seems self-defeating.

Looks like I need to read up on max bet - I'd assumed max bet varied based on the bet so as to be whatever the maximum was that would incur loss to the house of 1% of capital.  From what you're saying it's a fixed amount regardless of which bet is chosen (so X BTC whether they go for a 1 in a million shot or a a 98% shot).  I'd assumed the main exposure would be on people gambling the max they could on the most extreme odds bets.    So if there was 100k of capital (and 1% risk exposure) then 1 BTC would be the max bet with a 1/1000 chance of winning and .001 BTC the max bet on the 1 million to 1 shot.  Mean bet size doesn't mean much (in terms of exposure) without accounting for the odds at which the bets occurred.

And yeah - little point discussing details.  Personally I'd like a very complicated system as the more options there are the more advantage there is to be gained.
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June 27, 2013, 10:42:36 PM
 #120

Looks like I need to read up on max bet - I'd assumed max bet varied based on the bet so as to be whatever the maximum was that would incur loss to the house of 1% of capital.  From what you're saying it's a fixed amount regardless of which bet is chosen (so X BTC whether they go for a 1 in a million shot or a a 98% shot).  I'd assumed the main exposure would be on people gambling the max they could on the most extreme odds bets.

Assuming is a much worse strategy than actually dtr.

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