Just-Dice.com : Invest in 1% House Edge Dice Game - page 68.

oda.krell

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Activity: 1470

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Quote from: dooglus on November 24, 2013, 11:48:03 PM

Quote from: oda.krell on November 24, 2013, 09:18:41 PM

Umm... you're right in the first part, but to the last paragraph I could add: given any fully specified Martingale (odds, betting size progression, ending conditions), I can construct an equivalent single bet strategy. The only reason to employ a Martingale over a single bet strategy is that the former seems easier to risk-manage intuitively for the human mind.

I disagree, but will allow you to prove me wrong...

Suppose I have 127 BTC and want 128. I propose betting 1 BTC at 49.5% (2x payout). If it wins, stop, else double and repeat until it wins. So bet:

1, 2, 4, 8, 16, 32, 64

until one of them wins. If none wins, I've lost all 127 BTC. If any wins, I've got the 128 BTC I wanted.

This strategy will work so long as any one of the maximum of 7 bets wins. ie. unless all 7 lose. The probability of all 7 losing is 0.505^7 = 0.008376, so I have a 100 * (1 - 0.008376) = 99.1624% chance of success.

It's pretty likely that I'll end up betting less than the full 127 BTC. My expected total stake is less than 127. So my expected loss is less than 1.27 BTC.

What's your equivalent single bet strategy? How much does it expect to risk? How much does it expect to lose?

Jup. You're right. The equivalence only holds for betting without an edge. If there's an edge against the player, Martingale is slightly more favourable than a single bet with equal profit.

nicolaennio

member

Activity: 99

Merit: 10

Quote from: dooglus on November 24, 2013, 02:30:33 PM

Quote from: nicolaennio on November 24, 2013, 09:43:12 AM

You can make the following reasoning when you see a martingale that will show you that it is a gambler's fallacy:

- A martingale is a strategy with low probability (let's say it is 0.001%) of busting
- If you have two strategies with the same probability of busting, you should choose the one which plays less times, because the less you interact with the adversarial edge, the better
- You can always play the vanilla strategy of betting all your money at 99.999%.
- Thus the vanilla strategy must be better than the martingale

A martingale is just a way to hide a bad way to play with a low probability of busting strategy

This again?

Your reasoning is faulty, leading you to an incorrect conclusion.

The part where you went wrong is "choose the one which plays less times, because the less you interact with the adversarial edge, the better". It's not the number of bets that determines your expected profit; it's the amount you risk. If you risk less, you expect to lose less. A carefully planned martingale progression can cause you to expect to risk less and so lose less than a single large bet. We've gone over this many times before both on the forum and in the on-site chat.

The correct conclusion is that any single large bet can be replaced by a series of smaller bets which achieve the same return as the large bet but with a better chance of success.

You are actually right, I did not see the previous discussions and I didn't realize that the risk is related to the amount of bet money rather than number of times to bet.

Thank you for the patience of explaining this again :-)

fluidjax

hero member

Activity: 750

Merit: 601

Quote from: dooglus on November 24, 2013, 09:03:18 PM

I've never gone to great lengths to hide who I am but I do try to keep my precise whereabouts a secret, for my own personal safety, and for the safety of the coins in cold storage.

Some investors have said before that they would feel safer if my location was public knowledge, but I don't think they've thought that through, because:

a) if everyone knows where I am then it's easier to rob me, and
b) if I was going to steal the coins, I'm sure I would move to a new location first!

I understand your desire for secrecy, especially with that 50k+ wallet.
I think we need to move to another paradigm when it comes to the anonymity of people like you. $50M is obviously a staggering amount of money which would push many people into criminal behaviour. The data stored in that wallet is possibly worth more than your entire street.
(Please note I am not suggesting anything here, you have shown honesty throughout everything I have seen on this site),
We also clearly need a dead mans switch and provisions in case your house burns down etc.
Perhaps, we need some information that is handled by a trusted 3rd party, in escrow (lawyer?) or shared between some trusted agents.
Clearly I don't want to damage any existing security you have in place at the moment, but security through obscurity is not really sufficient.

No doubt this is all moot until something terible happens, but bank managers are held ransom for a few tens of thousnds of dollars, and following the Tradefortress event, publicly understood procedures need putting in place to mitigate risks to both you and the investors.

dooglus

legendary

Activity: 2940

Merit: 1333

Quote from: oda.krell on November 24, 2013, 09:18:41 PM

Umm... you're right in the first part, but to the last paragraph I could add: given any fully specified Martingale (odds, betting size progression, ending conditions), I can construct an equivalent single bet strategy. The only reason to employ a Martingale over a single bet strategy is that the former seems easier to risk-manage intuitively for the human mind.

I disagree, but will allow you to prove me wrong...

Suppose I have 127 BTC and want 128. I propose betting 1 BTC at 49.5% (2x payout). If it wins, stop, else double and repeat until it wins. So bet:

1, 2, 4, 8, 16, 32, 64

until one of them wins. If none wins, I've lost all 127 BTC. If any wins, I've got the 128 BTC I wanted.

This strategy will work so long as any one of the maximum of 7 bets wins. ie. unless all 7 lose. The probability of all 7 losing is 0.505^7 = 0.008376, so I have a 100 * (1 - 0.008376) = 99.1624% chance of success.

It's pretty likely that I'll end up betting less than the full 127 BTC. My expected total stake is less than 127. So my expected loss is less than 1.27 BTC.

What's your equivalent single bet strategy? How much does it expect to risk? How much does it expect to lose?

bittymitty

sr. member

Activity: 294

Merit: 250

I think I broke the odds and math as I made 1 BTC profit and now it is making me some yummy satoshi's per week in the bank roll.

oda.krell

legendary

Activity: 1470

Merit: 1007

Quote from: dooglus on November 24, 2013, 02:30:33 PM

Quote from: nicolaennio on November 24, 2013, 09:43:12 AM

You can make the following reasoning when you see a martingale that will show you that it is a gambler's fallacy:

- A martingale is a strategy with low probability (let's say it is 0.001%) of busting
- If you have two strategies with the same probability of busting, you should choose the one which plays less times, because the less you interact with the adversarial edge, the better
- You can always play the vanilla strategy of betting all your money at 99.999%.
- Thus the vanilla strategy must be better than the martingale

A martingale is just a way to hide a bad way to play with a low probability of busting strategy

This again?

Your reasoning is faulty, leading you to an incorrect conclusion.

The part where you went wrong is "choose the one which plays less times, because the less you interact with the adversarial edge, the better". It's not the number of bets that determines your expected profit; it's the amount you risk. If you risk less, you expect to lose less. A carefully planned martingale progression can cause you to expect to risk less and so lose less than a single large bet. We've gone over this many times before both on the forum and in the on-site chat.

The correct conclusion is that any single large bet can be replaced by a series of smaller bets which achieve the same return as the large bet but with a better chance of success.

Umm... you're right in the first part, but to the last paragraph I could add: given any fully specified Martingale (odds, betting size progression, ending conditions), I can construct an equivalent single bet strategy. The only reason to employ a Martingale over a single bet strategy is that the former seems easier to risk-manage intuitively for the human mind. (Which, btw, is a pretty good reason, and probably why so many bet Martingale)

dooglus

legendary

Activity: 2940

Merit: 1333

Quote from: dooglus on November 17, 2013, 11:14:05 PM

Lots of volume and lots of profit this week:

OMG a losing week!

Somebody was asking in the chat how they would have done if they were invested. I checked the balances of the biggest two investors who didn't touch their investment this week, and found:

Quote

16:53:56 (1) the biggest investor who didn't touch his investment last week went from 2245.96439731 -> 2243.82297252 - so investors made -0.0953% on the week?

and

Quote

16:56:19 (1) next biggest went 998.75716158 -> 997.80489210 - so -0.0953% again - seems to be consistent for all investors

As usual, the investor balances as they stood after the weekly commission run are posted here:

http://just-dice.blogspot.ca/search/label/bankroll

Magazine

member

Activity: 112

Merit: 10

Dooglus has Millions of dollars in his house, encrypted yes but if his full whereabouts was known then I'm sure there are people out there who would go ahead and try rob dooglus so it's better if he keeps his location hidden

dooglus

legendary

Activity: 2940

Merit: 1333

Quote from: TheFuneral on November 24, 2013, 07:33:51 PM

Quote from: fluidjax on November 24, 2013, 03:49:07 PM

I am considering an investment in just-dice, However I have a question I couldnt find an answer to, Dooglus are you anonymous or is your identity known publicly?

He is anonymous sir

I've never gone to great lengths to hide who I am but I do try to keep my precise whereabouts a secret, for my own personal safety, and for the safety of the coins in cold storage.

Some investors have said before that they would feel safer if my location was public knowledge, but I don't think they've thought that through, because:

a) if everyone knows where I am then it's easier to rob me, and
b) if I was going to steal the coins, I'm sure I would move to a new location first!

TheFuneral

sr. member

Activity: 356

Merit: 250

Quote from: fluidjax on November 24, 2013, 03:49:07 PM

I am considering an investment in just-dice, However I have a question I couldnt find an answer to, Dooglus are you anonymous or is your identity known publicly?

He is anonymous sir

fluidjax

hero member

Activity: 750

Merit: 601

I am considering an investment in just-dice, However I have a question I couldnt find an answer to, Dooglus are you anonymous or is your identity known publicly?

dooglus

legendary

Activity: 2940

Merit: 1333

Quote from: nicolaennio on November 24, 2013, 09:43:12 AM

You can make the following reasoning when you see a martingale that will show you that it is a gambler's fallacy:

- A martingale is a strategy with low probability (let's say it is 0.001%) of busting
- If you have two strategies with the same probability of busting, you should choose the one which plays less times, because the less you interact with the adversarial edge, the better
- You can always play the vanilla strategy of betting all your money at 99.999%.
- Thus the vanilla strategy must be better than the martingale

A martingale is just a way to hide a bad way to play with a low probability of busting strategy

This again?

Your reasoning is faulty, leading you to an incorrect conclusion.

The part where you went wrong is "choose the one which plays less times, because the less you interact with the adversarial edge, the better". It's not the number of bets that determines your expected profit; it's the amount you risk. If you risk less, you expect to lose less. A carefully planned martingale progression can cause you to expect to risk less and so lose less than a single large bet. We've gone over this many times before both on the forum and in the on-site chat.

The correct conclusion is that any single large bet can be replaced by a series of smaller bets which achieve the same return as the large bet but with a better chance of success.

nicolaennio

member

Activity: 99

Merit: 10

Quote from: dooglus on November 23, 2013, 08:40:10 PM

Quote from: optimator on November 23, 2013, 06:55:32 PM

Hi! I can appreciate your request, but it seems a little contradictory. You want someone to tell you why you, as an investor, should trust just-dice so you don't have to do your own homework? (reading 189 page thread).

I suspect the reason nobody replied is that no investor wants to encourage new investors.

The max profit on the site is already so large that it is almost never used, so new investment just spreads the site's profits thinner.

"Hey Mr. Prospector! Can you explain to me why it's safe to come join your gold rush?"

At least investors are decent enough to not discourage new investors ;-)

nicolaennio

member

Activity: 99

Merit: 10

Quote from: dooglus on November 23, 2013, 12:30:12 PM

Is there a mathematician in the house?

How do I analyse the odds of this strategy working?

He bets at 66%, which pays out 1.5x. He starts at 0.06 BTC (this first bet is not shown in the screenshot), doubles on loss, halves on win, never halves below 0.06.

So it's a random walk, which makes a net profit of 0.03 BTC each time it gets back to betting 0.06. Steps down are about twice as likely as steps up, so it seems unlikely to reach max bet and bust very quickly.

But the question is how do I calculate the probability of such a progression busting, given that he can afford to go N steps up the random walk?

Is it a Markov Chain thing? Or how do I analyse it?

You can make the following reasoning when you see a martingale that will show you that it is a gambler's fallacy:

- A martingale is a strategy with low probability (let's say it is 0.001%) of busting
- If you have two strategies with the same probability of busting, you should choose the one which plays less times, because the less you interact with the adversarial edge, the better
- You can always play the vanilla strategy of betting all your money at 99.999%.
- Thus the vanilla strategy must be better than the martingale

A martingale is just a way to hide a bad way to play with a low probability of busting strategy

dooglus

legendary

Activity: 2940

Merit: 1333

Quote from: itod on November 23, 2013, 10:25:10 PM

Thanks. Is this somewhere documented in detail, is that number 287.47 changing and how, etc?

It's 0.5% of the site's bankroll, updated in real time.

itod

legendary

Activity: 1974

Merit: 1077

^ Will code for Bitcoins

Quote from: msm595 on November 23, 2013, 09:49:49 PM

Quote from: itod on November 23, 2013, 09:21:21 PM

Quote from: msm595 on November 23, 2013, 03:08:28 PM

It's just an "improved" Martingale betting system. It's still guaranteed to lose money if betting ad infinitum. I put together a quick script to simulate betting, I'm no statistician though, so I'm not sure what numbers are needed.

Code:

maxProfit = Decimal("287.47")
maxBet = maxProfit/(payout-Decimal(1))

...

            bet = min(maxBet, bet*Decimal(2))

Would you care to elaborate this part of the code above, whats that "287.47" MaxProfit number which limits the whales maximum bet? Shouldn't the size of his wallet be the only limiting factor?

Just-dice doesn't have a max-bet, instead it has a max-profit. That is the max just-dice is willing to give you for a single bet. So if there is a 1.5x payout, your max bet would be (maxProfit)/(payout-1) = 2*maxProfit.

Thanks. Is this somewhere documented in detail, is that number 287.47 changing and how, etc?

optimator

sr. member

Activity: 351

Merit: 250

Quote from: dooglus on November 23, 2013, 08:40:10 PM

Quote from: optimator on November 23, 2013, 06:55:32 PM

Hi! I can appreciate your request, but it seems a little contradictory. You want someone to tell you why you, as an investor, should trust just-dice so you don't have to do your own homework? (reading 189 page thread).

I suspect the reason nobody replied is that no investor wants to encourage new investors.

The max profit on the site is already so large that it is almost never used, so new investment just spreads the site's profits thinner.

"Hey Mr. Prospector! Can you explain to me why it's safe to come join your gold rush?"

Your take on it is probably correct

Although, I read it as "why should I trust dooglus?" Which I then expounded to the more general phenomena of individuals sending a currency that can't be reclaimed to unknown people simply because the hive says "GO".

In the words of the Class M-3 Model B9, General Utility Non-Theorizing Environmental Control Robot - "Danger, Will Robinson!"

Thus, I still would encourage individuals to think for themselves and do their own due diligence. Bitcoin empowers but you must be willing to accept the responsibility that comes with power

msm595

full member

Activity: 185

Merit: 100

Quote from: itod on November 23, 2013, 09:21:21 PM

Quote from: msm595 on November 23, 2013, 03:08:28 PM

It's just an "improved" Martingale betting system. It's still guaranteed to lose money if betting ad infinitum. I put together a quick script to simulate betting, I'm no statistician though, so I'm not sure what numbers are needed.

Code:

maxProfit = Decimal("287.47")
maxBet = maxProfit/(payout-Decimal(1))

...

            bet = min(maxBet, bet*Decimal(2))

Would you care to elaborate this part of the code above, whats that "287.47" MaxProfit number which limits the whales maximum bet? Shouldn't the size of his wallet be the only limiting factor?

Just-dice doesn't have a max-bet, instead it has a max-profit. That is the max just-dice is willing to give you for a single bet. So if there is a 1.5x payout, your max bet would be (maxProfit)/(payout-1) = 2*maxProfit.

Dabs

legendary

Activity: 3416

Merit: 1912

The Concierge of Crypto

Yeah, don't trust dooglus with less than 60,000 BTC. You'll get better returns if you deposit more.

BTCSTOCKS

newbie

Activity: 14

Merit: 0

Quote from: dooglus on November 23, 2013, 08:40:10 PM

Quote from: optimator on November 23, 2013, 06:55:32 PM

Hi! I can appreciate your request, but it seems a little contradictory. You want someone to tell you why you, as an investor, should trust just-dice so you don't have to do your own homework? (reading 189 page thread).

I suspect the reason nobody replied is that no investor wants to encourage new investors.

The max profit on the site is already so large that it is almost never used, so new investment just spreads the site's profits thinner.

"Hey Mr. Prospector! Can you explain to me why it's safe to come join your gold rush?"

who me? because doog is the best of the worst lol Wink

jmo

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