Bitcoin Forum

Let's get off Martingale for a while.

Akio Kashiwagi’s won a record breaking US$6 million from the Trump Plaza in Atlantic City in February 1990. Instead of paying it, Donald Trump invited Akio back in May for a freeze out competition. The terms were as follows. Kahiwagi was to bet no more than $200K per hand in baccarat. The game would end when Akio either lost back his $6M or he was ahead $12M. Of course free rooms, the best food and alcohol in unlimited quantities were comped. The house edge in baccarat when you play the 'player' is 1.365%.

In 2013 dooglus's whale Tawaka beat the house for 10K BTC. So JD makes an offer to Tawaka that he bet no more than 250 BTC each bet, and the match would end when Tawaka doubles to 20K BTC, or until he loses back the original 10K BTC. Being gentleman they both agree to play to the bitter end, but dooglus promises to send a bottle of Dom Perignon for every day that the balance moves 1000BTC up or down. A final caveat, the investors get excited enough about the game, that the bank swells so that the maximum bet of 250BTC is always covered even if Tawaka starts winning.

Following questions
1) If Akio plays "player bet" in baccarat, what is the probability that he would win the bet?
2) If Tawaka plays JD, what is the probability that he will win the challenge?
3) Would this be a smart move by dooglus? His he just taunting the bear that bit him?

If you can answer these questions, I will tell you what happened to Akio and Trump.

I have trouble with the crazy big numbers that result from using paper as money.  Let's divide everything by 200k.  So:

Kahiwagi was to bet no more than 1 unit per hand in baccarat. The game would end when Akio either lost back his 30 units or he was ahead 60 units. The house edge in baccarat when you play the 'player' is 1.365%.


Because it's hypothetical?  Or are you accidentally spelling 'nakowa' wrongly?  Also, he's not "mine", he's his own.  Or maybe he belongs to the Chinese government.  I'm not sure how things work over there.


Again, let's divide throughout.  This time by 250 BTC:

So JD makes an offer to Tawaka that he bet no more than 1 unit each bet, and the match would end when Tawaka doubles to 80 units, or until he loses back the original 40 units.


1) I'll try to work that out.  it would be easy to arrive at an approximate answer by simulation.  To clarify, is the "player bet" even money?  ie. you double your stake when you win it?
2) You didn't state the chance he's playing at.  I think it matters.  nakowa always played at 49.5%, 2x so I guess we assume that's how he plays, but:
2a) How does the chance of winning each bet affect Takawa's chances against the house?
3) I expect it is a +EV move, but whether it is "smart" depends on dooglus' risk aversion.  If you have 10k BTC is it "smart" to risk it all on a coin flip that triples it if you win?  You have a 50% chance of making 20k profit, and a 50% chance of going bust.  It's +EV but I don't want a 50% chance of going bust.  I'll stick with the 10k, thanks.  It depends on the price of the booze I'm sending him, too.

+1  ;D

It was an open question. Anyone can try and do the calculation, it doesn't have to be dooglus.


I accidentally spelled 'nakowa' wrong. I tried to do it from memory, but as you can see my memory is terrible. I only meant he was yours as opposed to Donald Trump's whale in 1990.



1) Yes it is even money
2) Yes, 49.5%
2a) I am not sure I understand the question.
3) Donald Trump seemed to think that his decision was smart. I was curious what you thought.


BTW, the probability of doubling your bankroll before you go broke is always lower than the probability of winning one trial (obviously). But it clearly depends on your bankroll management as well. I find that people don't have a real feel for a 1% or a 2% or even a 5% house edge. But if you express it as probability of doubling before you go bankrupt, it is much clearer.


EDIT
The story of Akio Kashiwagi is true, but it raises some interesting points. First of all, presumably Akio was under some maximum bet restrictions when he won the $6 million originally. I don't know what they were, but I doubt that he was allowed to play more than $200K per hand. So Donald Trump basically asked him to come back under the same rules and try to hurt him again. Is that clever?

So bottom line, I am asking another casino owner, if he would do the same thing as Donald Trump. The terms very similar. The max bet of 250BTC at JD is worth about $150K, the house edge is similar for the two games, but Akio had to double 30 units ($6million/$200K=30) while JD would have to double 40 units (10000BTC/250BTX=40). So JD has more units, but a lower house edge.


I substituted expensive liquor instead of Trump's room, and unlimited comps. Assume DP is $225.95 per bottle, and given the terms I outlined, the whale should get a minimum of 10 bottles, but could get a lot more.

The mathematics is an open question to anyone reading this post. People who claim to understand martingale should be able to figure out flat betting. If it was your casino what would you do?

If it was my casino I would have done it if my bankroll was sufficient ;) I presume Trump roll was more than 100m$

I don't think you can consider that the max bet will stay the same no matter what in the JD case

1-Less than 2% but more than 0.3%
2-Less than 2% but more than 0.3%
3-In an ideal world the max bet would have been 0.5% of the bankroll from the start but considering it was 1% it could have been lowered to 0.5%; dooglus was risking his whole business to make some money, he considered it was not worth it.

An interesting probability would be : when dooglus lowered the max bet from 1% to 0.25% what was the probability of Nakowa to win 25% of the bankroll? 50%? 75%? Considering he had 18k to lose and the max bet was 1% (the bankroll was 32,000BTC which is irrelevant to calculate the probabilities here)

Nakowa probably played on other casinos because gamblers keep gambling especially when they still have the fantsay to have a secret method to win, I wonder if he won/lost big; maybe he will come back and play on JD the max bet is now close to what it was when he stopped playing

The three Trump casino had gross revenue of $2.2m /day (from gambling) back in 1990

Probably not, but I was trying to simplify the mathematics if someone wanted to make a stab.

Well, when you say "risking his whole business" you are looking at it after the fact. No matter what the parameter settings there is still risk of extreme swings. There was a play in October where he hit the 0.5% threshold repeatedly. The player stopped for two hours and came back to play one more time to lose 7000BTC.

Yes, you could raise HE, and lower max bets to the point that there is no fear, but investors would drop out and players would not play at this level.
The next time the investors may be pleased to have a big win.

1,768   BTC   @   92.00%   won   134   BTC
1,768   BTC   @   92.00%   won   134   BTC
1,768   BTC   @   92.00%   won   134   BTC
2,171   BTC   @   92.00%   won   165   BTC
2,336   BTC   @   92.00%   won   178   BTC
2,514   BTC   @   92.00%   won   191   BTC
2,514   BTC   @   92.00%   won   191   BTC
2,896   BTC   @   92.00%   won   220   BTC
3,117   BTC   @   93.00%   won   201   BTC
3,318   BTC   @   93.00%   won   214   BTC
3,534   BTC   @   95.00%   won   149   BTC
3,683   BTC   @   95.00%   won   155   BTC
3,847   BTC   @   93.01%   won   248   BTC <=== probably max profit from here on
3,847   BTC   @   93.03%   won   247   BTC
3,847   BTC   @   93.09%   won   244   BTC
3,847   BTC   @   93.20%   won   239   BTC
4,825   BTC   @   94.30%   won   240   BTC
5,066   BTC   @   94.55%   won   238   BTC
5,304   BTC   @   95.09%   won   218   BTC
5,520   BTC   @   95.21%   won   220   BTC
5,520   BTC   @   95.21%   won   220   BTC
5,959   BTC   @   95.51%   won   218   BTC
6,177   BTC   @   95.71%   won   212   BTC
6,390   BTC   @   95.81%   won   213   BTC
6,602   BTC   @   95.95%   won   210   BTC
6,812   BTC   @   96.04%   won   210   BTC
7,016   BTC   @   96.20%   lost   7,016   BTC   


Perhaps I wasn't clear on these questions.
1) I assume Akio is paid the $6M that he is owed by Trump in the form of large value chips. Assuming that Akio plays $200K each time, what is the chance that he will reach $12M before going to zero. He must have a 'reasonable' chance or he wouldn't play.
2) If Tawaka plays JD and brings his own 10,000 BTC that he won last year, and is limited to 250BTC per bet, what is the chance that he will make it to 20,000 BTC before going bust. To make matters simple consider that the BANK always stays above 50,000 BTC so there is no limit. Tawaka takes it as a gentleman's challenge and plays to bust or until 20K.
3) I am saying that Donald Trump extended this challenge in 1990. Would dooglus be smart to mimic the Donald? I haven't seen Tawaka's individual bets last summer. I don't know if he was playing for profits above 250BTC by taking advantage of the 1% maximum bet.


These answers are clearly not correct for questions #1 and #2. As I said, I may not have been clear.
The difference between the two questions is different house edge (1.36% vs 1.00%) and different number of units ($6,000,000/$200,000=30 units and 10,000BTC/250BTC= 40 units).

I figured you wanted to use 30units @ 1.36% casino edge or 40units @ 1% casino edge has the same because it is in the same order of magnitude in terms of probability

As I said before, the most interesting probabilities would be the odds of winning 25% 50% and 75% of the bankroll for Nakowa when the max bet was 1% of the roll and considering he probably won 10K and may had 8K more available if needed

If investors want the maximised their final wealth they need to follow the kelly criterion for bets giving a 1-1 payout because they are the most commun

I didn't pick the terms (30units @ 1.36% casino edge or 40units @ 1% casino edge) They were the historical terms of the Trump agreement. The JD terms are the ones existing on the website.

But yes, they do happen to cancel each other out, so that the odds of Akio winning are the same for a hypothetical return of Nakowa. I would also like to point out that Nakowa could come back to JD any time he wants looking to repeat his performance. He doesn't need an invitation or free champagne.

Donald J. Trump is quoted as saying that Akio was up more than US$10 million and then he started losing. He lost all his original $6 million that he had won a few months earlier and kept losing more. After 6 days Akio broke the agreement of the freeze out and returned to Japan still in debt. Trump had to write off the debt in January 1992, when Akio was found dead at his Mount Fuji home with 150 stab wounds.

Why would he play anymore if he won that much ?

He can buy all the alcohol and drink everything even build a small casino with that money .

If Nakowa is indeed one of these investors who bout 25,000 BTC back in the early days of 2009 then he has already beaten the longest of odds. Why would he gamble at all?

For those of you who are having trouble calculating if Akio would win the $6 million freeze-out in 1990, or if Nakowa would win the hypothetical 10,000 BTC freeze out the calculations are shown in the spoiler.

Remember that Akio has to bet in maximum $200K bets in baccarat, and Nakowa can bet in 250BTC increments on Just-Dice. The odds of Akio or Nakowa doubling there money before losing their stake are very similar.

You're using the equation found in section 12.2 of http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter12.pdf

https://i.imgur.com/qTbQeKk.png

Briefly:


I hadn't see it before.  Thanks.  :)

I am using that equation, but my motivation for breaking it out into several different lines is that each line can be understood to mean something. The final result does not seem so mysterious.

The probability of doubling your bankroll before losing your bankroll depends on house edge and number of betting units. Nothing else! It's also a good way to compare house edge in a more easily comprehensible manner to the average person.

For example consider the possibility of doubling your bankroll with 10 unit bets for different games.

• Just Dice   Bacc. PB   Satoshi
• 1.00%    1.36%    1.98%
• 45.02%   43.24%   40.23%

• Eur Roul.   Am. Roul.
• 2.70%     5.26%
• 36.80%   25.85%

The difference between playing JD or Satoshi is more obvious. And you may wonder why people play roulette at all (European or American version).

Lastly, and most importantly these calculations are unchanged regardless of you betting scheme (even if you use Martingale).

=======================
Given the 30% | 70% relationship, do you think what Donald Trump did was smart? Can you imagine the day when you might publicly challenge Nakowa to try and double his winnings?

BTW, it is clear that max profit was 1% of Bank when Nakowa began. I don't know what the Bank was in those days. Was max profit more than 250BTC back then? Did he play it repeatedly?

Gamblers usually don't play because it is smart to play so that answers the question of why did nakowa and akio kept playing

I like the idea of a public challenge to nakowa but let's hope he will come back by itself to entertain us

Max bet was between 500-600BTC when nakowa started playing, he was betting that much usually after having played for lower amounts

I thought this statement that I made might get more comment, since JD clearly attracts so many Martingale players.

You have better odds doing a single bet than playing the martingale ie if you want to get 50% from your bankroll you have better odds of achieving it if you go maxbet/1.5payout than playing a martingale

Both players should call it a day. The more time you spend on the game the less likely you gonna win  ;)

The question was wether it was a good business practice for the casinos owners to propose the bets

Given that Nakowa was playing 500 BTC bets (that means 10,000/500=20 units) there is a 40% chance of doubling 10K before losing the stake.
But now that he is restricted to roughly 250 BTC bets  (i.e. 40 units) there is only a 30% chance of doubling 10K. It may not be a bad business decision to publicly goad him into playing again.

I am not sure about Donald Trump in 1990. Typically there is not a lot of information. The first time he won $6M it is unknown how big a bet he was permitted. Keep in mind that in 1990 all three of Trump's casinos combined were making over $2m per day (gross revenue).

You're saying that you have a higher chance to turn 10 into 15 if you bet it all on a single bet than if split the 10 into smaller pieces and bet them at a higher multiplier, smallest first, until you win one, and then quit?

Because that seems obviously incorrect to me.  Betting all your coins you expect to lose more than betting just some of them.

An easier example:

Suppose you have 7 coins and want to have 8.

You could bet all 7 on a 1.125x bet.

Or you could bet 1 at 2x, then 2 at 2x, then 4 at 2x, stopping if you win at any point.

Is the single 7 or the 1,2,4 martingale better?  What are the odds of success of each one?  What's your expected return for each?

Work it out.  The 1,2,4 martingale is *better* than the single 7.

I mean if nakowa flat bet at 9% for an 11x payout until he doubled or bust, what are his chances of success then?  What is the optimal chance-per-bet to double your bankroll before busting, given a constant profit per bet?  The equation we used assumes the random walk is taking equally large steps backwards and forwards, but in this case we aren't.


I would definitely allow the betting to happen. Since the bankroll is crowd-funded, each individual would decide for themselves whether they wanted to take on the mighty nakowa. Historically it has been a losing proposition to do so, but even at the height of his power when he was kicking us all over the place, the vast majority of the crowd had faith in math and the house edge, and were quite vocal in protesting me reducing the maximum profit per bet to 0.25% of the bankroll.  They wanted a rematch.  They wanted their chance to take back what he had won from them.  I'm sure most still feel the same way, that math will win in the end.

I don't know if I would personally remain part of the bankroll myself. I couldn't help but take it personally when he won so much, like he was attacking me and the site. I know that's stupid, but it's how I felt. Not being a part of the bankroll made it a little better, and allowed me to sleep at night, so that's what I did.

This chart (https://blockchain.info/charts/balance?address=14o7zMMUJkG6De24r3JkJ6USgChq7iWF86) pretty closely follows the amount in the bankroll over time.  It's actually showing how many coins the site was holding in offline cold storage over time, which also includes player balances, and doesn't include the flat that is kept on-site, but those two pretty much cancel each other out.

So the bankroll was around 30k in mid July and around 40k in late September.  Those are the two times nakowa played a lot.

Here's a video somebody made of him playing on 20th September, when he was getting warming up for his 2nd attack on the house.  https://www.youtube.com/watch?v=hjMnKtTWeKM

Note the bankroll is 48k and the maximum profit per bet is 478 BTC.  Almost all his large bets are for 100 or 200 BTC, so he's not betting more than 0.5% of the bankroll even though he could.

Here's a table showing all nakowa's bets on account 2548 at 49.5% of 1 BTC or more:


The biggest bet was for 303 BTC.

Very interesting. So you actually did very little by reducing the max profit to cramp his style.

You are correct :

If you want xBTC and you either get it with a martingale starting at x : x; 2x ;4x; 8x or a big bet of 15x at 1.067 you are better off playing the martingale

BUT

When you play a martingale you are usually looking for a bigger win than a single unit win, for exemple it is commun for martingales to wait to get 30% 50% or 100% before stopping

-Your expected loss for a single bet of 127 @payout 1.5 is 1.27BTC

-Your expected loss for a 1;2;4;8;16;64 martingale where you stop when you reach a 62.7profit is twice as much (I only give an order of magnitude)

I may be wrong  ;D

Right.  The best way to play is to risk as little as possible.  Running a single martingale sequence is a good way to do that.  If you run it over and over again, you're increasing the amount you expect to lose.

If you want to win more than a single unit, you need to redesign your martingale sequence such that you achieve your target in a single run...

The thing is martingale are fun and playing casino should be about having fun

So looking at your table and my summary table, there can be plenty of activity at 0.5% max profit.
You were still getting 25K of wagering on the three days that MaxProfit was 0.25%. Your ideal level of activity would be 10K BTC per day. Investors see some ups and down on a daily basis, but overall you have much better returns.

I don't understand why you say 10K/day would be the ideal level of activity, the more the better!?

While investment is a type of gambling, most investors want to see a lot less variance than a gambler. If the bank is about 50,000BTC you can tolerate the amount of day to day variance with an average of 10,000 BTC or fewer being bet per day, while still getting a great return over the long run.

Adding the last two days of the year to the table, I just think most investors don't want to see people wagering many times the value of the bank in a day. It makes them feel like they are the gamblers.

FULL 365 DAY YEAR

The variance is not necessary higher if more is wagered everyday!!

Yes you are correct, but the wagering doesn't seem to zoom because thousands of extra people have just discovered JD. It is because a few people are making huge bets. That is what makes the variance large.

As we observed, the profit has been 1.23% of the wagers over the last 250 days. There was one day when 70K BTC were wagered, but all other days have been 30K or less. The median has been only 3K bitcoins.

I agree that when a lot if wagered it is probably because a big player is placing big bets so the variance increases but you implied that more wagered=more variance; big bets=more variance, if the operator doesn't want the big bets he can limit the max bet

I'm fairly convinced that the 1% Max Profit had almost no effect on Nakowa. It is pretty clear that the 60 some hours when it was reduced to 0.25% was subduing, but there was little or no difference between 0.5% and 1.0%.

I am curious about that cold storage data. Why is there over 100 data points in one day, and then no data points for days to 2 weeks at a time?


I admit, my post was sloppy.

Even 0.1% of bankroll is actually a large bet. Even the biggest casinos will not routinely admit bets over $10,000 routinely. Ceasar's Palace and other big gambling casinos have a few tables, but you still have to ask permission if you are going to placing $100K bets.

Why wouldnt this work if you had a massive bank roll. Bet 1 BTC 49.5% you win store it to the side, keep betting till you lose, whne you lose a bet increas your bet by double till you win back lost bet. 50% chance at worst you have to roll 4x-5x your original bet to win it back. Every BTC you win you either set to the side IE send it to you wallet then use your main bank roll for winning your bets back. If you have a 500 BTC bank roll big deal rolling 5x to settle back out, then start again winning BTC then covering losses.

I manage that address manually.

I used to move coins in and out of it a lot more frequently than I do now.

The way I manage the coins now is that there are usually enough coins available to the site to process most withdrawals. Whenever there are too many online, the excess are automatically sent to a local (to me) online wallet.  When that in turn gets "too full", I move 500 BTC into the cold wallet. So the local wallet acts as a buffer to save me having to go to the offline machine too often, because frankly it's a pain to use the offline machine. I never use networking or physical storage devices on it; I only use webcams and QR codes to pass messages to and from it, to keep it airgapped from the 'net. This 'buffer' wallet between the 'hot' and 'cold' wallets will be why you see weeks of inactivity on the cold wallet - the buffer was big enough to smooth out the ebb and flow of coins.

The 100 data points in a single day would probably be the day that I decided I was going to use individual transaction outputs of 500 BTC in the cold wallet, and tidied the whole thing up into neat 500 BTC bundles - that's the big dip you see over the word 'Nov' in the chart.

It might if you were lucky.

But in the long term it wouldn't, because the payout is always less than the reciprocal of the probability.

If you bet with a 0.2 probability of winning, the payout is a little (1%) less than 1/0.2 = 5 times your stake when you win.