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Topic: Challenge: What's the best way to win 1 BTC with 1 BTC? - page 2. (Read 15977 times)

legendary
Activity: 1386
Merit: 1016
So basically you are saying that strategy is good and the best thing you can use no matter what?  No matter the amount of large rolls you do you should always be doing this is what I am gathering, is that correct?

nope, what we are trying to show u is that no matter how many different stragety we can come out with, the chance of getting it right is always less than 50%. so in another words, it is more likely you lost it all than to gain. so best is dont bet.
legendary
Activity: 1302
Merit: 1005
New Decentralized Nuclear Hobbit
...you do you should always be doing this is what I am gathering, is that correct?

Not really. If you are concerned about increasing your EV and beating the edge, you shouldn't play. Whichever strategy you pick, you can only minimize the impact of house edge on your EV.

Maximize impact of HE on EV : bet at 98% win chance. Grin
Minimize impact of house edge : follow the winning strategies of Dooglus and the other winner. Smiley
Nullify impact of house edge : Don't play.
Beat the house edge : Not possible.
sr. member
Activity: 308
Merit: 250
So basically you are saying that strategy is good and the best thing you can use no matter what?  No matter the amount of large rolls you do you should always be doing this is what I am gathering, is that correct?
legendary
Activity: 1386
Merit: 1016
Doog, how did you learn all of this?  I would love to try and figure out about calculations and what actually gives you the best odds.  Did you take a lot of stats classes in college or what?  Any thoughts?

I`m pretty sure it comes from either majoring in math..

That alone or picking up and building the dice itself and studying the game which lead to his site? who knows lol.

for my country(in asia), probability is learn at y7 to y10, where you need to learn how to calculate when you throw up to 3 dices or pick 3 balls. of course, for good sch, they have to learn on how to calculate for n throws where n can be large. for advance y11 to y12, we learn for large n, what probability for specific k times of winning. but i believe dooglus even learn up to university standard as he mention that he know about L'Hôpital's rule which is only taught when your major has things to do with math where you have to look at the big picture.
full member
Activity: 138
Merit: 100
Doog, how did you learn all of this?  I would love to try and figure out about calculations and what actually gives you the best odds.  Did you take a lot of stats classes in college or what?  Any thoughts?

I`m pretty sure it comes from either majoring in math..

That alone or picking up and building the dice itself and studying the game which lead to his site? who knows lol.
legendary
Activity: 1386
Merit: 1016
Doog, how did you learn all of this?  I would love to try and figure out about calculations and what actually gives you the best odds.  Did you take a lot of stats classes in college or what?  Any thoughts?

well it is actually quite simple mathematical calculation. you can start using it when you learn probability with tree diagram. but instead of picking 2 or 3 people or throwing 2/3 dice, the same occuring series can be applied to larger number of trials.

on higher level(my country use terms diff from you so i may use the wrong term) in pre-u school, you can learn even how to estimate your probability by approximating the binominal distribute to other form of distribute that allow more easy of calculation.

And to be honest, this is the first time i ever encountered after learning L'Hôpital's rule in uni. lol. finally what i learn got some use to it!
hero member
Activity: 560
Merit: 500
You can do all calculations but only one thing will allow to earn 1 btc playing with 1 btc that is lucky the 49% means nothing besides you can loose as win anytime.
hero member
Activity: 784
Merit: 1000
Doog, how did you learn all of this?  I would love to try and figure out about calculations and what actually gives you the best odds.  Did you take a lot of stats classes in college or what?  Any thoughts?
hero member
Activity: 882
Merit: 1000
Exhausted
Are you able to beat 49.6522222%, or do you think that is a hard limit?

After going through post #198 carefully, I agree the number 1 - 2**-0.99 you get should be the limit under perfect conditions (the bet size and multiplier can always be set to make the balance after winning a bet to be exactly 2 btc). Under actual conditions (bet size cannot contain a fraction of satoshi, bet win chance % can only contain 2 decimal place) it cannot be done and so the "best" way would be slightly lower than that.

BTW, I have not heard of the word "L'Hopital's rule" for like a decade lol.


My recent post shows strategies that give a 49.6522222% percent chance of winning, so your post (which came after) doesn't beat mine.

As mentioned in the OP, the betting sequence has to be well-defined and subject to the constraints of a dice site such as Bitdice or PRC. IMHO, the numbers you get in that post does not seem to qualify. Tongue


I notice the word "them" in the quote. Do I get 0.1 btc for beating dooglus' solution? Tongue

Damn it. Guess that serves me right for trying to use gender-neutral pronouns. What's your MP or BaB username?

(Give me a day or two to verify the solution, and after this, no more prize money will be given out   Grin)

Received the 0.1 btc. Thanks Ryan. Grin

hero member
Activity: 560
Merit: 500
On the begining for sure bet 1 btc worthing 1 dollars weren nothing nowadays is worthing 250dollars soo why the hell i should try with 1 btc to double since i know and most of us know that the lucky usually stays with the owner of the project being casino,dice or any other way.
hero member
Activity: 966
Merit: 501
I think its possible but at the same time it is little difficult too. I believe that the best way to earn 1 btc is sports betting only If you have good knowledge about sports and if you are able to predict the result. So as per me you can take a chance with sports betting as there are many chances to make some good profit.
Avoid the other ways of gambling where you can loose the money.

Agreed with you that it is possible but at the same time its difficult too. People can loose the money while trying to earn one btc in gambling, they should follow some techniques and other strategies to minimize the loss or else they will loose their 1 btc instead of earning 1 btc.
legendary
Activity: 2940
Merit: 1333
I'd love an explanation of why it tops out at 0.496522222!

It turns out that number doesn't end with recurring 2's, but is in fact:

>>> 1 - 2**-0.99
0.49652222497164056

I calculated it using L'Hôpital's rule, which I vaguely remember learning about in high school.
legendary
Activity: 2940
Merit: 1333
Chance of winning = 1 - ((1 - 0.02%) ^ 3430 * (1 - 0.01%)) = 49.649851332%.

Chance of winning = 1 - ((1 - 0.03%) ^ 2287) = 49.651579392%

I notice the word "them" in the quote. Do I get 0.1 btc for beating dooglus' solution? Tongue

My recent post shows strategies that give a 49.6522222% percent chance of winning, so your post (which came after) doesn't beat mine.

Are you able to beat 49.6522222%, or do you think that is a hard limit?

Here's a chart showing your two strategies, and where they fit on the curve of possible martingale strategies. The higher the payout multiplier you play with, the closer you get to the 49.652222% chance:



I wonder if flat-betting would be better?

Like we could divide the 1 BTC into N=10 0.1 bets.
Bet the first 0.1 at 11x. If we win, we're 1 BTC up, so we stop.
Bet the 2nd 0.1 12x. If we win, we're 1 BTC up, so we stop.
Etc.
Bet the Nth at (10+N)x. We're always 1 BTC up if we win.

Turns out it isn't better. What's funny is it is exactly the same.

Here's a Python script that calculates the chance of doubling up using this flat-betting strategy for various N:

Quote
for m in range(0, 6):
    for N in range(10**m, 10**(m+1), 10**m):
        p = 1.0
        for i in range (1, N+1):
            p *= (1 - 0.99 / (N+i))

        print "%6d %.8f" % (N, 1 - p)

And here's its output:

Quote
     1 0.49500000
     2 0.49582500
     3 0.49607333
     4 0.49619171
     5 0.49626081
     6 0.49630606
     7 0.49633797
     8 0.49636168
     9 0.49637999
    10 0.49639455
    20 0.49645915
    30 0.49648035
    40 0.49649088
    50 0.49649718
    60 0.49650137
    70 0.49650436
    80 0.49650660
    90 0.49650834
   100 0.49650973
   200 0.49651599
   300 0.49651807
   400 0.49651911
   500 0.49651973
   600 0.49652015
   700 0.49652044
   800 0.49652067
   900 0.49652084
  1000 0.49652098
  2000 0.49652160
  3000 0.49652181
  4000 0.49652191
  5000 0.49652198
  6000 0.49652202
  7000 0.49652205
  8000 0.49652207
  9000 0.49652209
 10000 0.49652210
 20000 0.49652216
 30000 0.49652218
 40000 0.49652219
 50000 0.49652220
 60000 0.49652220
 70000 0.49652221
 80000 0.49652221
 90000 0.49652221
100000 0.49652221
200000 0.49652222
300000 0.49652222
400000 0.49652222
500000 0.49652222
600000 0.49652222
700000 0.49652222
800000 0.49652222
900000 0.49652222

It converges on 49.6522222% chance of doubling up again!
legendary
Activity: 1463
Merit: 1886
I notice the word "them" in the quote. Do I get 0.1 btc for beating dooglus' solution? Tongue

Damn it. Guess that serves me right for trying to use gender-neutral pronouns. What's your MP or BaB username?

(Give me a day or two to verify the solution, and after this, no more prize money will be given out   Grin)
hero member
Activity: 784
Merit: 500
I think its possible but at the same time it is little difficult too. I believe that the best way to earn 1 btc is sports betting only If you have good knowledge about sports and if you are able to predict the result. So as per me you can take a chance with sports betting as there are many chances to make some good profit.
Avoid the other ways of gambling where you can loose the money.
hero member
Activity: 882
Merit: 1000
Exhausted
Hmm just thought about it, has OP yet paid the prize he has claimed to pay to the best method or is he still searching for more strats?

He already paid, and it's likely we have the best strategy already.

It is dangerous to jump to the conclusion quickly. Tongue


leading to a 49.64716% chance of winning.

you have a 49.64812% chance of winning.

chance of winning =  100 * (1 - ((100 - 1.0664) / 100) ** 64) = 49.649475445976265%

With 1 btc, I should be able to make a total of 3430 x4950 (ie 0.02%) bets, each with a bet size of roundup((2-balance)/4949) to the nearest satoshi that could bring my balance to slightly over 2 btc if the bet wins. After that, I will have 0.00027093 left and a final x9900 (ie 0.01%) bet can be made which could bring my balance to 2.682207 btc.
Check http://pastebin.com/TL7xLTx4 for the complete betting sequence in details in CSV format.

Chance of winning = 1 - ((1 - 0.02%) ^ 3430 * (1 - 0.01%)) = 49.649851332%.


Or, I should be able to make a total of 2287 x3300 (ie 0.03%) bets, each with a bet size of roundup((2-balance)/3299) to the nearest satoshi.
Check http://pastebin.com/Je5ujHH9 for the complete betting sequence in details in CSV format.

Chance of winning = 1 - ((1 - 0.03%) ^ 2287) = 49.651579392%


Yeah, but you also said:

added 0.1 to blockage's account. If someone can beat his solution, I'll give them 0.1 as well.

Ahh touché, forgot I wrote that.

I notice the word "them" in the quote. Do I get 0.1 btc for beating dooglus' solution? Tongue
hero member
Activity: 560
Merit: 500
Well one funny way to get fast 1btc ,im sure you cant play with 1 btc but you can earn 600% or even 1000% playing a game ,and well only need lucky and a good conection im playing yesterday i made 40ksatoshis with 10k fee xD,i guess i cant post any ref link here soo send me pm.
legendary
Activity: 2940
Merit: 1333
Could you point to the post which won it? And did it really have lower chances of losing?(highest EV I mean)

These two posts:

leading to a 49.64716% chance of winning.

you have a 49.64812% chance of winning.

chance of winning =  100 * (1 - ((100 - 1.0664) / 100) ** 64) = 49.649475445976265%

And yes, they have a higher EV because on average they risk less. The EV is -1% of the amount you risk, so minimising the amount you risk maximises the EV.

The corollary to this of course is that the optimal strategy for maximising your EV is to risk 0 - ie. stop playing.

A strange game. The only winning move is not to play. How about a nice game of chess?
hero member
Activity: 924
Merit: 1005
4 Mana 7/7
Hmm just thought about it, has OP yet paid the prize he has claimed to pay to the best method or is he still searching for more strats?

He already paid, and it's likely we have the best strategy already.
Could you point to the post which won it? And did it really have lower chances of losing?(highest EV I mean)
legendary
Activity: 2940
Merit: 1333
Hmm just thought about it, has OP yet paid the prize he has claimed to pay to the best method or is he still searching for more strats?

He already paid, and it's likely we have the best strategy already.
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