Challenge: What's the best way to win 1 BTC with 1 BTC?

[agustina2]

All of the suggested ways is risky and can't be called the best but if you win. Yeah party time.

Bet all 1BTC to a 2x payout in dice. Yes in just one click so result is fast.

[panjul07]

All of the suggested ways is risky and can't be called the best but if you win. Yeah party time.

Bet all 1BTC to a 2x payout in dice. Yes in just one click so result is fast.

So do you mean that your suggestion is not risky? I think there is no safe way to win 1btc with 1btc, most of strategies are always risky. But I agree with you that to bet all the 1btc with 2x payout is the fastest way to win and fastest way to lose as well

[jpouza]

My method is to feel my moves and if i feel or think im lose with this move im lowering my bet then if i feel it will win im higher the bet. thats my way  so you need to feel it and think before you bet.Then you need to sacrifice high amount before you get to win or double you capital..

Feel the dice? feel the moviment?

That´s very ethereous 

[darkangel11]

My method is to feel my moves and if i feel or think im lose with this move im lowering my bet then if i feel it will win im higher the bet. thats my way  so you need to feel it and think before you bet.Then you need to sacrifice high amount before you get to win or double you capital..

Feel the dice? feel the moviment?

That´s very ethereous  

You have to imagine holding the dice in your hand while clicking "roll" on the screen LOL

[StevenLiang]

All of the suggested ways is risky and can't be called the best but if you win. Yeah party time.

Bet all 1BTC to a 2x payout in dice. Yes in just one click so result is fast.

So far, this the the quickest way to double 1 BTC to 2 BTC.
Win or lose is your consequence's.
If you want try this way, try it in trusted site such as crypto-games.net, and many other dice sites.

[BTC Tipster]

How about this:

bet 0.01088928 BTC @ 1.0664%
if you win, your profit is ((99 / 1.0664) - 1) * 0.01088928 = 1.00002474 BTC
if not, martingale at the same chance of winning, to keep the same net profit
you can afford 64 bets
chance of winning =  100 * (1 - ((100 - 1.0664) / 100) ** 64) = 49.649475445976265%

Edit: here are the 64 bets:

       chance  multiplier      
        1.0664% 92.83570893x    
                  
bet #       stake  total lost      profit
-----  ---------- -----------  ----------
 1     0.01088902              1.00000087
 2     0.01100759  0.01088902  1.00000081
 3     0.01112745  0.02189661  1.00000065
 4     0.01124861  0.03302406  1.00000001
 5     0.01137110  0.04427267  1.00000036
 6     0.01149492  0.05564377  1.00000036
 7     0.01162009  0.06713869  1.00000051
 8     0.01174662  0.07875878  1.00000040
 9     0.01187453  0.09050540  1.00000048
10     0.01200383  0.10237993  1.00000031
11     0.01213454  0.11438376  1.00000032
12     0.01226667  0.12651830  1.00000004
13     0.01240025  0.13878497  1.00000078
14     0.01253527  0.15118522  1.00000019
15     0.01267177  0.16372049  1.00000049
16     0.01280975  0.17639226  1.00000021
17     0.01294924  0.18920201  1.00000063
18     0.01309024  0.20215125  1.00000022
19     0.01323278  0.21524149  1.00000024
20     0.01337687  0.22847427  1.00000007
21     0.01352254  0.24185114  1.00000091
22     0.01366978  0.25537368  1.00000026
23     0.01381863  0.26904346  1.00000022
24     0.01396910  0.28286209  1.00000011
25     0.01412121  0.29683119  1.00000014
26     0.01427498  0.31095240  1.00000051
27     0.01443042  0.32522738  1.00000047
28     0.01458755  0.33965780  1.00000020
29     0.01474640  0.35424535  1.00000075
30     0.01490697  0.36899175  1.00000041
31     0.01506929  0.38389872  1.00000021
32     0.01523338  0.39896801  1.00000024
33     0.01539926  0.41420139  1.00000057
34     0.01556694  0.42960065  1.00000032
35     0.01573645  0.44516759  1.00000045
36     0.01590780  0.46090404  1.00000005
37     0.01608102  0.47681184  1.00000003
38     0.01625613  0.49289286  1.00000036
39     0.01643314  0.50914899  1.00000007
40     0.01661208  0.52558213  1.00000001
41     0.01679297  0.54219421  1.00000009
42     0.01697583  0.55898718  1.00000020
43     0.01716068  0.57596301  1.00000020
44     0.01734755  0.59312369  1.00000086
45     0.01753644  0.61047124  1.00000016
46     0.01772740  0.62800768  1.00000067
47     0.01792043  0.64573508  1.00000031
48     0.01811557  0.66365551  1.00000070
49     0.01831283  0.68177108  1.00000065
50     0.01851224  0.70008391  1.00000077
51     0.01871382  0.71859615  1.00000078
52     0.01891759  0.73730997  1.00000032
53     0.01912359  0.75622756  1.00000088
54     0.01933182  0.77535115  1.00000024
55     0.01954233  0.79468297  1.00000076
56     0.01975512  0.81422530  1.00000015
57     0.01997024  0.83398042  1.00000073
58     0.02018769  0.85395066  1.00000016
59     0.02040752  0.87413835  1.00000072
60     0.02062973  0.89454587  1.00000001
61     0.02085437  0.91517560  1.00000025
62     0.02108146  0.93602997  1.00000085
63     0.02131101  0.95711143  1.00000028
64     0.02154307  0.97842244  1.00000067
                   0.99996551        

Edit: and the calculations showing that it works for the first 5 bets:

>>> 0.01088902 * (99/1.0664 - 1)
1.0000008712228057
>>> 0.01100759 * (99/1.0664 - 1) - 0.01088902
1.0000008112303074
>>> 0.01112745 * (99/1.0664 - 1) - 0.01088902 - 0.01100759
1.0000006493023257
>>> 0.01124861 * (99/1.0664 - 1) - 0.01088902 - 0.01100759 - 0.01112745
1.0000000137959488
>>> 0.01137110 * (99/1.0664 - 1) - 0.01088902 - 0.01100759 - 0.01112745 - 0.01124861
1.0000003597824456

Edit2: I can make ever increasing longer sequences which do slightly better, but it appears never to beat 49.65222222222% chance of doubling.

It worked in PD:

Code:

Session Wagered:
0.00000156

Session Profit:
0.00000214

Session Bets:
156

[Financisto]

Good discussion about math behind a dicegame.

Full of probability and statistics.

I like that...

[ndnh]

Initial bet : 0.0001BTC
On lose multiply by : 1.0001010101x

Playing at 9900x

With a bankroll of 1BTC, the player can afford 6912 rolls.

Chance to win is 49.90770579% on 1% edge. ?


or is it 49.5567818%?

[dooglus]

Initial bet : 0.0001BTC
On lose multiply by : 1.0001010101x

Playing at 9900x

If you win your first bet you stop with a profit of 9899 * 0.0001 = 0.9899 BTC

The goal is to make a profit of 1 BTC.

I think you need to play with a higher multiplier or something.

Let's set the payout multiplier (m) and work everything out from there.

m = 10001, say

The probability (c) of a bet winning at that multiplier is:
  c = 0.99 / m

The starting bet to win 1 BTC at multiplier m is:
  a = 1.0 / (m - 1)

The amount we need to multiply the stake by when we lose to maintain the same net profit is:
  r = (1+a) / ((m-1)*a) = a+1 = m / (m - 1)

The stake on the nth bet will be:
  a * r ** (n-1)

The sum of stakes for the first n bets will be:
  a * (1 - r**n) / (1 - r)

The number of bets we can afford to make is:
  math.floor(math.log((a - 1 + r) / a, r)) = math.floor(math.log(2, r))

The probability of winning in the first n bets will be:
  (1 - (1 - c) ** n)

And so the probability of doubling up successfully is:
  (1 - (1 - c) ** math.floor(math.log(2, r)))

Using this we can quickly calculate the chance of doubling up for various payout multipliers:

>>> for m in range(2, 20):
  c = 0.99 / m; a = 1.0 / (m-1); r = a+1;
  print m, (1 - (1 - c) ** math.floor(math.log(2, r)))

2 0.495
3 0.33
4 0.43374375
5 0.484150392
6 0.417817125
7 0.456617399413
8 0.483416946706
9 0.4415940551
10 0.465006203908
11 0.483238980643
12 0.452678497552
13 0.469363352144
14 0.483175196779
15 0.494793694573
16 0.472032613906
17 0.483147625356
18 0.492797130255
19 0.473835743219

>>> for m in range(100, 1000, 100):
  c = 0.99 / m; a = 1.0 / (m-1); r = a+1;
  print m, (1 - (1 - c) ** math.floor(math.log(2, r)))

100 0.491634447195
200 0.495807062928
300 0.495521270088
400 0.495378549439
500 0.496292293111
600 0.496068806433
700 0.495909161472
800 0.49641338199
900 0.496251020552

1000 0.496121110593
2000 0.496285044722
3000 0.496505870593
4000 0.496491615824
5000 0.496483063523
6000 0.496477362221
7000 0.496473289977
8000 0.496470235856
9000 0.496467860466

10000 0.496515810046
20000 0.496507258615
30000 0.496521023585
40000 0.496515444608
50000 0.496522066276
60000 0.496518173205
70000 0.49651539243
80000 0.49651953749
90000 0.496517223088

100000 0.496520356059
200000 0.496521993186
300000 0.496520877415
400000 0.496521565628
500000 0.496521978562
600000 0.496521423111
700000 0.496521738439
800000 0.496521974923
900000 0.49652215884

1000000 0.496521807542
2000000 0.496522220475
3000000 0.496522191972
4000000 0.496522177798
5000000 0.496522169092
6000000 0.496522163469
7000000 0.496522159358
8000000 0.496522218726
9000000 0.49652220935

1000000 0.496521807542
2000000 0.496522220475
3000000 0.496522191972
4000000 0.496522177798
5000000 0.496522169092
6000000 0.496522163469
7000000 0.496522159358
8000000 0.496522218726
9000000 0.49652220935

10000000 0.496522201834
20000000 0.496522218205
30000000 0.496522223275
40000000 0.496522214705
50000000 0.496522217672
60000000 0.496522221587
70000000 0.496522222003
80000000 0.496522225028
90000000 0.496522226175

100000000 0.496522217899
200000000 0.496522220646
300000000 0.496522230602
400000000 0.496522220218
500000000 0.496522232255
600000000 0.496522238624
700000000 0.496522223637
800000000 0.496522212528
900000000 0.49652220586

This is consistent with my post back in February where I found:

I can make ever increasing longer sequences which do slightly better, but it appears never to beat 49.65222222222% chance of doubling.

What's the significance of that 49.65222222222% number?

[ndnh]

Initial bet : 0.0001BTC
On lose multiply by : 1.0001010101x

Playing at 9900x

If you win your first bet you stop with a profit of 9899 * 0.0001 = 0.9899 BTC

The goal is to make a profit of 1 BTC.

I think you need to play with a higher multiplier or something.

hehehe yeah.

[dooglus]

Initial bet : 0.0001BTC
On lose multiply by : 1.0001010101x

Playing at 9900x

If you win your first bet you stop with a profit of 9899 * 0.0001 = 0.9899 BTC

The goal is to make a profit of 1 BTC.

I think you need to play with a higher multiplier or something.

hehehe yeah.

Here's a plot of the probability of doubling up against the payout multiplier you use:



I'd love an explanation of why it tops out at 0.496522222!

[mexxer-2]

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?

[dooglus]

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.

[mexxer-2]

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)

[dooglus]

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?

[knowhow]

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.

[Coef]

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.

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?

[wearepoor]

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.

[RHavar]

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

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   )

[dooglus]

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?

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:

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:

     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!