Dice Game Odds/Statistics Question

Hello,

This is my first post and I hope it is well received.

I am curious as to the odds of missing 23 'rolls' in a row. I will do the best to describe what I am speaking of, but am not too terribly versed in statistics terms:

primedice.com utilizes bitcoin as its gambling currency. It allows you to roll 'Provably Fair' number each time you 'roll the dice.'

The results can be from and including 0.00 to 99.99.

You bet on your roll being higher or lower than a certain number. The house does have an edge where it does not allow you to bet higher than 50.00 or lower than 50.00 to receive 2x payment of your bet. Rather, if you are looking for 2x payment, you need to bet over 50.49 or under 49.50 to receive 2x payment.

I have a plan and bankroll to do the following:

I would like to roll under 36.00 and recieve 2.75x my bet. If i lose the bet, i will increase my bet by 60% and try again. I have put this into an excel spreadsheet, and assuming I lose 23 times in a row right off the bat, I will be bankrupt.

My question is:

What are the odds that I would not hit under 36.00 23 times in a row? Please provide an explanation of your findings so others can verify or critique. Thank you so much for your help in advance!

Michael

0.36^23

Quote: mrbtc11

Hello,

This is my first post and I hope it is well received.

I am curious as to the odds of missing 23 'rolls' in a row. I will do the best to describe what I am speaking of, but am not too terribly versed in statistics terms:

primedice.com utilizes bitcoin as its gambling currency. It allows you to roll 'Provably Fair' number each time you 'roll the dice.'

The results can be from and including 0.00 to 99.99.

You bet on your roll being higher or lower than a certain number. The house does have an edge where it does not allow you to bet higher than 50.00 or lower than 50.00 to receive 2x payment of your bet. Rather, if you are looking for 2x payment, you need to bet over 50.49 or under 49.50 to receive 2x payment.

I have a plan and bankroll to do the following:

I would like to roll under 36.00 and recieve 2.75x my bet. If i lose the bet, i will increase my bet by 60% and try again. I have put this into an excel spreadsheet, and assuming I lose 23 times in a row right off the bat, I will be bankrupt.

My question is:

What are the odds that I would not hit under 36.00 23 times in a row? Please provide an explanation of your findings so others can verify or critique. Thank you so much for your help in advance!

Michael

I'm not sure how this post will be received, Michael. You see, the thread title is an advertisement and the forum rules prohibit that. Perhaps you could ask one of the administrators to change the title to something more acceptable. I recommend Face or Mission.

1BB,

Thank you for the advice and heads up! I am really just interested in the answer, and hope that without the site, it can still be given. So, um, Admin, if you are reading this, can you please change the title to: 'Dice Game Odds/Statistics Question'

Thank you!

Quote: mrbtc11

1BB,

Thank you for the advice and heads up! I am really just interested in the answer, and hope that without the site, it can still be given. So, um, Admin, if you are reading this, can you please change the title to: 'Dice Game Odds/Statistics Question'

Thank you!

You're welcome, Michael. I have every confidence that our fair admins will accommodate you and correct this innocent and minor oversight. Welcome to the forum! May you enjoy it as much as I have.

FWIW I vote for clemency as no ill intent on the title. That and $1 will get the poster a cup of coffee.

I do request please report back. I have wondered about this kind of thing at various sites myself. "Systems" can work short-term if you do not mind a total loss and if you have a wide enough spread to bet with. Sadly any bonuses online I see are such that it is too hard to make it work. Good luck!

AZDuffman... much appreciated good sir!

The goal here is to deposit 1 Bitcoin(btc) to the site, and use the method I described above. I will have my base bet be .00001 btc. Upon loss you can see the next bet below. Upon winning, no matter where on the table, I start back at .00001 btc. According to my test simulations, if I have it run for 24 hours on autobet with these settings I will then have 1 btc in profit. Sounds easy huh? likely not, I agree that it may just be a lucky streak thing.... which is why I am very curious about the odds on missing 23 rolls with the settings I mentioned in my original post.

Either way, I'm likely going to do it and will get back at y'all with results!

Sum Wager Roll Winnings Profit
0.00001000 0.00001000 1 0.00001750 0.00001750
0.000026000 0.00001600 2 0.00002800 0.00001800
0.000051600 0.00002560 3 0.00004480 0.00001880
0.000092560 0.00004096 4 0.00007168 0.00002008
0.000158096 0.00006554 5 0.00011469 0.00002213
0.000262954 0.00010486 6 0.00018350 0.00002540
0.000430726 0.00016777 7 0.00029360 0.00003065
0.000699161 0.00026844 8 0.00046976 0.00003904
0.001128658 0.00042950 9 0.00075162 0.00005246
0.001815853 0.00068719 10 0.00120259 0.00007393
0.002915364 0.00109951 11 0.00192415 0.00010829
0.004674583 0.00175922 12 0.00307863 0.00016327
0.007489333 0.00281475 13 0.00492581 0.00025123
0.011992932 0.00450360 14 0.00788130 0.00039197
0.019198692 0.00720576 15 0.01261008 0.00061715
0.030727907 0.01152922 16 0.02017613 0.00097743
0.049174651 0.01844674 17 0.03228180 0.00155390
0.078689441 0.02951479 18 0.05165088 0.00247623
0.125913106 0.04722366 19 0.08264141 0.00395197
0.201470970 0.07555786 20 0.13222626 0.00631316
0.322363552 0.12089258 21 0.21156202 0.01009105
0.515791683 0.19342813 22 0.33849923 0.01613568
0.825276693 0.30948501 23 0.54159877 0.02580708
1.320452709 0.49517602 24 0.86655803 0.04128133

Here's what I get: (All numbers should be multiplied by 0.00001)

Rolls before winning	Probability	Losses up to this point	Amount won on the winning bet	Expected Value
0	0.36	0	1.75	0.63
1	0.2304	1	2.8	0.41472
2	0.147456	2.6	4.48	0.27721728
3	0.09437184	5.16	7.168	0.1894986547
4	0.0603979776	9.256	11.4688	0.1336486448
5	0.0386547057	15.8096	18.35008	0.0982015066
6	0.0247390116	26.29536	29.360128	0.0758193312
7	0.0158329674	43.072576	46.9762048	0.0618060277
8	0.0101330992	69.9161216	75.16192768	0.0531562732
9	0.0064851835	112.86579456	120.259084288	0.0479468403
10	0.0041505174	181.585271296	192.4145348608	0.044947047
11	0.0026563311	291.5364340736	307.8632557773	0.043369445
12	0.0017000519	467.4582945178	492.5812092436	0.0427102598
13	0.0010880332	748.9332712284	788.1299347898	0.0426472728
14	0.0006963413	1199.2932339655	1261.0078956637	0.042974466
15	0.0004456584	1919.8691743448	2017.612633062	0.0435601948
16	0.0002852214	3072.7906789516	3228.1802128992	0.0443204181
17	0.0001825417	4917.4650863226	5165.0883406387	0.0452015664
18	0.0001168267	7868.9441381161	8264.1413450219	0.0461695774
19	0.0000747691	12591.3106209857	13222.626152035	0.0472028781
20	0.0000478522	20147.0969935772	21156.201843256	0.048287895
21	0.0000306254	32236.3551897235	33849.9229492097	0.0494161791
22	0.0000196004	51579.1683035576	54159.8767187355	0.0505825671
23	0.0000348449	82527.6692856921	0	-2.8756695696

The total Expected Value is -0.3022652445

If you were do this once, or a small number of times, you would book a very small profit. If you set it to autobet, and run it millions of times, you will lose your bitcoin.

As the others have shown, the odds of losing 23 times in a row is just 0.64^23 = 0.000035

Small, but will happen eventually.

ThatDonGuy,

Thank you so much for putting this together! So, I am good at math and calculations... however, statistics and meanings.... not so much.

Would you be kind enough to answer a couple questions?

The probability keeps going down because there are more chances to hit the wrong side of my bet than the correct side yes? Can you explain what exactly the probability means to me?

What exactly is expected value? Also, I noticed on roll 14 the expected value reversed course and started to go back up... is this a good thing for me? Should I look into betting less on the first roll to increase the amount of rolls I can afford with my bankroll to achieve a higher expected value?

Thanks again and pardon my ignorance to this field of math. Your help is much appreciated!

Quote: mrbtc11

Sum Wager Roll Winnings Profit
0.00001000 0.00001000 1 0.00001750 0.00001750
0.000026000 0.00001600 2 0.00002800 0.00001800
0.000051600 0.00002560 3 0.00004480 0.00001880

Your "Profit" column is misleading; it only shows the profit for that winning roll, not the profit compared to everything you have wagered up to that point.

For example, in the second row, the overall profit is 0.000002, and in all subsequent rolls the overall profit is negative.

Quote: mrbtc11

The probability keeps going down because there are more chances to hit the wrong side of my bet than the correct side yes? Can you explain what exactly the probability means to me?

The probability column is the probability of having the listed number of losing rolls and then winning, except for the last row, where it is the probability of 23 losing rolls in a row without a winner.
The probability of winning after 0 losing rolls - that is, winning on the first roll - is 0.36
The probability of winning after 1 losing roll - that is, winning on the second roll - is 0.64 (the probability that the first roll is a loser) x 0.36 (the probability that the second roll is a winner) = 0.2304
The probability of winning after 2 losing rolls is 0.64 x 0.64 (the probability that the first two rolls are both losers) x 0.36 (the probability that the second roll is a winner) = 0.147456
The probability goes down because you multiply each row's value by 0.64 to get the value below it.

Quote: mrbtc11

What exactly is expected value?

Expected value = probability x profit (or loss, if it is negative). The expected value of a bet is the sum of all (probability of a particular result x profit of that result) over all possible results.

Quote: mrbtc11

Also, I noticed on roll 14 the expected value reversed course and started to go back up... is this a good thing for me? Should I look into betting less on the first roll to increase the amount of rolls I can afford with my bankroll to achieve a higher expected value?

The individual expected values go up because you are betting more and more as you get more and more consecutive losses.

For any particular roll, the expected value = (0.36 x (1.75 x the bet)) + (0.64 x (-1 x the bet)) = -0.01 x the bet. Regardless of how you shuffle the bets around, you can expect to lose 1/100 of what you bet with each roll.