Topic: The reason why Crash Games usually crash at lower values - page 4. (Read 883 times)

So 857 times out of 10 000 times it will crash below 1.05 (on average). So lets say that you are going to play 10 000 games putting 1$ in each game cashing out at 1.05. In this situation you will win 9143 times winning 9143*0.05 = 457.15$ and lose 857 times losing 857 * 1$ = 857$ ending up with 399.85$ net loss.

I'll check rest of your calculation in free time

Great thread.

A lot of people go on to accuse provably fair games unfair when they don't even understand the mathematics behind it.

I'm not sure why - it seems like people are either lazy, or don't get maths, or perhaps a combination of both.

I read the reply a couple of times and recall what I learnt from the college stat., I think it really gives me good information on how everything is being controlled. I am planning to write an app to reproduce this game for fun. I did some research and I see the following formula to approach the cumulative probability function for the multiplier given as  crash_multiplier = (100 * e - h) / (e - h) / 100

P(X<=x) = 1 - 1/x

where X is a random multiplier and x is the certain cap of the multiplier, it is saying that the chance to see any multiplier less than a given value of x is the complement of 1/x. So when x=2, it is 1-1/2 = 0.5 or 50% of chance to have any multipliers less than 2x. Here I am confused about the gameplay. What should I do to pick the crash_multiplier for each game? I saw that P(X<=x)=1-1/x is derived in the assumption that h is a uniform random number so I guess   I should just pick a uniformly random number (h) between for [0, e-1] as the crash_multiplier for each game and let the player bet on it and wait for the player's cashing out? And that is all?

What about the incremental of the multiplier in time, could the multiplier increase at any interval?

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After reading this, I read more online and I found this one https://github.com/MindingTheData/Crash-Analysis/blob/master/Crash.ipynb
 it uses a similar formula for multiplier but better approximation for the cumulative prob function, I run the code and add all the expectation values for multiplier from 1 to 1000


it ends up with a return of about 96%. If I take multiplier=1.05, should I have P(X<=1.05) = 1/33 + 32/33*(0.01 + 0.99*(1-1/1.05)) = 8.57%, which is pretty low, it doesn't mean if I bet on 1.05x each time, only 8.57% of chance it crashes with multiplier less than 1.05? I am quite confused. I don't understand why all the discussions in this thread are about winning the double of the bet (2x). If I win 1.05x, deduct the bet=1 I made, I still have 0.05 win, isn't it?

I try the following simulation

which gives something close to 96% but if I fixed the bet_mul to 1.05, I get about 96.9%. Why is it?

If I understand it correctly, the advantage the casino took is on the 1/33 chance to crash instantly, but the bet it still has 32/33 of chance that fixing the 1.05 may end up with a higher return in the simulation, I don't know what is wrong in my code.


[moderator's note: consecutive posts merged]

with 1.05x you need to bet and win 20 times to double your 1$. When you lose you lose your 1$. The problem with this strategy is that crash (and every casino game) is calculated in a way that casino has statistic advantage over you. So in this case you will lose once each 19 times (ON AVERAGE! You can have 100 wins strike but sooner or later your luck will end). So each time you will win 95 cents with this strategy, you will lose 1$ and be short 5 cents (ON AVERAGE!).


Each bet on provably fair casino is completly random. So no ... resetting seed, "avoid betting continuously", wearing talismans does not work.


"theoretically" ?

Most of the time I don't really play crash really realizing all the things and this is honestly the first formula that I saw in my life regarding these games.
When we talk about this formula how would all the casinos follow the same one ?
Crash games for me are really one based on luck but seeing your formula I feel like I should get more into see how it works and how it would be beneficial for the player to encash every once in a while when they start.
Usually you would have to avoid betting continuously since it would make your chances of winning go down and I heard a lot of players say how fixing the seeds again works for them, so therefore I usually use crash after resetting my seeds and not continually at the same time.

Mathematics is always theoretically correct but an interesting point to analyze here.

ah, now I understand. Many thanks.

If a player decides to bet $1 at a time but chooses to cash out when it is 1.05x reaches and repeat this strategy thousands of times, will it benefit the player to have positive gain? Why not and how does the math forbid that to happen?

Maybe because E=2^52 = 4 503 599 627 370 496 so H=1000 is close to 0, even 1E8 is close to 0 in this scale, because comparing to E=2^52 your pick - H=1E8 is 50 million times smaller. Use H=2^50 or something like this (or 2^52-1) to check if you calculate everything correct.

Thanks. But I think that example is valid when E=10, what I am confused about is the casino chose E=2^52, even I choose H=1000 or 1E8, the formula still gives me 1 instead.

No. There is always the same risk/reward ratio. There is no difference in strategy you pick. There is no diifference in multiplier you aim to hit. You always have ~90-98% from your bet back to your account from each bet, on average. This 2-10% is casino house edge. There is no way to outperform other, not even saying about outperforming casino. The only way to win is by having luck.


Its not 1. OP gave few examples. You had to make a mistake in the order of performing mathematical operations

Thanks for the great post. I am studying the game for fun and happen to see the math in the forum. It is the first time I understand how it works with my limited college knowledge in statistics. I do understand the formula to produce the multiplier as follows

crash multiplier = (100 * e - h) / (e - h) / 100

e is the maximum multiplier one could have, but from other replies, it mentioned e will be 2^52 in javascript, does it mean the multiplier could go up that that high? I don't know javascript but I try to implement the formula (with e=2^52) in c++, no matter what h is, the crash multiplier is always ONE?

Besides, I saw someone said there is at least 50% of chance the multiplier is 2 or less. If I bet 1 dollar at a time, each time I cash out if saw the multiplier raised to 1.1x, will it give me more chance to win something small each time? If no,  why not?

Yes you're right X=H/E

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You're right it's the v1 version
https://github.com/Dexon95/Bustabit/blob/master/gameserver/server/lib.js

But in this version the house edge is computed like that as far as I understand :

  // In 1 of 101 games the game crashes instantly.
    if (divisible(hash, 101))
        return 0;

    // Use the most significant 52-bit from the hash to calculate the crash point
    var h = parseInt(hash.slice(0,52/4),16);
    var e = Math.pow(2,52);

    return Math.floor((100 * e - h) / (e - h));

While in the Roobet version, 101 has been replaced by 25.
It means there is an instant crash every 25 game rounds, ie 4 times out of 100.
So we can assume the house edge is at 4% on Roobet...  

If it hits many times above 2x or more then what will be the benefit of the house who is hosting the crash game ? Ofcourse as with every other game, you have very few chances to get more out of gambling houses and crash game is not any different. You can only hit big in a crash games if you have money to take risk in many bets before you land on a big milestone.

While crash shows that it's hitting many times under 2x, the one or two times we also see it hits thousands or even millions of wins. I think it's evenly spread out and even in other games, the chances of hitting 2x is exactly the same of what is in crash. Thanks for the nice explanation of how it originated and how it's calculated!

Not all crash game shows actual odds of winnings. It is not roulette or dice where you can calculate your odds and house edge easily. Formula with E and H is shown only in fairness section and only for few gambling sites (big part of "provably fair" casinos are "provably fair" only for 1-2 games, rest games "provably fair" section is under construction forever). House edge on these games can be set to 20% and you don't know it. Does it mean that output is "manipulated" and "not fair"? To me, As long as casino share formula how crash is calculated it is fair. It's gambler fault that did not check how high casino set house edge.

But back to OP. Great explanation how crash is calculated. Good work.

Formula with H and E is very clever because it provides consistent commission for the casino no matter where players positions their bets.

You want to double? You have 4x% to do so
You want to tripple? you have <33% to do so - 3/10 above 3

You want to do 10x? you have <10% to do so

and so on and on. No matter where you put your bet. Math take care that you have same risk/reward ratio and casino have it's share.

Just because Roobet is growing successfully, that doesn't mean it is a pioneer of Bitcoin Gambling Industry! Stop believing gambling sites blindly. Here's the proof that Roobet's crash game is based on the same algorithm (taken right from the 'Fairness' page of Roobet):



Do you see a red box? Can you read the formula inside? Isn't it same to the one in OP?

Don't think that I will write random things anywhere on forum without any knowledge. If I was sure enough to include that line in OP, it does mean that I am sure about the fact. Period!

I think that the algorithm is what matter the most in software controlled games.In slot machines it is the algorithm that controls everything and although most of the providers say each spin is independent of each other we all know that getting on the reels the top combination happens rarely because the algorithm has decided so bu being programmed by the developers of the game to behave that way.Same with crash games and other software related games.

I have derived formula on my own. It's basically the same. What you are showing are the steps to find the result from coding point-of-view. But in compact form it's exactly same as the second formula I derived in the OP, let me show you how:

Step 1: Starting point -> 99 / (1-X)

Step 2: Inserting the value of X in the formula:



where R is a random number taken from first 52-bits of the hash and E is 2⁵²

Step 3: Taking LCM in denominator:



R = H

Step 4: Taking 'E' to the numerator:



Step 5: Finally dividing the result by 100 to get multiplier value:




I just missed one step, if the resulting value of multiplier is below 1 then return 1. Rest of the formula is completely correct.

But IMO, there are a lot of gambling sites out there that uses their own algorithm and had their limits or was being manipulated. I've encountered a lot of issues in many gambling platforms I've tried back then and read many accusations of them being either too much fair that they made others win drastically big, or they made many loss too much. And that leads me to another idea that algorithms doesn't matter nowadays, as many enters gambling mostly not as their profit making habit, but a time to enjoy playing gambling games.

But then if they would ever made an unfair one, it would simply make a huge impact in their reputation as the possibility of loses are bigger than the wins. I think they are making their own algos that would fit their categories such as how many wins can a user have in their crash games together with the chances they could have from time to time.

 But I do disagree with Insanerman, that algorithms do have impact in gambling and knowing it would make a gambler be attentive when to bet and what strategy to use. If we didn't knew algorithm, we'll soon be losing our money as we only know how to make fun and be satisfied.

Can't really expect the casino to create an algorithm that would prove to be an advantage to players now, can we. I've never really seen crash games being unfair tbh, I mean, even my common sense would indicate that if they didn't crash at lower values, they'd probably be losing out quite a lot.
I guess Op just wanted to prove that Crash games are provably fair, and is not manipulated by the gambling sites. Well, the core idea of the algorithms of crash should closely follow what Op said and shouldn't deviate that much. They may change it up to increase their house edge or vice versa, but the idea remains the same. Besides, with the amount of crash matches that happen every day, someone winning big every now and then isn't even that weird or odd.