The reason why Crash Games usually crash at lower values

[fiulpro]

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.

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?

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.

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

no matter what h is, the crash multiplier is always ONE?

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

Possibilities	Multiplier
H=0	1
H=1	1.11
H=2	1.24
H=3	1.42
H=4	1.66
H=5	1.99
H=6	2.48
H=7	3.31
H=8	4.96
H=9	9.91

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.

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[Tytanowy Janusz]

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?

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!).

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.

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

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

"theoretically" ?

[gin.zhe]

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?

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!).

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.

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

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

"theoretically" ?

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?

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?

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!).

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.

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

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

"theoretically" ?

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

Code:

e = 0
N = 0
for multiplier in np.arange(1, 1000, 0.01):
  N = N+1
  e = e + 1 + ((1/33) + (32/33)*(.01 + .99*(1 - 1/(multiplier-.01))))*-1 + (multiplier-1)*(1 - ((1/33) + (32/33)*(.01 + .99*(1 - 1/(multiplier-.01)))))

e/(N/1.0)

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

Code:

e = 2**52
N = 20000
M = 100000
win = 0
for n in range(M):
    h = np.random.randint(0, e-1, size=N)
    crash_mul = (((100 * e - h) / (e-h)) // 1) / 100.0
    crash_mul = (np.random.uniform(size=N)>=(1/33.0))*crash_mul
    bet_mul = np.random.uniform(1.05, 100.06, size=N)
    win = win + bet_mul[bet_mul<crash_mul].sum()

win/(N*M)

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]

[timerland]

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.

[Tytanowy Janusz]

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. If I win 1.05x, deduct the bet=1 I made, I still have 0.05 win, isn't it?

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

[gin.zhe]

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. If I win 1.05x, deduct the bet=1 I made, I still have 0.05 win, isn't it?

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

Yes, I think it sounds right to me. What I am going to say is the math may guarantee for gambler will lose for the long term (the return is just 96% for all possible multipliers taken into account); however, if you bet the small multiplier always, since the probability of getting the crash multiplier less than your betted multiplier is smaller than 10% (if my math is correct), it will not increase the return above 100% but it will gain a bit advantage to players?

[AicecreaME]

~

Does algorithm really matter? It's not just the crash game that usually has low values and less possibility of winning, it is also in every game in gambling, and in any platform. But I don't think that Roobet uses the old algorithm as there are already huge number of players that win a big amount in playing Roobet's crash game. And how are you even sure that they are using RHavar's code and not their own? I think only those famous betting platforms with crash games back then only uses that, and new innovating ones are making their own adjustments with the code.

Algorithm is important, because you'll know how the game works. You'll know a lot of things that could help you to verify how many percentage of winning you have in a certain gambling game. Also, I don't know how they found out the algorithm of a game since gambling sites would never make it public, unless someone from inside made a leaked information about it. Knowing the code or algorithm make a game boring, since everyone knows the secret.

[Tytanowy Janusz]

Yes, I think it sounds right to me. What I am going to say is the math may guarantee for gambler will lose for the long term (the return is just 96% for all possible multipliers taken into account); however, if you bet the small multiplier always, since the probability of getting the crash multiplier less than your betted multiplier is smaller than 10% (if my math is correct), it will not increase the return above 100% but it will gain a bit advantage to players?

Player never have advantage over casino. If you plan to grab 1.05 once with more than 90% probability of success and than run away with your profit and thats where you find "advantage" you need to know that even now casino has advantage. Because out of 10 people who will test your strategy 1 will lose more than the other 9 will win. You may in the lucky 9 or in unlucky one guy. You never know, but risk/reward ratio is negative.

[goaldigger]

Yes, I think it sounds right to me. What I am going to say is the math may guarantee for gambler will lose for the long term (the return is just 96% for all possible multipliers taken into account); however, if you bet the small multiplier always, since the probability of getting the crash multiplier less than your betted multiplier is smaller than 10% (if my math is correct), it will not increase the return above 100% but it will gain a bit advantage to players?

Player never have advantage over casino. If you plan to grab 1.05 once with more than 90% probability of success and than run away with your profit and thats where you find "advantage" you need to know that even now casino has advantage. Because out of 10 people who will test your strategy 1 will lose more than the other 9 will win. You may in the lucky 9 or in unlucky one guy. You never know, but risk/reward ratio is negative.

This sounds interesting but confusing at the same time.
Crash game is just like a slots game with a little twist since you can control when to take profit, and the house always win on this kind of game since its based on their system and they already worked to that numbers so someone will really lose the money, this is gambling after all.

[Mahanton]

Yes, I think it sounds right to me. What I am going to say is the math may guarantee for gambler will lose for the long term (the return is just 96% for all possible multipliers taken into account); however, if you bet the small multiplier always, since the probability of getting the crash multiplier less than your betted multiplier is smaller than 10% (if my math is correct), it will not increase the return above 100% but it will gain a bit advantage to players?

Player never have advantage over casino. If you plan to grab 1.05 once with more than 90% probability of success and than run away with your profit and thats where you find "advantage" you need to know that even now casino has advantage. Because out of 10 people who will test your strategy 1 will lose more than the other 9 will win. You may in the lucky 9 or in unlucky one guy. You never know, but risk/reward ratio is negative.

This sounds interesting but confusing at the same time.
Crash game is just like a slots game with a little twist since you can control when to take profit, and the house always win on this kind of game since its based on their system and they already worked to that numbers so someone will really lose the money, this is gambling after all.

Basing up with those calculations and numbers on where OP had written then not all would really able to get on whats been said on that yet everyone would really presume out on general perspective when it comes to odds and chances with crash games.

House do always win in the end and its always been like this.Doesnt matter you are dealing with crash games,dice or slots then it will really be just giving off
the same vibe.

Thing here is that you do enjoy on what you are doing.

[AmoreJaz]

Yes, I think it sounds right to me. What I am going to say is the math may guarantee for gambler will lose for the long term (the return is just 96% for all possible multipliers taken into account); however, if you bet the small multiplier always, since the probability of getting the crash multiplier less than your betted multiplier is smaller than 10% (if my math is correct), it will not increase the return above 100% but it will gain a bit advantage to players?

Player never have advantage over casino. If you plan to grab 1.05 once with more than 90% probability of success and than run away with your profit and thats where you find "advantage" you need to know that even now casino has advantage. Because out of 10 people who will test your strategy 1 will lose more than the other 9 will win. You may in the lucky 9 or in unlucky one guy. You never know, but risk/reward ratio is negative.

This sounds interesting but confusing at the same time.
Crash game is just like a slots game with a little twist since you can control when to take profit, and the house always win on this kind of game since its based on their system and they already worked to that numbers so someone will really lose the money, this is gambling after all.

Basing up with those calculations and numbers on where OP had written then not all would really able to get on whats been said on that yet everyone would really presume out on general perspective when it comes to odds and chances with crash games.

House do always win in the end and its always been like this.Doesnt matter you are dealing with crash games,dice or slots then it will really be just giving off
the same vibe.

Thing here is that you do enjoy on what you are doing.

and if you are playing this crash game in manual mode, i definitely can say, you will have adrenaline rush. but time and time, if you will continue to play, you will end up losing in this game if you don't know when to stop. i don't consider this game to where you can possibly gain profits, but just a mere entertainement only. as you said, at the end, house always win in most classic games.

[Mahanton]

Yes, I think it sounds right to me. What I am going to say is the math may guarantee for gambler will lose for the long term (the return is just 96% for all possible multipliers taken into account); however, if you bet the small multiplier always, since the probability of getting the crash multiplier less than your betted multiplier is smaller than 10% (if my math is correct), it will not increase the return above 100% but it will gain a bit advantage to players?

Player never have advantage over casino. If you plan to grab 1.05 once with more than 90% probability of success and than run away with your profit and thats where you find "advantage" you need to know that even now casino has advantage. Because out of 10 people who will test your strategy 1 will lose more than the other 9 will win. You may in the lucky 9 or in unlucky one guy. You never know, but risk/reward ratio is negative.

This sounds interesting but confusing at the same time.
Crash game is just like a slots game with a little twist since you can control when to take profit, and the house always win on this kind of game since its based on their system and they already worked to that numbers so someone will really lose the money, this is gambling after all.

Basing up with those calculations and numbers on where OP had written then not all would really able to get on whats been said on that yet everyone would really presume out on general perspective when it comes to odds and chances with crash games.

House do always win in the end and its always been like this.Doesnt matter you are dealing with crash games,dice or slots then it will really be just giving off
the same vibe.

Thing here is that you do enjoy on what you are doing.

and if you are playing this crash game in manual mode, i definitely can say, you will have adrenaline rush. but time and time, if you will continue to play, you will end up losing in this game if you don't know when to stop. i don't consider this game to where you can possibly gain profits, but just a mere entertainement only. as you said, at the end, house always win in most classic games.

In most crash games i do play there are  even people who do set out automatically 1.01x multiplier and when they do bust up since theres 1.00x number bust  up then those penny profits would gone in an instant or on a breeze which i dont really see to be that relevant or interesting on setting up those numbers considering that
crash could  happen in number of  bets.When playing crash then i do much prefer on setting it on 2x profit then cash out but there  are times when
greed kicks in then  you do go YOLO.

[YOSHIE]

Most of the sites having Crash as a game are using one or the other version of his algorithm. Basically, crash game is based on this mathematical formula:

I also think that the algorithm works to sort the steps in completing the Crash game in the shortest time and the highest time, for example: 2.68X to 100.00X and so on.

Gambling sites using algorithms, especially Crash games, they can be defined as computer programs in determining steps and instructions as I know (input or output) this is logical.

Because I see in some game crashes, one or two rounds can reach 2.78X and the third 10.56X so on can shift in the sixth round can reach 100X, here it can be said, if I predict the Algorithm system is needed, 5% I think someone who controls the game crash may not at all let alone apply 24 hours.

[KTChampions]

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.

Knowing the algorithm is quite interesting, but in fact, if it does not contain any errors, it does not give you any information that you could use in the game to improve your results. As for the relationship between spins, it does not occur at the level of programming of each spin, but at the level of the algorithm + a random number generator that provides input signals to this algorithm. We can say that each spin is really independent.

[Tytanowy Janusz]

and if you are playing this crash game in manual mode, i definitely can say, you will have adrenaline rush. but time and time, if you will continue to play, you will end up losing in this game if you don't know when to stop. i don't consider this game to where you can possibly gain profits, but just a mere entertainement only. as you said, at the end, house always win in most classic games.

There is no game that is designed in a way to be a place "where you can possibly gain profits". Each game is designed in a way to let you win back what you put in minus house edge (on average) with every bet you make. It does not matter what game you play. If you plan to cash out at x2 on crash you can go to dice and play high/low with x2 reward or roulette black/red. It will have the same output for you. In the end of the day its all about emotions during playtime (not about winning in a long run because its impossible). Thats why crash is so popular, especially when you have no plan about when you want to exit.

[Distinctin]

Great effort on analyzing the game but honestly IMO it's not necessary anymore as knowing the house has the edge, even how small it is, would already tell us that we will never win in the long run. That's why in my case, I don't spend much time and effort anymore on analyzing how to win in a game where there's a house edge as I know my real chance, I call that a luck-based game.

[JohnBitCo]

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. If I win 1.05x, deduct the bet=1 I made, I still have 0.05 win, isn't it?

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

It won't be reasonable to take profit at 1.05 on 10,000 games. Lets suppose if some one take profit at 2x on every crash game, will be be profitable even with you losing more games and wining few ?  Or you can try with taking profit at 30x in the 100 games with 1 dollar in each game. I tried to calculate with different values but could not find a fool proof winning formula.

[robelneo]

This sounds interesting but confusing at the same time.
Crash game is just like a slots game with a little twist since you can control when to take profit, and the house always win on this kind of game since its based on their system and they already worked to that numbers so someone will really lose the money, this is gambling after all.

I'm playing the Crash game and it's one of the exciting and less boring games I always check if there are crash games on casinos I'm playing but compared to the other luck-based game you have control over when you want to stop and to pass, I never think of probability unless I have a big wage and decided that I will try to beat the house edge, but in the long run after all the computation the house will still win, unless someone uses that formula and claim that he wins big using that formula.

[Woodie]

wow it actually gets mathematically interesting getting to the reason why Crash crashes at lower values but unfortunately the OP has a handful of information to really get how the whole algorithm works in such a way.

There is no game that is designed in a way to be a place "where you can possibly gain profits". Each game is designed in a way to let you win back what you put in minus house edge (on average) with every bet you make.

at the end of the day casino games arent all about fun and games, this is a profit making business and i will disagree to this statement that it will late you break even in all your runs....if it were designed like this then martingale would have been the best strategy to win  on casino games!!

It does not matter what game you play. If you plan to cash out at x2 on crash you can go to dice and play high/low with x2 reward or roulette black/red. It will have the same output for you.

crash games are volatile and unpredictable , i have seen on several occasions a string of less than x1.3 get hit and nothing of a x2 which makes this unpredictable, roulette has to be a better choice of games

[Beparanf]

This sounds interesting but confusing at the same time.
Crash game is just like a slots game with a little twist since you can control when to take profit, and the house always win on this kind of game since its based on their system and they already worked to that numbers so someone will really lose the money, this is gambling after all.

I'm playing the Crash game and it's one of the exciting and less boring games I always check if there are crash games on casinos I'm playing but compared to the other luck-based game you have control over when you want to stop and to pass, I never think of probability unless I have a big wage and decided that I will try to beat the house edge, but in the long run after all the computation the house will still win, unless someone uses that formula and claim that he wins big using that formula.

There's no way to beat the house since we don't have any idea on the size of there bank roll. The only way that you can possibly defeat the house is when your money greater than to the house bank roll since your enemy is a fixed percentage of your bet and you will lose in the long run if your bank roll can't withstand the long lose streak. As the OP probability tabulated, You can possibly win if you can bet most of the round with fixed amount and cashout on same target price for as many round as possible until the long green streak come. Playing it randomly will not gonna give a significant result overtime.