Topic: The reason why Crash Games usually crash at lower values - page 6. (Read 1247 times)
I'm not into the algorithm and other development related conversation. From my understanding crash games too have got specific house edge. According to that the crash will happen, we can't say it isn't going high. Most of the players set value above two gets success, but out of greed people keep on trying to crash above 50. This won't happen everytime, and if there is no crash at lower point then there won't be big profit for the gambling house.
So yesterday a forum member asked me why do Crash Games usually crash at lower multiples (mostly lower than 2x)? Does that mean these games are not fair? Does that mean owner of the site manipulated the game so lower multipliers appear more often than the higher multipliers? I thought other forum members may have these doubts too so I decided to create this thread.
First of all, the algorithm for Crash Game is originally developed by RHavar for his well-known site: bustabit.com
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:
E is the extreme value and refers to as limit. While H is a whole number which can be any number but smaller than E. So for example, if E is 10 then H can be any number between 0 and 9. Hence, range for H is 0 to (E-1).
Now let's calculate crash multiplier value for every possibility of H when E = 10.
So what do we notice above? Among 10 possible values of H, multiplier value as calculated by the formula gave value lower than 2 for 6 events! We can practically ignore H=0 case because it won't be possible practically. Hence, in 5 out of 9 case, value is lower than 2x. This is nothing but probability. By the rule of probability, there is always 50% chance that multiplier value will be lower than 2x and 50% chance for more than 2x value. However, there is another catch, did you notice that H is subtracted from the numerator in the formula before dividing it with (E-H)? This subtraction gives House Edge to casino owner.
So, apart from this catch (which is fair since casino is running business), Crash Games are 100% fair and it's due to the law of probability that multiplier crashes below 2x almost 50% of the times.
After Bustabit v2, most of the crash games started using this formula to calculate multiplier:
This formula is almost similar to earlier formula. Only fixed House Edge of 1% is the difference. However, sites like Roobet are still using old formula.
Note: Casino owners can practically take any value as E and then range of [0,E-1] will become H. However, since provably fair results are based on hashes which represents value in binary, E has to have value in the multiple of 2 e.g. 22,23,24 and so on. But there is inherit limitation of Javascript that it cannot precisely show floating number beyond 64 bits so most of the site uses 252 as E and range of [0,252-1] for H. With recent introduction of BigInt, it is now possible to precisely represent numbers larger than 253-1 in Javascript. Let's see if any casino will use whole hash i.e. 256 bits number as H in future which will make E = 2256.
First of all, the algorithm for Crash Game is originally developed by RHavar for his well-known site: bustabit.com
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:
CRASH MULTIPLIER = [(E*100 - H)/(E-H)]/100
E is the extreme value and refers to as limit. While H is a whole number which can be any number but smaller than E. So for example, if E is 10 then H can be any number between 0 and 9. Hence, range for H is 0 to (E-1).
Now let's calculate crash multiplier value for every possibility of H when E = 10.
| 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 |
So what do we notice above? Among 10 possible values of H, multiplier value as calculated by the formula gave value lower than 2 for 6 events! We can practically ignore H=0 case because it won't be possible practically. Hence, in 5 out of 9 case, value is lower than 2x. This is nothing but probability. By the rule of probability, there is always 50% chance that multiplier value will be lower than 2x and 50% chance for more than 2x value. However, there is another catch, did you notice that H is subtracted from the numerator in the formula before dividing it with (E-H)? This subtraction gives House Edge to casino owner.
So, apart from this catch (which is fair since casino is running business), Crash Games are 100% fair and it's due to the law of probability that multiplier crashes below 2x almost 50% of the times.
After Bustabit v2, most of the crash games started using this formula to calculate multiplier:
CRASH MULTIPLIER = 0.99*E/(E-H)
This formula is almost similar to earlier formula. Only fixed House Edge of 1% is the difference. However, sites like Roobet are still using old formula.
Note: Casino owners can practically take any value as E and then range of [0,E-1] will become H. However, since provably fair results are based on hashes which represents value in binary, E has to have value in the multiple of 2 e.g. 22,23,24 and so on. But there is inherit limitation of Javascript that it cannot precisely show floating number beyond 64 bits so most of the site uses 252 as E and range of [0,252-1] for H. With recent introduction of BigInt, it is now possible to precisely represent numbers larger than 253-1 in Javascript. Let's see if any casino will use whole hash i.e. 256 bits number as H in future which will make E = 2256.
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