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Author Topic: Stake Crash: I analyzed all 8.2M rounds since 2019 - Math Explained (Video)  (Read 422 times)
ProvablyFair.org (OP)
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July 06, 2026, 06:54:16 PM
Last edit: July 07, 2026, 11:29:27 AM by ProvablyFair.org
 #1

Hi guys,

I made a math explainer video breaking down Stake Crash.

Stake's Crash game has taken $26B in wagers over 7 years. Is it actually fair? I re-derived all 8.2 million rounds it has ever played and checked the maths.

Full breakdown (7 min): https://www.youtube.com/watch?v=hkZLSdRtkVc

How it works: before the first round in 2019, Stake committed to a future Bitcoin block hash (584,500) and a chain of 10 million pre-generated hashes, published in https://bitcointalk.org/index.php?topic=5162888.0 before any round went live. Those two values determine every crash point through one cryptographic calculation. Every result was fixed in 2019, and one altered result breaks the chain instantly and publicly.

Code:
Target             Rounds reached   Observed     Theory
Instant (1.00x)         [COUNT]       1.97%      1.98%
Reach 1.5x            5,442,953     66.000%    66.000%
Reach 2x              4,083,123     49.511%    49.500%
Reach 5x              1,633,849     19.812%    19.800%
Reach 10x               817,238      9.910%     9.900%
Reach 50x               163,711      1.985%     1.980%
Reach 100x               81,773      0.992%     0.990%
Aggregate RTP         8,246,854     99.087%    99.000%

The 1% edge holds at every cash-out target, so no strategy changes the return.

The interesting part: Stake has known all 10 million results since 2019 and still can't touch one. The original seed is the master key; anyone holding it could regenerate the chain and predict every remaining round. Seven years without a leak is impressive OPSEC.

Disclosure: I run ProvablyFair.org. Stake is not a client, no affiliate or referral links, nobody paid for this.

This is the first video I've made, If you find it valuable and want another game broken down let me know.
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July 07, 2026, 05:10:07 AM
 #2

Cant stake just change the formula whenever they like and the hash will still show correct?
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July 07, 2026, 05:25:42 AM
 #3

Impressive use of data. Hard to believe that 26 billion dollars has been wagered on this game. I’ll admit a couple of those dollars are from me. Still, it is absolutely shocking seeing the numbers so big. If Stake takes 1% as you say then that is 260 million dollars in profit from a single game. Quite impressive.

..Stake.com..   ▄████████████████████████████████████▄
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July 07, 2026, 10:10:01 AM
Last edit: July 07, 2026, 01:18:45 PM by [btc]
 #4

This is the first video I've made, If you find it valuable and want another game broken down let me know.

This is really, really dope. Nice work, here. I really like that airplane game where you launch it and it catches multipliers or bombs in the air, and you have to land on an aircraft carrier (win) or water (lose). Well, I guess I'd have to say I like watching clips online of other people playing it - I've never played it myself. I'm curious as to what a breakdown would look like, as seen here with the crash game you did.


Impressive use of data. Hard to believe that 26 billion dollars has been wagered on this game. I’ll admit a couple of those dollars are from me. Still, it is absolutely shocking seeing the numbers so big. If Stake takes 1% as you say then that is 260 million dollars in profit from a single game. Quite impressive.

It's a testament to how popular online gambling has become. I'd like to see some IRL casinos pull that shit off nowadays.

BTC

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July 07, 2026, 10:31:40 AM
 #5

Since this thread involves some mathematical analysis, I predict it won't have dozens of replies, because people won't be able to shitpost as easily.

Code:
Target             Rounds reached   Observed     Theory
Instant (1.00x)         [COUNT]       1.97%      1.98%
Reach 1.5x            5,442,953     66.000%    66.000%
Reach 2x              4,083,123     49.511%    49.500%
Reach 5x              1,633,849     19.812%    19.800%
Reach 10x               817,238      9.910%     9.900%
Reach 50x               163,711      1.985%     1.980%
Reach 100x               81,773      0.992%     0.990%
Aggregate RTP         8,246,854     99.087%    99.000%

Ultimately, what we see is that, in large samples, the difference between the expected result and the actual result is minimized.

The 1% edge holds at every cash-out target, so no strategy changes the return.

The strategy regarding changing the multiplier doesn't change the return, but here I'd like to highlight the compounding effect of 1% working against you. A $1 bet repeated enough ends up at $0.

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July 07, 2026, 11:10:42 AM
 #6

Wow! Shocked That is cool. 8.2 million rounds. Awesome!

Anyway, I have my share of playing this game for like 200 rounds maybe, and I still pick Stake Crash over other Stake Original games because of the fact that you can stop the game if you want and make a profit. That's not available on any other games, either in casino or slots, which makes it more interesting. Although it can be boring sometimes because of the waiting time, especially when it hits x1000+, and you have already cashed out.

Reached x100 with 81,773. 1 percent of the total rounds. I guess I am lucky I got one of those.

..Stake.com..   ▄████████████████████████████████████▄
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July 07, 2026, 11:13:07 AM
 #7

I do not play at Stake anymore except in very early days,,, but did your calculations take into account also promotional periods where they lowered the house edge for Crash?

IIRC they did this sometimes but I cannot remember if it was only for Dice or also for Crash. For me even though it is very tiny,,, that could also account for Observed higher percentage? People behaviour I think is to go big volume during low house edge.


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July 07, 2026, 11:26:45 AM
 #8

Cant stake just change the formula whenever they like and the hash will still show correct?

The formula is public, so not without detection

Impressive use of data. Hard to believe that 26 billion dollars has been wagered on this game. I’ll admit a couple of those dollars are from me. Still, it is absolutely shocking seeing the numbers so big. If Stake takes 1% as you say then that is 260 million dollars in profit from a single game. Quite impressive.

Yes approx thats how much stake has taken from players for 1 game. Dice and plinko are around 70-80B each too so not even their biggest one.


This is the first video I've made, If you find it valuable and want another game broken down let me know.

This is really, really dope. Nice work, here. I really like that airplane game where you launch it and it catches multipliers or bombs in the air, and you have to land on an aircraft carrier (win) or water (lose). Well, I guess I'd have to say I like watching clips online of other people playing it - I've never played it myself. I'm curious as to what a breakdown would look like, as seen here with the crash game you did.


Impressive use of data. Hard to believe that 26 billion dollars has been wagered on this game. I’ll admit a couple of those dollars are from me. Still, it is absolutely shocking seeing the numbers so big. If Stake takes 1% as you say then that is 260 million dollars in profit from a single game. Quite impressive.

It's a testament to how popular online gambling has become. I'd like to see some IRL casinos pull that shit off, nowadays.

Yes if there was enough interest, I assume you are talking about aviamasters by Bgaming

Since this thread involves some mathematical analysis, I predict it won't have dozens of replies, because people won't be able to shitpost as easily.

Code:
Target             Rounds reached   Observed     Theory
Instant (1.00x)         [COUNT]       1.97%      1.98%
Reach 1.5x            5,442,953     66.000%    66.000%
Reach 2x              4,083,123     49.511%    49.500%
Reach 5x              1,633,849     19.812%    19.800%
Reach 10x               817,238      9.910%     9.900%
Reach 50x               163,711      1.985%     1.980%
Reach 100x               81,773      0.992%     0.990%
Aggregate RTP         8,246,854     99.087%    99.000%

Ultimately, what we see is that, in large samples, the difference between the expected result and the actual result is minimized.

The 1% edge holds at every cash-out target, so no strategy changes the return.

The strategy regarding changing the multiplier doesn't change the return, but here I'd like to highlight the compounding effect of 1% working against you. A $1 bet repeated enough ends up at $0.


Thats ok I don't expect normal players to be interested in deep math and technical topics, but might be interesting for some.

Wow! Shocked That is cool. 8.2 million rounds. Awesome!

Anyway, I have my share of playing this game for like 200 rounds maybe, and I still pick Stake Crash over other Stake Original games because of the fact that you can stop the game if you want and make a profit. That's not available on any other games, either in casino or slots, which makes it more interesting. Although it can be boring sometimes because of the waiting time, especially when it hits x1000+, and you have already cashed out.

Reached x100 with 81,773. 1 percent of the total rounds. I guess I am lucky I got one of those.

Nice, yes they have ~1.7m more rounds and then they'll have to do another seeding event

I do not play at Stake anymore except in very early days,,, but did your calculations take into account also promotional periods where they lowered the house edge for Crash?

IIRC they did this sometimes but I cannot remember if it was only for Dice or also for Crash. For me even though it is very tiny,,, that could also account for Observed higher percentage? People behaviour I think is to go big volume during low house edge.



The calculation is done against 1% house edge, so it wouldn't capture a change in formula although I assume they prob didn't change the formula just gave bonus for difference in the promotional period if true.

The 8.2M rounds were tested against cashout targets 1.5x, 2x, 5x, 10x, 50x because it would be impossible for me to know what exact cashout every player chose for every game ever played.
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July 07, 2026, 02:03:11 PM
 #9

What a serious effort!

Provably fair should be all about the close match between observed and theoretical probabilities especially the consistent 1% house edge across all multipliers.

This further confirms that no strategy can beat the math. But I can say the transparency is still valuable compared to other black box games.

 
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July 07, 2026, 03:09:21 PM
 #10

$26B? This is a large number. As it was said, Crash game is purely a mathematical equation and it is only the smart gamblers who understand the game can make profit. Gamblers can't really say whether it is fair or not but your wins are withdrawing without issue, then you don't have a problem. The 1% Cash-out target is the most important thing in the stake casino, they are not playing with it. The aggregate is high too. Op you made a good calculation. Once a gambler of crash understand the movement, he will make good wins. But 1% edge in 7 years with $26B is the high side. Though depends on the participants within this period.

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July 07, 2026, 07:14:15 PM
 #11

What a serious effort!

Provably fair should be all about the close match between observed and theoretical probabilities especially the consistent 1% house edge across all multipliers.

This further confirms that no strategy can beat the math. But I can say the transparency is still valuable compared to other black box games.

Yes across 8.2m bets the real rtp should converge tightly to the theoretical which it did in this case. 0.087% is acceptable at that size
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July 08, 2026, 06:20:57 AM
 #12

I notice when a lot of players are in on a round like more wagering the crash point seems to crash very early can you explain how this pattern happens? Is it possible stake crashes the curve when more bets are on the line oir is this just paranoia?
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July 08, 2026, 07:49:10 AM
 #13

I notice when a lot of players are in on a round like more wagering the crash point seems to crash very early can you explain how this pattern happens? Is it possible stake crashes the curve when more bets are on the line oir is this just paranoia?

It's just paranoia, or seeing patterns where they aren't. The results follow a random pattern, and that impression is due to a kind of confirmation bias—but in reverse.

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July 08, 2026, 11:19:41 AM
 #14

Well crash and aviator games are some of the most popular games in any casino, so the profit of 26 billion dollars in 7 years is still low for me considering how much do people wager on a single round of such game. The average I have seen is like 1500 to 4000 dollar per round and since one round lasts from very few seconds to a few minutes max I think the winning should be much more than that in seven years, however I am no expert in math nor in provably fair, mine is just a rough estimate from the numbers I see when I play these games.


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July 08, 2026, 11:47:54 AM
 #15

Impressive use of data. Hard to believe that 26 billion dollars has been wagered on this game. I’ll admit a couple of those dollars are from me. Still, it is absolutely shocking seeing the numbers so big. If Stake takes 1% as you say then that is 260 million dollars in profit from a single game. Quite impressive.
I am not surprised anyway because I have always know that running a big popular and successful casino is like owning an oil well, it like owning a money printing machine in your own house that prints you any amount of money you want anytime you want it.

All I am saying is that, owning an online casino as good and as big as stake is owning a very lucrative business, one that even your entire generations to come after you are long gone won't taste what poverty is of feels like if they will manage the business well and keep the cash flowing in and even get better at it since as each day breaks, technology gets better and makes online businesses easier to manage/run.

Anyways, away from the above, thanks to the op for this research and sharing the outcome with the community here, I believe this should serve as a proof that stake is a trustworthy casino, has always been and will continue to be.
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July 08, 2026, 12:19:51 PM
 #16

Kudos.

Do you have some pattern perbaps, like some medians based on the data maybe the range reached certain number x multiplier like over 50x whats the range.

Loke around 60-70 round, something like thats.

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July 08, 2026, 02:15:13 PM
 #17

Thank you OP for the effort put in assembly this data, I remember I had an argument with someone on this forum about the games that are mostly played in casino and when I mentioned crash, the person disagreed but this amount you mentioned here and the number of wagering already proved the obvious, this is my favorite game and apart from the stake casino I have also played this game in other casinos.

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July 09, 2026, 08:00:10 AM
 #18

Kudos.

Do you have some pattern perbaps, like some medians based on the data maybe the range reached certain number x multiplier like over 50x whats the range.

Loke around 60-70 round, something like thats.

Yes it's in the original post. We checked round 1 - 8,246,854 - you can see exactly how many of the rounds reached the multipliers below. eg. 50x was reached 163,711 times out of the 8.246m

Also fun fact the highest multiplier ever was 2.17m x but stake caps at 1m anyway so anyone that rode it to 2.17m would have been paid out at 1m x

Code:
Target             Rounds reached   Observed     Theory
Instant (1.00x)         [COUNT]       1.97%      1.98%
Reach 1.5x            5,442,953     66.000%    66.000%
Reach 2x              4,083,123     49.511%    49.500%
Reach 5x              1,633,849     19.812%    19.800%
Reach 10x               817,238      9.910%     9.900%
Reach 50x               163,711      1.985%     1.980%
Reach 100x               81,773      0.992%     0.990%
Aggregate RTP         8,246,854     99.087%    99.000%


Thank you OP for the effort put in assembly this data, I remember I had an argument with someone on this forum about the games that are mostly played in casino and when I mentioned crash, the person disagreed but this amount you mentioned here and the number of wagering already proved the obvious, this is my favorite game and apart from the stake casino I have also played this game in other casinos.

Thanks was a bit of effort to put it together. Crash is top 5 game on stake originals with dice, mines and plinko the top 3 games by volume. But crash was released a couple years after those. Also as crash is multiplayer it is a slower per bet amount vs those games so the lower volume makes sense. Still a massive success for stake.
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July 09, 2026, 08:23:09 AM
 #19

Great data, OP. It's refreshing to see the actual math laid out instead of the usual speculation. 26 billion in volume sounds crazy, but the social aspect of crash games keeps people clicking way longer than standard slots.
The conspiracy theories about manual crashes don't make much sense anyway. With a 1% house edge on that kind of volume, Stake is already printing hundreds of millions on autopilot. They have zero reason to risk a rigged hash scandal just to snipe a whale for a few extra grand. The math already does the heavy lifting for them.

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July 09, 2026, 11:58:33 AM
 #20

Crash games have a fairly well-defined mathematical model !

If we condense the entire Crash game into a single formula, then:
P(M≥x)=(1-h)/​​ x

where M is a random crash multiplier, x is the cashout coefficient you choose, and h is the house edge.
For example, when h = 1%:
P(M≥1.2) = 0.99/1.2 = 82.5%

And the entire "economics" of the game can be derived from this same formula:
EV = x * P(M≥x) - 1 = x  * ((1−h)/x) - 1 = -h

In other words, no matter what multiplier you choose: 1.01x, 1.5x, 5x, 100x - the expected value of a single unit of currency wagered is the same: -h !

To put it in a single line:

x * P(M≥x)=1-h​

Crash is a game where the probability of winning is inversely proportional to the payout amount.
That is precisely why choosing a cashout point changes the frequency of wins and the risk, but does not change the long-term RTP.


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