Limbo is a popular in-house game available at most crypto casinos. Similar to crash games Limbo is about waiting for as long as possible before collecting your profit. But wait too long, and you lose it all. Do you have the nerves of steel that it takes to reach the heights (and profit) others can only dream of? And precisely what are the chances of reaching the stars?

Betting & Probability

I made a bet of 10 Satoshi in the hope of making a profit of 70 Satoshi (10 x 8 = 80 and subtract the initial bet = 70 Satoshi).

The game states that I have a 12.375% chance of hitting my targeted 8x. 100/12.375 = 8.080. So statistically speaking, I should hit 8x once every eight games (that wouldn’t be very profitable!)

For my first try, I got 8x on my 6^th try, so I made 10 Satoshi in profit.

On my second try, it took 22 tries to get 8x. Let’s add them together!

6 + 22 = 28 and I got 8x two times, so 28/2 = 14. I’m not a genius at math, but 14 is more than 8!

It doesn’t seem like a 12.375% chance to me! More like 7.149% chance (100/7.149 = 13.987 – close enough!).

Why is that? Is this some kind of scam!?

Let’s try betting the same amount 100 times, and see what happens.

Well, that’s more like it. Out of 100 games, I got 8x 12 times, exactly 12%!

What can we learn from this? First, we can say that a ~12% chance of winning doesn’t mean that every 8^th game will give you a win. The possibility of winning can be interpreted in a few different ways.

Large Samples

Given a large enough sample, the number of winning games will eventually amount to ~12%. While collecting this large sample, you will sometimes have longer streaks without hitting 8x at all, and other times you will hit 8x several times within a few games. The larger the sample (i.e., the more games you’ve played), the more accurate the chance of winning.

Single Sample

Every game you play, you will have a 12% chance of hitting 8x, which means there’s an 88% chance that you lose. On every game you play.

Misconception

I’ve played 12 games without hitting 8x, which means that 8x has to come within just a couple of games.

Incorrect, sort of. Of course, you will eventually hit 8x, but the chance of hitting 8x doesn’t increase every time you don’t hit it. During the 100 games I played above, my longest streak of not getting 8x was 25 (just to hit 8x twice in a row right after).

Lies, Damned Lies, and Statistics!

Famous words attributed to Mark Twain (who himself attributed it to the British prime minister Benjamin Disraeli). But could you claim that statistics lie?

I don’t think so. You can, however, misinterpret statistics or misrepresent them to mislead someone. Now I don’t believe the statistics at BC.game is misleading. But I understand how it might seem that way for someone who doesn’t know how to interpret it. When it says you have a 12% chance of winning, it’s 100% correct.

If you were to try and hit the green ring by throwing darts from a 10 feet distance, you wouldn’t expect it to grow bigger every time you missed, would you? It’s precisely the same as the chance of winning in Limbo works.

You can read more about the probability of winning and losing various games here: Why is it so hard to win?

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