Every cash-out target costs the same three cents per dollar

Where the hit rates come from

The published return is 97 per cent, so the house keeps 3 per cent. That subtraction is arithmetic rather than a second fact, and the case for reading the 97 as a printed figure rather than a measured one belongs to the return number itself.

Getting from that to a hit rate needs one assumption stated in the open. If a target of m× pays m times the stake, and the return is the same 97 per cent whichever target you choose, then the chance of a round climbing as far as m is 0.97 divided by m. That is how a crash distribution is ordinarily constructed, and nothing published about this game either confirms or contradicts it. Everything below stands on it.

Run the division and the shape of the game appears:

• 1.10× reached in 88.2 per cent of rounds
• 1.20× in 80.8 per cent
• 1.50× in 64.7 per cent
• 2.00× in 48.5 per cent
• 3.00× in 32.3 per cent
• 5.00× in 19.4 per cent
• 10.00× in 9.7 per cent
• 100.00× in 0.97 per cent

At the bottom of that list sits the edge in its plainest form. Because 0.97 divided by 1.00 is 0.97, about three rounds in a hundred end before any target at all can be taken, and those three rounds are the whole 3 per cent.

Two targets, one round at a time

Put a dollar on 1.20×. Four rounds in five it comes back as $1.20, a profit of 20 cents; the fifth time the dollar is gone. Weighted: 0.8083 × $0.20 minus 0.1917 × $1.00 gives 16.2 cents earned against 19.2 cents lost, so 3 cents down.

Put the same dollar on 2.00×. In 48.5 rounds out of a hundred it doubles, a profit of $1.00, and in the other 51.5 the dollar is gone. Weighted: 48.5 cents against 51.5 cents, so 3 cents down.

Identical to the cent, by construction.

What differs is the spread. Round to round, the standard deviation of the dollar on 1.20× is about 47 cents; on 2.00× it is about $1.00. Same expectation, twice the swing.

The hole each target digs

A losing run at 1.20× means the round failed to reach 1.20 nineteen times in a hundred, so two misses back to back come up about once in 27 attempts, three about once in 142, four about once in 741, and five about once in 3,866. A losing run at 2.00× is a different animal entirely, because a miss there is the majority outcome: five in a row about once in 28, seven about once in 104, ten about once in 762, thirteen about once in 5,578. Sit through a thousand rounds and the cautious target will hand you a run of four with roughly two-thirds probability and a run of five with under one-fifth, while the bolder target will produce a run of seven with near certainty and a run of ten about 47 per cent of the time.

Now price those holes. Four misses at 1.20× cost $4, and each subsequent hit repays 20 cents, so filling the hole takes 20 winning rounds, which at an 80.8 per cent hit rate is about 25 rounds of play. Ten misses at 2.00× cost $10, and each hit repays a dollar, so filling it takes 10 winning rounds, about 21 rounds of play.

Measured in rounds the two recoveries are almost the same length. Measured in money the second hole is two and a half times deeper. And in both cases the recovery is a description of the average case, which drifts downward at 3 per cent and therefore never actually arrives.

Why the cautious target is behind more often

Flat dollar, one hundred rounds, nothing clever. To finish ahead at 1.20× you need 84 hits, because 84 hits earn $16.80 against $16.00 lost on the 16 misses; the average number of hits is 80.8. Exact binomial probability of getting there: 25.4 per cent.

To finish ahead at 2.00× you need 51 hits out of 100, against an average of 48.5. Probability: 34.4 per cent.

So the target that wins four times in five leaves you behind after three sessions in four, and the target that loses more often than it wins leaves you ahead in about a third of them. Neither has the better expectation, and that is precisely the reason. The low target compresses almost every outcome into a narrow band, and the band sits just under the line because the drift is negative; there is nothing wide enough in it to carry a session over. Variance is the only thing that ever puts a player in front, and the cautious setting is the one that removes it.

What the clock costs

A round takes between 10 and 30 seconds, so an hour holds somewhere between 120 and 360 of them. A flat dollar therefore turns over $120 to $360 in that hour, and 3 per cent of that is an expected cost of $3.60 to $10.80. At the 10 cent minimum the same hour costs between 36 cents and $1.08.

The charge falls on turnover, not on the deposit. Nothing about a target changes the rate; the pace changes the bill.

What is genuinely left to decide

Three things, and none of them is a way to win: how much goes on the table, where the automatic cash-out sits, and when the session stops. A fourth choice, splitting the stake across the two slots the game gives you, changes the shape further without touching the rate, and it is worked through in the two-bet layout.

Staking patterns are a different claim and they fail differently. Doubling after a loss does not reduce the edge; it raises turnover, which raises the bill in exact proportion, and the doubling ladder shows the ladder against several stake ceilings.

Anything that promises to reach past the stake and into the crash point is answered by the way a round is built rather than by argument, and the procedure for checking that a round was settled on values fixed in advance is set out on the verification page.