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Variance Labs

Variance · Stake Analyzer · 6 min read

Streaks, gaps and independent rounds

How long losing streaks get in a normal session, what a tracker's gap and heat figures measure, and why none of them change the odds of the next round.

Long streaks feel meaningful. Ten losses in a row on a coin-flip bet feels like something has gone wrong. In fact, a streak that long is an ordinary part of a session of a few thousand bets, and the round after it is exactly as likely to win as any other.

Why rounds are independent

On a provably fair game, each result is an HMAC of the seeds and that bet’s nonce. The previous results are not an input. Bet 501 is computed the same way whether bets 491 to 500 all won or all lost. The verification guide shows the derivation.

How long streaks get

Take Dice at 49.5% to win, so each bet loses with probability 0.505. The chance that a given ten bets all lose is:

0.505¹⁰ ≈ 0.00108   (about 1 in 930)

That looks rare, but a session gives a streak many places to start. Over 10,000 bets the numbers below are what chance alone produces, from 2,000 simulated sessions:

Dice at 49.5%, 10,000 bets per session
MeasureResult
Losing streaks of 10 or more, on averageabout 5
Longest losing streak, median session12
Longest losing streak, 80% of sessions11 to 15

A twelve-loss streak in a long session is the expected case, not a sign that the game is cold. The same holds for winning streaks: they do not mean a game is hot.

What gap and heat figures measure

A tracker records history. In Keno, Stake Analyzer counts how many rounds each number or combo has gone since its last hit and compares that gap with the expected interval, which comes from the hypergeometric probability of the combo landing. A gap well past its expected interval is labeled overdue, and the heat score ranks combos by gap and hit count.

These figures describe the session so far. An overdue combo is no more likely to land on the next draw than it was on the first, because the draw does not read the history. Stake Analyzer’s own pickers, which choose numbers from session data, carry the same house edge as a random pick. The Stake Analyzer post on whether patterns matter on Mines and Keno (opens in new tab) tests this on real results.

What session stats are useful for

  • Seeing the size of normal swings, so a bad run reads as variance rather than a reason to raise the bet.
  • Checking that hit rates over a long session land near the published odds.
  • Keeping an exact running profit and loss, and stopping at a limit set in advance.

The Seed Hunter (opens in new tab) shows the other side: it runs thousands of seed pairs and finds the ones that contain a chosen pattern, which shows how often such patterns occur in random data. The Stake Simulator (opens in new tab) lets you play through a streak with a virtual balance.