Hong Kong Mark Six Odds Calculator

Sure, 1 in 13,983,816 for the jackpot is vanishingly small (about the same as being struck by lightning three times). But the 7th-prize odds of 1 in 61 are quite friendly — a single ticket already has a roughly 1.86 % chance of winning some prize. Most players are buying entertainment, not investment: HK$10 buys several days of "what if I win?" daydreaming, a kind of voluntary dream tax. The calculator is meant to show the numbers clearly, not to encourage betting — by pure expected value Mark Six returns about 54 cents on the dollar to players.

Both expand your selection into many 6-number tickets. Multiple-entry: any 6 of your n numbers form a ticket — you get C(n, 6) tickets in total. Banker: you fix 1 to 5 "bankers" that must appear in every ticket, then take any (6 − bankers) of your legs — giving C(legs, 6 − bankers) tickets. Each ticket has identical odds (1 in 13,983,816 for the jackpot); the only difference is which 6-number combinations you actually own. Banker suits players with strong conviction on specific numbers; multiple-entry suits broader coverage. As for "better value", both lose money on average: expected return is roughly 54 % per HK$10. Multi spreads risk more evenly; banker concentrates it.

No, they are mathematically different. "Expected winning tickets" is an expectation: N tickets × per-ticket probability — this is exact even when tickets share numbers, thanks to the linearity of expectation. The "at least one win" probability is 1 − P(no wins anywhere), which is sensitive to correlation between tickets and is usually slightly lower than the expectation. For most everyday use (expectation well below 1) the two numbers are very close; the gap only matters once expectation approaches or exceeds 1.

When the jackpot is not won, the HKJC rolls it over into a Snowball Pool; on certain special draws (Mid-Autumn, Christmas, Lunar New Year) the draw fund tops it up by another HK$8–10 million. A typical 1st prize might be HK$8M; Snowball draws can exceed HK$50M. The Snowball lifts the prize amount but does not change the probability — so it makes a player's pure expected value better. In the extreme (jackpot above ~HK$13.98M) the expectation per ticket can approach break-even, but tax, parimutuel splitting between winners and the very low odds keep the real-world return negative. The probabilities here are fixed math; you have to check the HKJC site for the current Snowball amount.

In theory yes: there are C(49, 6) = 13,983,816 possible 6-number combinations. Buying every one guarantees the jackpot (and all other prizes) at a total cost of HK$139,838,160 — roughly HK$140 million. In a big Snowball draw this can be marginally profitable. In practice, no: the time to fill the tickets, the HKJC per-draw stake limits and logistics make it almost impossible. Lottery-buyout attempts in 1992 (Irish National Lottery) and 2005 (Australia) succeeded narrowly but were retired because operational complexity outweighed the return. For an ordinary player the practical answer is "no — do not try".