BENZ GAME · 2026-10-21

BENZ GAME: Two Nine-High Straights, One Unnecessary Argument

Two exposed five-card poker straights tie in rank; neither suit preference nor an extra imagined card can separate them under the stated rules.

The two rows are five cards long. Row A: 5♣, 6♦, 7♥, 8♠, 9♣. Row B: 5♦, 6♥, 7♠, 8♣, 9♦. This BENZ GAME puzzle starts with a complete comparison, yet the players keep searching for an extra deciding detail.

Equal straight endpoints

Both rows contain five consecutive ranks ending at nine. Both use mixed suits, so neither is a straight flush. Under ordinary high-poker hand comparison, these are equal nine-high straights.

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One reader prefers Row B because its nine is a diamond. Another prefers Row A because it has a spade eight. Their suit preferences have no role in the stated hand-ranking rule. A visible difference need not be a ranking difference.

Someone suggests comparing the bottom card. Both are fives anyway, but the deeper point is that equal straight endpoints already determine equal rank patterns. A five-card consecutive run ending at nine must run from five through nine.

There is no sixth card in this five-card example. Adding a spare ace from a pocket would change the available information and still would not create a six-card poker hand. The defined comparison has to remain five cards.

A change that really matters

To see a meaningful difference, build a separate ten-high straight: 6♣, 7♦, 8♥, 9♠, 10♣. Its endpoint is higher. Compare it on a new sheet, not as extra cards silently inserted into one of the original rows.

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The original rows remain tied. Recording a tie is a complete answer. How a game distributes a pot or handles administrative details is a separate matter governed by its rules, not by an improvised preference for hearts or spades.

For a teaching caption, write “same category, same highest rank, equal hand strength”. This is more informative than simply writing “draw”, because it tells another reader which comparisons have already been completed.

Relevant and irrelevant differences

Ask a learner to identify one irrelevant difference and one potentially relevant change. Suit distribution is irrelevant here because neither row forms a flush. Raising the straight's highest rank is relevant because it changes the straight's rank.

The BENZ GAME exercise ends when the group stops trying to force a winner. Good comparison includes recognising equality. Finding another difference on the table is useful only if the agreed ranking gives that difference a job.

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