Welcome to Scratch Seven. Deal to begin.

POT: 0

▸ HOW TO PLAY + AARON’S STRATEGY

Objective

Find the subset of your 3 hole cards + 4 community cards that sums to the highest multiple of 7. Higher total wins the pot.

Card Values

A=1, 2–10 face value, J=11, Q=12, K=13. Suits irrelevant. No wilds.
If you use all four 7s (hand + board combined), their value doubles: 28 → 56.

N-Number System (Aaron)

Your hand strength is rated N0–N11 vs. the best possible hand for the current board (N0 = the nuts). N1 produces a total 7 less than the best possible hole cards, N2 is 14 less and so on.
N0–N2: Maximize pot · N3–N4: Play cheap to showdown · N5+: Fold or bluff

Pre-River Strategy (Aaron)

• Total ≤ 14: bluff or fold — never call
• Total ≥ 28, or ≥ 26 with a 7, or ≥ 21 with two+ 7s: build the pot from the start
• 3 non-duplicate low cards (<7) e.g. 4,5,6: bet big early (plays well any board)
• 2 non-dup lows + total ≥ 21, or 1 non-dup low + total ≥ 26: bet big early
• All other hands: stay cheap until the river, then reassess by N-number

Bluffing (Aaron)

Bluff only with your worst hands (not mediocre ones). Start with no bluffs; add bluffs to your range each time a strong hand goes uncalled. Reduce bluffing when a bluff gets called.

Tactics (Aaron)

Bluff — Make large bets and raises, typically equal to the size of the pot, but consider folding if reraised, or on the next round if called. Never call. Your goal is to either induce a fold, or encourage the other player to call your bets on strong hands.

Bet big early — Make large bets and raises, typically equal to the size of the pot, and consider reraising if you are reraised. But exercise some caution.

Build the pot — Make moderate bets and raises, typically around half the pot, but consider checking or calling if you think the other player might fold.

Stay cheap until the river — Check and consider calling a single moderate bet around half the pot. Generally fold to large or repeated bets.

Randomize — Don’t use the tactics mechanically; vary from time to time so the other player can’t be sure what you’re doing.

Observe — Try to figure out how the other player reacts so you can modify your tactics.

Learn — Whenever you make a bet intended to do something, remember whether it worked. It’s cheaper to learn decision-by-decision than only by losing chips.

RAISE

The Mathematics of Scratch Seven

Aaron Brown · August 2023 · SSRN 4547376

Covers combinatorics, modular arithmetic, and game theory for optimal Scratch Seven play — including the N-number hand classification system and Aaron’s 8-rule strategy summary implemented in this game’s AI.