[Sand Sketched Plan] - Increase your Win Rate by 0.01%

Never feel dull with Sand Sketched Plan.

What do you do if you go first starting with this hand?

Hand and Context

- Hand: Quad blue (four blue cards), 2 Sand Sketched Plans (SSPs), no Wrecker Romp.

- Situation: Going first, rare case (~0.1% probability).

- Options:

1. Roll a dice: Chance to get 0, 1, or 2 Bloodrush Bellows (BRB) based on die roll and probabilities.

2. Don’t roll: Fetch 1 BRB with guaranteed probabilities.

- Deck Velocity (D.V.): Represents cards drawn or cycled, affecting future turns. It’s a parameter I consider to have when playing flesh and blood. Measured how fast you are circling the deck. Gravy bones, Kano, Cheetah Brutes, mechanologists, Oscillio etc. all have ways to accelerate deck circulation.

Math Breakdown

Option 1: Roll the Dice

- Dice Roll Probabilities

- 16.66% (1/6) to roll a 1 → D.V. = 5 (You arsenal a card, draw 1. Sees 5 cards in the deck)

- 33.33% (2/6) to roll a 2 or 3 → D.V. = 6 (You play a SSP, fetch a BRB, discard a card, arsenal, draw 2. 6 cards out of the deck.)

- 50% (3/6) to roll a 4, 5, or 6 → D.V. = 7 (You play 2 SSP, fetching 2 brb and discards 2 cards, arsenal 1 and draw 3 cards. 7 cards out of the deck.)

- BRB Outcomes:

- 0 BRB:

- Roll 1: 16.66%

- Roll 2 or 3: 33.33% × 25% = 8.33%

- Roll 4, 5, or 6: 50% × 8.5% = 4.25%

- Total: 16.66% + 8.33% + 4.25% = **29.24%**

- 1 BRB:

- Roll 2 or 3: 33.33% × 75% = 25%

- Roll 4, 5, or 6: 50% × 75% = 37.5%

- Total: 25% + 37.5% = 62.5%

- 2 BRB:

- Roll 4, 5, or 6: 50% × 33% = 16.5%

- Expected Value (EV) of BRB:

- EV = (0 × 29.24%) + (1 × 62.5%) + (2 × 16.5%) = 0 + 0.625 + 0.33 = 0.955

Option 2: Don’t Roll

- BRB Outcomes:

- 25% chance of 0 BRB → D.V. = 4

- 75% chance of 1 BRB → D.V. = 5

- Expected Value (EV) of BRB:

- EV = (0 × 25%) + (1 × 75%) = 0 + 0.75 = 0.75

- Comparison

- Rolling: ~4% higher chance of 0 BRB (29.24% vs. 25%).

- Rolling: ~16.5% chance of 2 BRB vs. 0% for not rolling.

- Rolling EV (0.955) > Not rolling EV (0.75).

- Rolling increases D.V. (5–7 vs. 4–5), improving future draws.

Strategic Decision

The choice depends on the matchup and the value of higher damage potential (2 BRB) versus consistency (guaranteed 1 BRB).

1. Against Verdance/Florian and most of other Ninja/Guardian except Bravo/Warrior/Brute/Wizard/Ranger/Mechanologist/illusionist/Assassin

- Roll and fetch: Higher damage potential from 2 BRB (16.5% chance) is valuable in a race. The increased D.V. (5–7) helps maintain pressure.

The risk of 0 BRB (4 extra %) is offset by the potential for a game-winning turn with 2 BRB.

2. Against Prism (Control Deck):

- Roll and fetch once, then pass: prevent prism from putting up the aura

3. Against Bravo, Jarl, LL Nuu, Slippy, Arakni Huntsman (Fatique Heavy deck)

- Fetch directly: Against midrange or less-defined matchups, the guaranteed 1 BRB (75% chance) with lower D.V. (4–5) prioritizes consistency. The risk of 0 BRB (29.24% when rolling) is less appealing when matchup dynamics are unclear.

Optimal Play

- General Recommendation: Roll the die in most cases. The higher EV (0.955 vs. 0.75) and increased D.V. (5–7 vs. 4–5) make rolling superior for maximizing both BRB potential and deck cycling, especially in a rare hand where early aggression can capitalize on the quad blue setup.

The decision’s impact is small (~0.01% win rate, 1 in 10,000 games), but in high-stakes scenarios, rolling maximizes your edge, win rate by…. 0.01%, like 1 in 10,000 games. But who knows, maybe it’s the game between you and me.