Battleship

Introduction

Battleship, developed by Atmosfera, is an engaging live game available in online casinos. Drawing inspiration from the classic board game cherished by many, it introduces a modern twist to the traditional concept. In this adaptation, every vessel, regardless of its size, is universally termed a battleship, offering players a unique and immersive gaming experience.

Game Rules:

  • Battleship is played on a 10×9 card, featuring squares numbered from 1 to 90.
  • Each card contains one 4×1 battleship, two 3×1 battleships, and three 2×1 battleships, with the option for players to manually select ship placements or let the game choose randomly.
  • Players can opt to play 1 to 1,000 cards and bet between $0.50 to $5 per card.
  • Once betting is closed, the game draws 70 numbers, without replacement, from a hopper containing balls numbered 1 to 90.
  • If a drawn number matches a square occupied by a battleship, it’s marked.
  • A battleship is considered “sunk” if all its squares are marked.
  • Players can win in four ways:
    1. Jackpot: Sink the 4×1 battleship within the first 10 balls, paying 300 for 1.
    2. Battleships: Sink at least two ships covering 4 to 7 squares between them. Payout depends on the number of squares and balls required, as detailed in the pay table.
    3. Fleet: Win based on the number of balls needed to sink all six ships.
    4. Bonus Fleet: Win based on the number of balls needed to mark every square on every ship except one. Payout depends on the number of balls required.

Jackpot Analysis

The likelihood of sinking the 4×1 battleship within 10 balls is combin(86,6)/combin(90,10) = 1 in 12,168. With a win of 300, the expected return from this feature is 300/12168 = 2.47%.

Battleship Analysis

Echelon Analysis

An Echelon consists of any two 2×1 battleships, covering four squares. With three 2×1 battleships available, there are three combinations of choosing 2 out of 3. The table below illustrates the probability of winning with exactly 4 to 30 balls for any one Echelon, along with the win and contribution to the return (product of win and probability).

The expected win per Echelon is 0.027405. Considering three combinations of Echelons, the total return from Echelons is 3 * 0.027405 = 0.082215.

Division Analysis

A Division comprises one 2×1 battleship and one 3×1 battleship, covering a total of five squares. With three 2×1 battleships and two 3×1 battleships available, there are six possible combinations. The table below outlines the probability of winning with 5 to 35 balls for any one Division, along with the win and contribution to the return (the product of win and probability).

The expected win per Division is 0.022780. Considering six combinations of Divisions, the total return from Divisions is 6 * 0.022780 = 0.136681.

Brigade Analysis

A Brigade encompasses any combination of two or three ships, totaling six squares. This could involve three 2×1 ships, two 3×1 ships, or the 4×1 ship paired with a 2×1 ship. There is one way to select all three 2×1 ships, one way to choose both 3×1 ships, and three ways to select the 4×1 ship along with any one 2×1 ship. This results in a total of 5 possible combinations. The table below illustrates the probability of winning with exactly 6 to 40 balls for any one Brigade, alongside the win and contribution to the return (the product of win and probability).

The expected win per Brigade is 0.026373. Considering the five combinations of Brigades, the total return from Brigades is 5 * 0.026373 = 0.131867.

Squadron Analysis

A Squadron comprises any combination of two or three ships, covering a total of seven squares. This can be achieved with two 2×1 ships and one 3×1 ship or by using the 4×1 ship alongside one 3×1 ship. There are three ways to select 2 out of 3 2×1 ships and two ways to choose one 3×1 ship, resulting in a total of 3 * 2 = 6 ways to choose ships in a 2+2+3=7 configuration. Similarly, there are two ways to choose two out of two 3×1 ships and one way to choose the 4×1 ship, leading to a total of 2 * 1 = 2 ways to choose ships in the 4+3 configuration. Overall, there are 6 + 2 = 8 possible ways to achieve this. The table below presents the probability of winning with exactly 7 to 45 balls for any one Squadron, along with the win and contribution to the return (the product of win and probability).

The expected win per Squadron is 0.015128. Considering the eight combinations of Squadrons, the total return from Squadrons is 8 * 0.015128 = 0.121021.

Fleet Analysis

Fleet Analysis examines the potential outcomes and probabilities associated with winning by sinking the entire fleet in the game. This analysis delves into various factors such as the number of balls required to achieve this feat, the likelihood of success, and the corresponding return to the player. It provides valuable insights into the overall strategy and potential rewards associated with aiming to sink all ships in the fleet.