Ask The Wizard #302

Assuming both players see all the way to the river, I've found that the strongest competing hand is a suited 5-6. If the suited cards are not represented in the Ace pair, the potential outcomes are:

• Win: 22.87%
• Tie: 0.37%
• Lose: 76.76%

If the suited cards are included in the pair of Aces (reducing the chance of a flush), the potential outcomes change to:

• Win: 21.71%
• Tie: 0.46%
• Lose: 77.83%

Overall, the possible outcomes are:

• Win: 22.290%
• Tie: 0.415%
• Lose: 77.295%

Press the button below to find the answer.

Press the button below to view the solution.

Answer:

For the benefit of other readers, games with 'Multiway' wins encompass all conceivable pay-lines. However, the game only compensates players once per winning symbol combination. Playlines terminate when a reel is encountered with no winning symbols present.

Let's consider a case involving a five-reel game with three visible rows. All winning combinations align to the left. Imagine the player lands a winning symbol on reels 1, 2, 3, and 5. In this scenario, the player would receive payment only once for three of that symbol. Even though there are 9 potential ways to connect reels 4 and 5, the pay-lines cease at reel 3 in this context.

Now, let's say the player achieved the same winning symbol occurrence as follows on each reel:

• Reel 1: 2
• Reel 2: 1
• Reel 3: 3
• Reel 4: 2
• Reel 5: 1

The player would receive payment for 2×1×3×2×1 = 12 distinct pay-lines.

If the player filled the entire screen with the same winning symbol, their payout would amount to 3.⁵=243 pay-lines.

Now, let's proceed to the answer. We will consider wins that consist of 3 to 5 symbols only.

Let's define some terminology:

• t_x= total reel stops on reel x.
• n_x= total quantity of the winning symbol on reel x.
• p_x= locations on reel strips x where no winning symbol is visible.


For reel 3 the answer is 3³× n₁× n₂× n₃× p₄× t₅.

For reel 4 the answer is 3⁴× n₁× n₂× n₃× n₄× p₅.

For reel 5 the answer is 3⁵× n₁× n₂× n₃× n₄× n₅.