Data Science in Action: To Drop or Not to Drop in Online Rummy

Written by Anurag Garg, Div Jain

This blog also gives a sneak-peak into the research paper that was published and presented by the Data Science Group (Gameskraft) at the IEEE 2024 Conference on Artificial Intelligence Singapore

In Online Rummy, sometimes not ‘Playing’ is a better option (Image Credits: Diwakar Pradhan)

In the previous blog, we discussed various algorithmic approaches for efficiently grouping cards.

In this blog, we focus on one of the most essential skills in Online Rummy: First Drop. We will explain what First Drop is, its importance, and what high-skilled players consider when deciding to drop. We also discuss how we adapted SPADENet architecture to build models that can determine when to Drop or Play a hand for any variant of online Rummy with great accuracy.

What is “Drop” in Online Rummy?

“Drop” refers to a player’s option to quit or withdraw from the deal, typically at the beginning or during the deal. Playing a hand that should be dropped can lead to the worst outcome for the players (losing by 80 points). However, by dropping, the players take a lesser penalty (usually 20 or 40 points) and forfeit the deal.

There are usually two types of drops in Online Rummy:

1. First Drop (or Initial Drop): This occurs at the start of a deal before the player picks any cards from the Open or Closed Deck. The player chooses to drop right after seeing their dealt hand. In most variations of Rummy, the first drop costs the player a minimum number of points, often 20 points.
2. Middle Drop: This occurs during the deal after the player has picked a card or cards from the Open or Closed Deck. The penalty for a middle drop is generally higher than the first drop, often around 40 points.

Dropping allows players to minimize their losses if they believe they have a ‘weak’ hand and have a very limited possibility of winning the round. It is similar to ‘Folding’ in Poker.

Why is First Drop important?

In Online Rummy, players aim to win or reduce the margin of their loss as much as possible. One of the strategies they employ to reduce the margin of their loss is the First Drop. If the players think they have a weak hand and the chances of making a declaration are less in the first few turns, they can drop out of the game before even picking a single card and get a fixed penalty (15/20/25 points depending upon the game type). This penalty would be comparatively lesser than their loss (up to 80 points) had they played, thus minimizing their losses.

Less skilled players might be tempted to play every hand to win more games, but such a strategy often leads to significant losses with ‘weak’ hands, thereby reducing their overall outcome.

Here are some real examples:

Example of a ‘strong’ hand

Hand Analysis:

1. Pure Sequence (PS: 3♥, 4♥, 5♥) and a joker (1♥) which is a part of another sequence (8♥, 9♥, 1♥, 11♥). Hand points are only 36 (considering cards from Invalid Meld).
2. High probability of completing the remaining sequences or sets since the player already has 2 sequences one of which is a PS.

Strategic Decision:

1. ‘Strong’ hand.
2. Consider Playing and either reduce hand points below 20 or even win the round.

Actual Decision and Outcome:

• The player played the game and won the round.

Outcome if the player had dropped:

• Would have lost by 20 points.

Example of a ‘weak’ hand

Hand Analysis:

1. No Pure Sequence and No Joker. Hand points are 80 (maximum).
2. Very low probability of either reducing points below 20 or even winning the round.

Strategic Decision:

1. ‘Weak’ hand.
2. Consider First Drop and incur a fixed penalty of just 20 points.

Actual Decision and Outcome:

• The player played the game and lost by 80 points.

Outcome if the player had dropped:

• Would have lost by just 20 points and saved losses worth 60 points.

Since the players’ natural tendency is towards playing, it becomes important for them to recognize the weak hands and drop them on their first turn itself. Quantitative analysis of the First Drop behavior of High Skilled Players also shows that players who drop well also win more and end up with higher rewards (Fig. 1).

Fig 1: Players who drop well also win more (Source: Gameskraft’s Online Rummy Platforms)

In the next section, we look at other factors that high-skilled players also consider when deciding whether to drop or play.

High-Skilled Players Drop or Play Behavior Analysis

Here are a few more Drop or Play insights based on High-skilled players’ (HSPs) behavior:

• HSPs tend to drop more when there are more players on the table. Hence:
  - For the same kind of hand, their drop rate is higher in a 6p game than a 2p game.
  - This could also result from either more players initially joining the table or fewer players dropping before their turn.
• For the same kind of hand, the Drop Rate of the HSPs also changes with the change in their turn number. As their turn approaches, they gain additional information about the remaining players, influencing their decision to drop.
• Their Drop Rate also changes with the change in the variant of Rummy. For instance, HSPs tend to drop relatively more in a Pool game than a Points game because they aim to stay until the last round of a Pool game and hence take fewer risks in the initial rounds.

The above insights have been derived from the data in Table 1 below. Please refer to the SPADENet paper for further insights.

Table 1: Analysis of High-skilled players’ Drop behavior for different game specific features (Source)

In the next section, we briefly introduce SPADENet and discuss how we use the above insights and the architecture proposed in the paper to solve the Drop or Play problem for different variants of Online Rummy.

SPADENet for Online Rummy

SPADENet presents a multi-input, single-output Deep Neural Network-based generic architecture designed to represent the overall game state and evaluate optimal actions in skill-based card games. Following the proposed architecture, we developed a deep neural network that could mimic the Drop or Play behavior of High-skilled players for all variants of Online Rummy.

Fig 2: SPADENet for Online Rummy (Source)

It is a combination of 2 separate neural networks (Fig. 2):

• Players’ Hand Information (CNN Block): The first network is a CNN model that takes an image representation of players’ hands and Open Deck Card. It learns to identify only those card patterns or melds that are relevant to the Drop or Play problem.
• Game Table Progression and Evolution (Dense Block): The second network is a feed-forward neural network that captures game-variant-specific features. While the same input is fed to the CNN network, different features are considered when building the Drop or Play model for various Online Rummy variants (Table 2).

Table 2: SPADENet Features (Online Rummy as a Case Study) (Source)

Results

With the SPADENet architecture, we observed significant improvement in Test F1 score across all Rummy variants with the highest being for Pool-6P from 0.767 (existing best-performing method) to 0.908 (18% increase) (Refer Table 3 and Table 4).

Table 3: SPADENet Model Performance vs other Models for Points variants respectively (Source)

Table 4: SPADENet Model Performance vs other Models for Pool variants respectively (Source)

We also observed that the odds of favorable game outcomes for Drop or Play action in Online Rummy also increased when players followed SPADENet model recommendations (Table 5). The players achieved favorable outcomes 72% of the time when their actions aligned with the model recommendation. In contrast, when players chose a different action, they could only turn the outcome in their favor in ~50% of them.

Table 5: Game outcome when HSPs played (Source)

In this blog, we discussed the importance of knowing when to drop in Online Rummy and how effective dropping can increase player rewards. We also saw how the SPADENet architecture can be seamlessly adapted to predict Drop or Play decisions for different Rummy variants.

In the next blog, we will explore how we are using the insights from these different Drop Models to upskill and create personalized learning journeys for our Rummy players.

This post is part of a 9-part blog series delving into the art and science of skillful play and defining what Skill means in Online Rummy.

• Part 1 — Introduction to Best Grouping Cards in Online Rummy
• Part 2 — Cracking the Code: Algorithmic Approaches to Determine Best Grouping in Online Rummy
• Part 3 — Data Science in Action: To Drop or Not to Drop in Online Rummy
• Part 4 — Empowering Players: Enhancing Hand Dropping Skills in Online Rummy — Coming Soon
• Part 5 — Data-Driven Insights: Picking from the Open Deck in Online Rummy — Coming Soon
• Part 6 — Analyzing Patterns: Optimal Discard Strategies in Online Rummy — Coming Soon
• Part 7 — Leveling up: Mastering Best Grouping Techniques in Online Rummy — Coming Soon
• Part 8 — Elevating Gameplay: Mastering the Art of Picking from the Open Deck in Online Rummy — Coming Soon
• Part 9 — Refining Strategy: Improving Optimal Discarding in Online Rummy — Coming Soon