Basic Strategy for some Simplified Blackjack Variants

TL;DR

The paper develops exact basic strategies for simplified Blackjack variants with only hit/stand decisions and analyzes how dealer information, deck count, and payout rules shape optimal play. It employs a exact-probability framework, enumerating hand-layouts and conditioning on initial hands to compute win, loss, and push probabilities as well as expected value under the basic strategy, with complete tables provided in the appendix. A key contribution is the demonstration that, as the number of decks $n$ grows, the strategy and overall expectation converge to those of a one-deck-with-replacement model, and that the no-counting limit preserves a positive player edge in many variants. The results illuminate how information about the dealer’s hand, payout structures like the 6-to-5 rule, and dealer-hit rules impact long-run outcomes, and they offer precise benchmarks for comparing traditional Blackjack to these toy variants. The asymptotic insights also raise practical implications for card counting and deck-design considerations in casino settings.

Abstract

In this paper, we calculate a basic strategy for several variations of a simplified version of Blackjack. In short, for these variants the player has only the two options of hit or stand, and they may only make either decision once. Other minor variations including rule modifications, changes in number of decks, alternate payout structures, and different given information about dealer's hand are also considered. An interesting theoretical result regarding the asymptotic behavior of the basic strategy and overall expectation as the number of decks increase is also proved.

Theorems & Definitions (18)

• Theorem
• Theorem 3.1
• Theorem 3.2
• Theorem 3.3
• Definition 4.1
• Proposition 4.2
• proof
• Remark 4.3
• Proposition 4.4
• proof