These are some results from HBJL. To be fair, not all of these can be considered "papers," as such, but all of them represent some sort of concrete results that have been obtained by the research lab.

This essay is a survey of the various methods of calculating a basic strategy for the game of blackjack.

The Derivation of a Basic Strategy

This essay is an evaluation of the side bet of "first 2 cards total 20, 4:1 payout". The essay goes into detail in calculations and might serve as a useful guide for evaluating various side bets in your own games.

Evaluating a new side bet

This chart shows how likely the dealer is to bust based on the upcard. This chart assumes a neutral deck. Obviously this chart represents non-continuous data (an upcard of 4.5 is meaningless), but the red line was added to emphasize the existing trends in the data. This chart was derived from combinatoric analysis.

This chart shows the probability of certain true counts being the maximum or the minimum true counts of a given shoe, plotted for multiple penetrations. The way to read this chart is to say that with 90% penetration there is about a 5% chance that a count of +10 or more will be reached, where for 60% penetration this probability is negligible. This chart was derived from simulation data.

This chart shows the actual relation between the true count and the advantage held by the player when playing basic strategy. It can be seen clearly on this chart that this relation is not linear as is generally assumed for quick calculations during play. The red line shows the actual data, and the blue line is a cubic least-squares interpolation of the data. This chart was derived from 10 billion hands of simulation.

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