What Blackjack hands do we get?

On the previous pages, we looked at the 34 initial hands that the player can get. But the dealer upcard is nearly as important. Here we will look a bit more deeply by including the upcard. As there are ten possible upcards, there are 340 possible initial two-card hands and dealer upcard. These charts are more complex and require three dimensions. As in the previous charts, the x-axis shows each of the 34 initial two card hands. The third dimension (depth) shows the ten possible dealer upcards. The peaks show the highest frequency hands. The chart on this page is the simplest 3-D chart. The most common hand is T,T vs. T. This is the very sharp peak at the far right rear. The next most common hands are player 12 and 13. The hands with a dealer upcard of ten are about four times as likely as the hands with upcards of ace–nine because there are four times as many tens in the shoe. However, they are not exactly four times as common since a dealer upcard of ten means there is slightly less likelihood of your hand having a ten. The legend at the lower left defines the colors. Red indicates that a hand occurs less than 0.5% of the time. Green indicates 0.5% to 1%, etc.

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 © 2009 Norman Wattenberger