Expected value tables

• Six deck soft 17 • Six deck hard 17

The two tables above list all initial three-card combinations and player actions for S17 and H17 six-deck games. They assume the following rules: DOA, DAS, split to four hands and full peek. There are four tables on each page, one for each of the possible actions of stand, hit, double and split. The stand, hit and double tables are divided into hard totals, soft totals and pairs for ease of reference.

The numbers down the left are the player initial two-card totals and along the top are the dealer upcards. The data in the cells are the EV numbers and the cells are coloured for greater clarity - yellow for positive numbers and grey for negative. If you mouse over the data cells, the ones that turn red contain little information tips which will be revealed if you keep the pointer still over the particular cell.

To give an example: if you want to find the EV for hitting 13 against a dealer 8 in the S17 game, click on the six deck soft 17 link above, scroll down to the “hit” chart and find the cell where “13” down the left coincides with “8” along the top. The number given is -0.32965, which is the average value of that particular action and card combination.

You can use these two charts for a number of purposes:

• To find the average value of any given wager. In the example above, hitting 13 vs 8 on a £10 wager gives us 10 X -0.32965 = -3.29, or £3.29 lost on average in that particular situation. Simply multiply the wager size by the number.

• To compare the values of the various actions. Using again the example above, 13 vs 8 yields -0.51353 for stand, -0.32965 for hit and -0.7042 for double. The number for “hit” has the least negative value, which is why basic strategy says to hit that particular hand.

• As an aid to understanding basic strategy. If you find a particular strategy bizarre, such as doubling A6 vs 3 or splitting 9s vs 9, the numbers will tell you why the strategy is correct and the tooltips - where they're present - will add further clarity.

The data for these tables was originally posted on BJ Math. The site no longer exists but it is, happily, preserved in the BJ Math EV tables web archive.

• Basic strategy EV table

This chart lists the EV of each basic strategy decision in the six-deck S17 game with the same rules as above. For example, 12 vs dealer 7 gives -0.2171, which tells us that the EV of the optimal play for that hand (“hit”) is -0.2171, or -£2.171 on a £10 bet. Since the chart doesn't indicate the plays that the EV numbers relate to you need to be acquainted with basic strategy for the table to be of use.