Sucker said:
This last chart indicates that if you KNOW that you can steer a 10 to the dealer as a hit card, your AVERAGE advantage is 5.683%.
I am not sure i think this is very useful number
, I should also add that the numbers in the last figures are INCREASE in EV when you steer the 10 to the dealer rather than actual OVERALL EVs. Because for A,7,8,9,T you have to include the EV of pat hands that are not hittable and will not be affected by that steered 10.
Sucker said:
In a REAL-LIFE situation it will be different than this, depending upon the situation. The accuracy of the game will obviously lower the edge quite significantly. Even with 100% accuracy, there will be times when the card CANNOT be steered to the dealer for one reason or another. There will be times when you will want to use the 10 YOURSELF, in the case of a double down or in splitting aces (This of course will ADD to your edge).
yep, that is true, i did write something up about that
http://www.blackjackinfo.com/bb/showthread.php?p=172003 , but as i have mentioned in the beginning of the post, we are ALWAYS assuming that we perfectly steer the card to the dealer. We also totally ignore HOW we spotted the ten because that will affect EV calculations.
Sucker said:
Also, the charts presented by the OP are assuming that the player gets to play basic strategy; and THEN gets to leave the ten.
As an example; suppose you know that the FIFTH card (first hit card) is a ten. If the dealer gets a ten as an upcard, you will take the hit (or double down) if you have 11 or less, or if you have 2 aces. The rest of the time you will obviously be standing on ALL stiffs. According to my simulation program this means that your advantage vs. a ten is only 6.41% rather than 11.87%.
I did say that we are neglecting EV penalties from departures of perfect playing decisions to ensure proper steering (usually a good approximation).
As far as the discrepancy for the advantage vs a dealer's ten you get from your simulator vs the number i calculated, they are not actually that far. The discrepancy is not mostly due to ignoring the loss in EV from sacrificial play but rather to a mis-comparison
As i have mentioned in the above the numbers in the second table represent the INCREASE in EV, what you calculated is the OVERALL EV, to calculate the OVERALL EV in my case, we will need to add the frequency-weighted EVs for pat hands when dealer is showing a ten. We will get 8.52% as OVERALL EV.
If we do the same thing to calculate the OVERALL EV from always steering hands by including all the non-hittable pat hands with their respective frequency weighted EVs we get +31.71% .