Question about a Player's Advantage Chart by Thorp

I have a book with a chart by Thorp called "Player's Advantage or Disadvantage for Certain Special Decks" and I'm not sure if I'm reading it right. It shows that removal of all the 5's from an otherwise complete single deck gives the player an advantage of 3.58% (no surprise) and removal of aces puts the player at a -2.42% disadvantage (no surprise again) -- but it also shows that a deck with no 10's gives the player a 1.62% advantage. That's the one I have trouble with.

Maybe some of you have seen this chart and know what I'm missing. It was in an article he wrote for The Gambling Times Guide to Blackjack, "The Principles of the Game and Why It Can Be Beaten".

Are there any similar charts/programs available on the internet or otherwise?

Thorp published this chart with all the tens removed also in "Beat the Dealer". It is of purely theoretical value because this situation will never occur in real life. Thorp assumes optimal strategy changes for the player and there lies the reason for his advantage. In spite of the dramatically reduced risk of busting the dealer will still have to stand on 17 and very often lose on points.

Francis Salmon

but it also shows that a deck with no 10's gives the player a 1.62% advantage. That's the one I have trouble with.

Think of it this way: the player can gain an advantage with most skewed deck distributions because he can change his strategy accordingly; the dealer is stuck hitting to [hard] 17 and can't split, double or surrender.

Thanks for the replies. Still having trouble with the concept.

Agreed that knowledge of the missing cards and perfect strategy will help a player. But the same table shows that a lack of aces are negative for the player, as are a lack of nines (-.41%). The idea of no 10's as a player's advantage seems to contradict basic counting principles.

I said in my first post that this is purely theoretical. In real life the ten will always be the most frequent card present in the shoe. But if you know that no tens are around you may want to hit hard 17 and gain an advantage over the dealer.

Francis Salmon

A BS player would get crushed if they were playing in a deck with no tens. However, here we are talking about changing the playing strategy to take into account the fact that there are no 10s.

I did Combinatorial Analysis. For the rules that Thorp used (S17-Rs4), I came up with a player edge of 1.73 and a SD of 0.982. This is based upon the best strategy could come up with. This included always hitting Hard 17, hitting soft 18, and never doubling. There are some splits.

I think Thorp assumed DAS, but that is not relevant since our strategy never doubles.

I think this figure is not quote the same as the one published in BTD. I don�t know which is more accurate. I am not quite sure my program is actually finding the optimal strategy, as it may be confused as to how to handle 18s and 19s. There may be other flaws in the analysis. OTH, computers were pretty primitive when BTD was done, and I believe that Thorp used approximation techniques.

Interestingly, when I changed the rules to H17, the advantage shifted to the House. I came up with a player edge of -.677%. When I first did this run, I did H17 because that is how much SD games are dealt now. I was surprised that I got an house advantage, until I decided to look at the H17 rules.