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Progressions, "Perfect" Blackjack and Other Ramblings on Gambling


GameMaster,
I have a question. In answer to a non-counting Blackjack player's question, in a recent advisor, you said, "since all the casinos will have a long term edge over you, there is no advantage in varying your bets."

I use a 50% progression---flat betting for two wins, then increase subsequent bets by 50% and back to the table minimum when I lose a bet. I know in the long run that I will lose. However, in a particular session, say I get really lucky and win twenty hands in a row at my normal $5 minimum bet table. If I were flat betting I'd win $100. With the progression betting I'd win $6,453. Looking at the game from a session standpoint, rather than the long run, wouldn't the basic strategy player be better off with some type of progression betting instead of the flat bet?
Best,
Mac

I've never really written a complete article about why progressions don't work and maybe I should. But let's look at them from a practical point of view before I get into all the mathematical mumbo-jumbo. If progressions worked, there wouldn't be any Blackjack games anywhere. Let's face it, progressions are easy to use and anyone can do it, so lots of people are and yet the casinos are still making a profit at Blackjack, so on a 'grand' level, they cannot be working. The corollary to this is the casinos paying 2 for 1 for a Blackjack. Why don't they? It would be easier for the dealers in that they wouldn't have to fuss with those half-dollar chips, etc. But if they did that, the average player would have nearly a 2% edge over the casino. So, you don't see any BJ games out there that pay 2 for 1 on a Blackjack. See my thinking here? If it's good for the casino, it will continue but if it's bad for the casino, it disappears. You can use a progression in any casino and it's because they don't work.

Now, to your specific question, what you say is true: If we consider them only from a short-term point of view, progressions can work. But what is "short-term"? If you mean playing 50 hands where there is a 20-hand winning streak, then I have to agree. But that's not how it works for most people. Few play 50 hands, win and then give up the game forever. On a more practical level, let's say we all play 200,000 hands in our lives. Since we both agree that the amount bet has no effect on whether or not we win or lose the hand, I think it's safe to say that the casino will end up with about a 1% edge over us. That basically means that we'll win 99,000 hands and lose 101,00 hands for a net loss of 2000 hands. The flat-bet player will lose 2000 of his bets. The progression player will also lose 2000 hands, and we don't know if some are minimum bets or top bets or something in between (remember that all progressions end with the loss of a large bet unless it's time to shuffle), but we do know that the average bet will be bigger than the minimum. So, the progression player will bet more and, even though s/he may capitalize on "streaks" like you describe, in the end it just comes out to them losing the same number of hands, but losing more $$$ in the process.


GameMaster,
Is there a book or paper that calculates the maximum advantage that, using a computer that plays perfect blackjack, can be obtained in a multi-deck game? Is that near 2% or more like 5%, 10%?
Thanks in advance.
Lepto

I am not aware of any such study on multi-deck games, but Peter Griffin calculated this for a single-deck game in his book, "The Theory of Blackjack". For a game dealt to the 10-card level (81% penetration), perfect play will produce an average edge of 2.74%. The key to this and to a multi-deck game is, first, the penetration and then the bet spread. Griffin's study was based upon a bet spread of 1 to 2 and the 2.74% average edge is a total of a 0.21% gain from perfect Insurance bets, 1.15% from other variations in Basic Strategy and 1.38% from betting variations.

Realistically, "perfect play" when flat-betting in a six-deck game with 50% penetration (like many games available on the 'Net) will cut the casino's edge to about 0.25% (assuming that the rules give the casino a 0.5% edge "off the top") so this must be overcome by the betting spread. If a player bets one unit in any negative count and, say, 50 units in any positive count, the average edge might be about 1.50%, but the swings in the bankroll would be breathtaking. A more realistic 1-16 spread will produce an average edge of about 1.10%. An additional gain is available to the player who leaves the game when the count goes minus. That can add 0.5% to the average edge. By the way, my calculations here are based upon empirical evidence, not mathematical calculation but I think they'll serve to make the point which is that it doesn't get much over 2% under the best of conditions when faced with shallow penetration.


GameMaster,
I've got a question: is it possible to card count against a blackjack video machine? Wouldn't that be pretty advantageous? No heat from the pit bosses. I just wonder whether the software would be able to detect a counter and start dealing bogus hands. I've also found that the machines have poor rules, such as DD only on 9, 10, or 11 and dealer must hit soft 17. Anyhow, hope you can answer these questions. The reason why I ask is because I just know that my personality is such that I would get really nervous just knowing that the eye in the sky is watching me, or the pit bosses might get suspicious. I guess what I'm saying is I have the brains to learn how to count, but I doubt I have the nerves for it. Everyone's different...
Vladimir

Yes, it would be advantageous to count the cards at video Blackjack machines and there's no way the software could tell if it was dealing to a counter. But the vast majority shuffle the cards after each hand that's played, so there's no way for counting to work. However, there has appeared on the scene a game called, I think, "Digital 21" which is a machine that deals into the deck. I've heard it's available in Las Vegas. Also consider the Internet casinos which offer some penetration. No one will be watching you there!


Hot Tip: Most Blackjack players never hit a hand of 12 against a dealer's up card of 2 and that's a mistake. By hitting, you reduce the overall loss of the hand to 25.3% from 29.2%. It may not seem like a lot, but this is a fairly common hand and it all adds up.


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