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Spread 'Em to Beat 'Em


Readers often write me asking if there's a way that they can win at Blackjack by using a lower "top" bet than what I recommend in my Blackjack School lessons and I generally have to tell them that a 6-deck game like I use as the "base" in my lessons requires a 1-12 bet spread ($5-$60) in order to get at least a 1% long-term edge. For example, you may feel comfortable with a $60 top bet, but if you're playing at a table where the minimum bet is $10, you're not getting a 1-12 bet spread. A $10-$60 spread is 1 to 6, not 1 to 12 and that's not going to get you the $$$ because you'll be making a lot of $10 bets when the casino has an edge over you, even if you leave the table when the True Count drops to -1 or lower.

But just how much does a smaller bet spread really cost and is there a way to get at least a 1% edge by betting less than $60 when the count is in our favor? Well, yes and no. I say "yes" because there is a way to get at least a 1% edge by betting less than $60 per hand when the count is in our favor, but I have to say "no" because the technique requires us to play two hands when the count is elevated. So while you won't have to bet over $40 per hand, the total on two hands is obviously $80, which is the mathematical equivalent of betting one hand of $60. However, there are some benefits to playing two hands, as well as some drawbacks. If you've read my series "Playing Multiple Hands", which is in the archives here, you know that betting more than one hand at a time on the same round of player causes something called "covariance" to kick in. What this basically means is that your two hands are related to one another in the sense that both will likely be lost if the dealer gets a 'natural' or both may be won if the dealer busts. Of course, there are a lot of possibilities in between those two outcomes, so oftentimes you'll win one and lose one or lose one and get a 'natural' (a "blackjack") on the other, or win one and lose a doubled bet on the other, etc., etc.

All of the possible outcomes for two hands average out to be a covariance of about 0.50, which means that there's about a 50% correlation between the two hands. (For a complete explanation of covariance, see Part 1 of "Playing Multiple Hands".) This relationship has considerable impact upon the bet schedule you should use, but it mostly breaks down to the fact that you can bet less on each of the two hands, yet still gain an edge over the casino. Understand that you'll be betting more in total per round of play, but because of the "hedging" effect of two-handed play, your risk has not increased greatly and, in the long run, you may actually make more $$$.

To quantify all this, I ran a series of simulations that examine the impact of various betting schedules on the long-term edge and profit potential of the "base" game that I use in my Blackjack School lessons. That game is 6-decks, the dealer stands on soft 17, you may double on any first two cards and after splitting pairs. Insurance is available, but surrender is not. For these sims I used a 70% penetration factor and assumed that the player used the "risk-averse" Basic Strategy variations that I show in the Advanced Course portion of my school. If your game has the dealer hitting soft 17and you do not use the Basic Strategy variations, subtract about 0.25% from the long-term advantages that I'll be showing you.

Okay, let's establish a frame of reference and then build from there. Here are the results of some simulations where everything remains the same, except the bet spread. The notation "Leave -1" means the player left the table whenever the True Count dropped to -1 or lower, as I stress in my lessons. The notation "play all" means that the counter never left the table, which you will see is much less desirable.

Reference Simulations

1. 1-12 Bet Spread (1 unit bet @ TC of 1 or lower; 2 @ 2; 4 @ 3; 8 @ 4; 10 @ 5; 12 @ 6 or more) Overall edge, 1.03%. Expected gain in 100,000 hands of play, 1809 units.
(Leave -1)
2. 1-12 Bet Spread (1 unit bet @ TC of 1 or lower; 2 @ 2; 4 @ 3; 8 @ 4; 10 @ 5; 12 @ 6 or more) Overall edge, 0.48%. Expected gain in 100,000 hands of play, 725 units.
(Play all)
3. 1-8 Bet Spread (1 unit bet @ TC of 1 or lower; 2 @ 2; 4 @ 3; 8 @ 4 or more) Overall edge, 0.90%. Expected gain in 100,000 hands of play, 1498 units.
(Leave -1)
4. 1-8 Bet Spread (1 unit bet @ TC of 1 or lower; 2 @ 2; 4 @ 3; 8 @ 4 or more) Overall edge, 0.36%. Expected gain in 100,000 hands of play, 520 units.
(Play all)
5. 1-6 Bet Spread (2 units bet at -1 or lower; 4 @ 2; 8 @3; 10 @ 4; 12 @ 5 or more; $10-$60.) Overall edge, 0.75%. Expected gain in 100,000 hands of play, 2269 units.
(Leave -1)
6. 1-6 Bet Spread (2 units bet at -1 or lower; 4 @ 2; 8 @ ; 10 @ 4; 12 @ 5 or more; $10-$60.) Overall edge, 0.21%. Expected gain in 100,000 hands of play, 565 units.
(Play all)

Comments: You can easily see that a 1-12 bet spread is the only one that delivers a long-term edge of over 1% and it happens only if you leave the table when the count drops. Play through all the counts and your edge is cut in half! That said, the 1-8 bet spread where you religiously leave the table when the count drops isn't far behind the 1-12 spread, which sort of surprised me and we'll deal with it in a bit. Remember, if you play where the dealer hits soft 17, even the game where you use a 1-12 bet spread and leave when the count drops will have an edge below the 1% I consider acceptable for serious play. The 1-8 spread when you "play all" is a disaster and, while the 1-6 spread (which assumes play at a $10 minimum table) looks like it produces some nice $$$ over a long period of play, you need to remember that you'd be betting twice as much on each hand, so your risk is effectively doubled. Cut the return of 2269 in half and the picture becomes clear: it's a losing game.

So, does this mean there's absolutely nothing that can be done to achieve a 1% edge without a 1-12 bet spread? No, it doesn't. In my never-ending quest to show as many people as possible how to beat as many Blackjack games as possible (on as small a budget as possible), I ran some more simulations to see what can be done. There are basically two ways to accomplish our mission: 1) use a bet schedule that gets the top bet of $60 on the table at a lower count (what we call a "quicker bet ramp"), or 2) play more than one hand when the count is in our favor. Here are some simulations that will demonstrate both of these ideas.

Quicker Bet Ramp Simulations

I'm only going to deal with the 1-12 and 1-8 bet spread here because all the others will be a waste of your (and my) valuable time. Getting your top bet on the table at a lower count isn't without its risks, as you can imagine. Now, I'll be the first to admit the 1-12 bet schedule that I teach is conservative, but it was designed for beginners and there's nothing wrong with being conservative when you're a beginner at something. Even so, making the top bet of $60 when the count is at 6 or more is fundamentally sound, especially when you're operating off a minimum bankroll of $3000. But, if you're willing to trade off more risk for more $$$, then a slightly modified 1-12 bet schedule may be the way to go. Just remember that such a change really calls for a bigger bankroll than the $3000 I recommend in my lessons. My guidelines for constructing a betting schedule for the "base" game are outlined in lesson 8 and there you'll see that if you get the top bet out at a True Count of 5 instead of 6, the bet should be no more than 1.52% of your total bankroll. Dividing 60 by 0.0152 shows us that the bankroll should be more like $4000 to stay within the same "risk of ruin" parameters as the original betting schedule.

Getting the top bet on the table at a TC of 5 isn't a huge change, of course, so you might be thinking we should do it at a TC of 4. That's fine, but then you'll start running into the second risk associated with a quicker bet ramp: detection by the casino personnel. Ramping up quickly involves a certain amount of "bet-jumping" that may attract unwanted attention and those loveable characters, the "pit critters", know all too well that an aggressive bet spread will beat the game, so you'll have to decide for yourself if it's plausible. You'll definitely need some good camouflage to pull it off, part of which must be a willingness to play the tables in a "hit-and-run" fashion, which is good because you don't want to stay through minus counts, anyway. That's not much of a problem if you routinely play at casinos with a lot of tables, but if you play in smaller casinos, you're going to be hard-pressed to pull it off. Anyway, the decision is yours, so here are some more simulations to help you decide:

7. 1-12 Bet Spread (1 unit bet @ TC of 1 or lower; 4 @ 2; 8 @ 3; 10 @ 4; 12 @ 5 or more) Overall edge, 1.10%. Expected gain in 100,000 hands of play, 2449 units.
(Leave -1)
8. 1-12 Bet Spread (1 unit bet @ TC of 0 or lower; 3 @ 1; 6 @ 2; 9 @ 3; 12 @ 4 or more) Overall edge, 1.01%. Expected gain in 100,000 hands of play, 2917 units. (Leave -1)
9. 1-8 Bet Spread (1 unit bet @ TC of 1 or lower; 2 @ 2; 6 @ 3; 8 @ 4 or more) Overall edge, 0.92%. Expected gain in 100,000 hands of play, 1805 units. (Leave -1)

Comments: The 1-12 bet spread where we "top out" at a TC of 5 produces about 30% more $$$ than the "regular" 1-12 bet schedule, but not a bigger advantage. That's because all we've done is raise the average bet size. The more aggressive 1-12 bet schedule, where we essentially are betting 3 times the True Count, offers a significant increase in profits over time, but the risk is much greater, so it calls for an increased bankroll of $5500. The 1-8 bet schedule is just below my 1% minimum edge and should not be used, but it does demonstrate that the game can be beaten by a smaller spread. Barely.

Playing Two Hands

But I still have one more trick in my bag and that's to play 2 hands when the count warrants. By playing two hands when appropriate, we can get the best of both worlds. It's a spread that will get the $$$, but shouldn't attract a lot of attention, however it can be difficult to implement because of crowded conditions and so forth. Most non-counting Blackjack players (gamblers) believe that switching back and forth from one hand to two messes up their game, so it usually attracts a lot of attention. Of course, it doesn't mess up their hands (you do know that, don't you?), but sometimes you'll have a nice, big, fat, juicy positive count and you won't be able to take advantage of it. That's why you need to remember that these simulation figures are ideal numbers, which most humans cannot attain, although you can come close. I recommend cutting the percentages and profit numbers of all these simulations by at least 10% in order to be realistic about the results they can produce. I didn't even try to develop a 1-12 bet spread for two-hand play because of the increased bankroll that's needed. However, a 1-8 bet spread where two hands are played when the count is into profit territory deserves a look:

10. 1-8 Bet Spread (1 hand/1 unit bet @ TC of 1 or lower; 2 hands/4 units @ 2; 2 hands/6 units @ 3; 2 hands/8 units @ 4 or more) Overall edge, 1.03%. Expected gain in 100,000 hands of play, 2656 units. (Leave -1)

Comment: Once again, we don't see any increase in our overall edge, but because we're getting more $$$ on the table, our expected income goes up and that's what really matters anyway. I fooled around with other bet schedules than the one above, but this one looks the best to me. It's no more risky than the 1-12 bet spread where the player leaves the table when the count drops to -1 or lower and with an 8-unit top bet, it probably won't attract undue attention at least from a spread point of view. The fact that the long-term return is just over the minimum 1% troubles me some, but that's more a function of the penetration than anything else. Keep everything the same but change the penetration to 5 of 6 (83%) and the overall edge jumps up to 1.35%, which underscores the fact that it always pays to go "shopping" for better penetration.

Conclusions

Hopefully this has shown you that it's futile to play with a spread of less than 1-12 for single hands or 1-8 for two hands at what is, perhaps a better game than you're playing now. Again, I want to say that if your local game has the dealer hitting soft 17 or if its penetration is less than 70%, it's going to be difficult to make any serious $$$. And if you're inclined to sit at a table through all counts, you really haven't got a prayer at most games. It's not just the spread that'll beat 'em, but your willingness to move when the count drops matters a great deal, too. Hey, I never said this stuff was easy!

I'll see you here next time.

 

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