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Beating Narrow Bet Limits

A reader contacted me recently about a 6-deck Blackjack game in her local area that has decent rules and great penetration, but the table bet limits are $50-$500, which is obviously just a 1-10 bet spread. If you've read my lessons, you know that I stress a minimum bet spread of 1-12 is needed to gain an edge at a 6-deck game, so it would appear that this is not a good opportunity. Casinos know that card counters need a wide bet spread to win at a multi-deck game and they're correct, at least on the surface. However, this particular game allows the player to bet in more than one box; that is, to play multiple hands when you're alone with the dealer.

I wrote a series of articles about the strategy for that ("Playing Multiple Hands"), which is in the archives on this page and pointed out there was no advantage in playing more than one hand when you're alone with the dealer. The reason is that proper money management allows you to bet only 150% more when playing two hands, but you'll also use 50% more cards, so the actual number of $$$ you'd bet in a plus count remains the same. There's nothing wrong with playing two hands "heads-up", but nothing is gained, except for one situation. The one situation where playing two hands can be worthwhile is when your bankroll will allow you to bet more than the table limit. In other words, if you could bet more than $500 per hand, say, $1000 per hand, then playing multiple hands is worthwhile.

Let me get more specific here. The reader uses a "session" bankroll of $10,000 and is willing to commit a total of $25,000 to the effort. The game is 6 decks, the dealer hits soft 17, you may double on any first two cards, including after splitting pairs and late surrender is available. The penetration is a consistent 5 of 6 decks, minimum. Those rules give the casino an edge of about 0.51% - decent, but not great. However, it's the penetration and the ability to spread to multiple hands at anytime that make this game appealing. (It's not in the U.S., by the way.) I ran some simulations to come up with a strategy to beat this game and the results were pretty good, considering. I first ran a "baseline" simulation that restricted play to 1 hand, heads-up with the dealer while betting $50-$500.

Simulation # 1: Six decks, H17, Da2, DAS, LS, 5/6 pen. - $50-$500, play one hand only through all counts - (Bet $50 at True Count (TC) of 1 or lower; $100 at TC 2, $200 at TC 3, $400 at TC 4 and $500 at TC 5 or higher). The overall edge gained was 0.86%, which is - not surprisingly - below the minimum one percent edge that I recommend for playing any game. Of course, we're dealing with a 1-10 bet spread, so the result is just about what the casino intended. A really skillful player might be able to make as few bucks at the game, but most "wannabe" counters will lose. From the sim data, it was shown that the average bet is about $85 (using $50 "units"), so at a rate of play of 200 hands per hour, which is reasonable in a heads-up situation, a player using this bet schedule would earn about 200 x $85 = $17,000 x 0.0086 = $146.20 per hour. That may sound pretty good, but it's not because the Standard Deviation (SD) is considerable. If one were to play 100,000 hands (roughly 500 hours), the expectation would be to win $70,000 or more, but just a two SD downswing would see you at a loss of over $25,000, which is my reader's entire bankroll. Sure, s/he's over betting anyway, but this is a person who has the means to replace that bankroll and is not a pro who must pay the bills from his or her winnings.

Let's see if we can do better. First of all, I want to increase the bet spread by playing two hands as the count rises. The first sim I ran like that had us betting $50 on one hand at a TC of 1 or lower, $100 on one hand at TC2, $200 on each of two hands at TC3, $300 on each of two hands at TC4 and $400 on each of two hands at TC 5 or higher, which is basically a 1-12 bet spread. Everything else remained the same.

Simulation # 2: Six decks, H17, Da2, DAS, LS, 5/6 pen. $50-$400, play one or two hands through all counts. (Bet $50 on one hand at TC 1 or lower; bet $100 on one hand at TC 2; bet $200 on each of two hands at TC3, $300 on each of two hands at TC4 and $400 on each of two hands at TC 5 or higher). The overall edge gained was a modest improvement of 0.94%; still not very exciting and still not over the one percent minimum I recommend. The average bet size is only $94, so we have more work to do.

This player told me s/he has a "wild gambler" image at the casino, so it's not a problem to bet the table maximum of $500 on more than one spot. That being the case, and the fact the s/he's willing to risk the entire $25,000 at anytime, I ran another simulation where two hands are played at a TC of 2 or more and the top bet of $500 on two hands is reached at a TC of 4. For that simulation, I set the bet schedule at $50 on one hand at TC 1 or lower; bet $100 on two hands at TC 2; bet $300 on each of two hands at TC3 and $500 on each of two hands at TC4 or higher, which is a 1-15 bet spread.

Simulation # 3: Six decks, H17, Da2, DAS, LS, 5/6 pen. $50-$500, play one or two hands through all counts. (Bet $50 on one hand at TC 1 or lower; bet $100 on two hands at TC 2; bet $300 on each of two hands at TC3 and $500 on each of two hands at TC 4 or higher). The overall edge gained was 1.15%, which is above my minimum, but still nothing special. The expectation for 100,000 hands of play is to win $132,000 and a 2 SD down-move would result in a loss of "only" $15,000 so it's an improvement but certainly not a game from which one can earn a living.

What if our player put out a third $500 bet when the count got to 5 or more? I ran Simulation # 4 on that and the result was an overall edge of just over 1.25%, which is pretty good, but the variance (bankroll swings up and down) will take your breath away. A 2 SD loss in 100,000 hands of play like this could still result in a loss of about $10,000. So, is there any way this player can make some serious $$$ at this game? There is, but it's not easy - simple - but not easy. The real trick is to do what I preach all the time: Leave the table when the count drops. This calls for sitting at tables with other players, which can mean you won't always have the opportunity to bet multiple hands, but if we go back to the original baseline simulation and have the player leave when the counts drops to TC 2 or lower, we can turn it into a beatable game.

Simulation # 5: Six decks, H17, Da2, DAS, LS, 5/6 pen. - $50-$500, play one hand only, leave when the count drops to TC -2 or lower. (Bet $50 at True Count (TC) of 1 or lower; $100 at TC 2, $200 at TC 3, $400 at TC 4 and $500 at TC 5 or higher). The overall edge gained is 1.30%, which is better than the best "play all" strategy shown above. An added bonus is that the variance is greatly reduced, so that after 100,000 hands of play, a profit is virtually assured; only a 3SD down-swing causes a loss. Such is the power of not betting when the casino has an edge over you.

I'll see you here next time.

  

2007 Articles