Whenever you make a secret bet, your opponents will be forced to guess what size bet you made. Of course, they may be in such good shape or such bad shape that they really don't care what you bet, but sometimes you can "bluff" them by making a totally unexpected bet. For example, if you're LB1 with, say, T25,500 chips and HB1 has T35,000 chips, while the others are spread in between, most will figure that you'll bet somewhere between one-half and all of your chips on an elimination hand, so they'll bet accordingly. But if you bet only T500 and then surrender your hand, anyone who bet more than just their lead over you will be trapped and will be forced to win their hand. Of course, they won't know that, so it's largely up to the Blackjack gods whether this succeeds or not. But I will tell you this: The vast majority of players in these tournaments do not expect LB1 to make a minimum bet! I've done this a few times and when it works, it's a beautiful thing.

I'll see you here next time.

Whenever I'm playing a "cash" game of Blackjack (as opposed to a tournament), I eagerly double hands like A-2 versus the dealer's up card of 6 because I know that play will produce a nice profit in the long run. Ah, there they are - those words - "the long run." But taking the long view is really the only way a professional Blackjack player can expect to succeed. Look, I know I can win at Blackjack on a consistent basis, yet I don't bet my entire bankroll on any one hand because I could easily lose that hand. But if I play several hundred hands at a decent game, I'm highly favored to show a profit for the effort.

In a multi-table (MTT) Blackjack tournament where one may play 75 or 80 hands at the most or in a single-table "sit & go" (SnG) tournament where one will play no more than 30 hands, those words - "the long run" - have much less meaning. The long run counts if I play a lot of tournaments, but in the case of just one specific tournament, playing my hand strictly according to Basic Strategy can oftentimes be a mistake. No, I'm not suggesting that you should start hitting all of your 17s against a dealer's up card of 10, but there will be times when that's the proper play. I discussed the role of Basic Strategy variations in a tournament setting in Lesson 3 of this series, so you might want to take a look at that when you get a chance. In there, I showed the difference between "expected value" in situations like standing with 12 against a dealer's 3, but that's not what I'm going to discuss here.

This time, I want to talk about doubling and splitting from more of what I call an "absolute" basis - which I define as winning or losing that particular hand. In other words, if you're playing Hand #1 of a tournament and you've bet the minimum, it really doesn't matter if you double, say, A-2 versus a dealer's 6 and go on to lose the hand; you can make up the loss in subsequent hands. But it might make a difference if you've placed a big bet on an elimination hand and now must decide whether or not you should double. A loss might cause you to be eliminated or a win might put you in first place and that cannot be measured by expected value alone. Just for the record, doubling A-2 vs. 6 in a game where the dealer hits soft 17 has an expected value of +.204, whereas the expected value for just hitting is +.166, so not doubling is a pretty serious error in most cases. But what if you really need to win this hand? Obviously, you have a better chance of beating the dealer by hitting, because when you double, your hand receives only one additional card and you're basically hoping the dealer will bust, rather than expecting to get an 8 as your double card, leaving you with a very satisfactory 21.

The way I view it, there are two types of doubling hands: "safe" doubles and "dangerous" doubles. This applies to splitting pairs as well and I'll discuss them in a bit. But back to doubling for the moment - specifically soft doubling where your hand contains an Ace - a hand like A-2 versus the dealer's 6. We know the dealer will bust this hand about 44% of the time - again, in "the long run" - but what if your tournament fate is tied to this one hand? There's a 56% chance the dealer will not bust, so hitting may or may not be the better play. If you double a hand of A-2, there are only four cards of the thirteen available to you that will improve your hand: the 5, 6, 7 and 8. Obviously, an 8 gives you 21; a 7 gives you 20; a 6 gives you 19 and a 5 gives you 18. Am I ignoring the 4, which gives you 17? Yes, because the dealer hits soft 17, she, he, (it?) will end with a 17 about 36% of the time and I'm assuming that a tie will do nothing for you - you're going to have to win the hand in order to proceed in the round. You really don't want to feel too comfortable when you're sitting with a 17 and the dealer shows a 6.

Anyway, this brings us to some pretty simple math. If you double A-2 versus a dealer's 6, there are 4 cards of 13 that will improve your hand to the point where you might beat the dealer - "might" being the operative word here; there are no guarantees, obviously. Four of 13 is a probability of 30.8%, which basically means you will likely lose (or push) the hand about 70% of the time if the dealer doesn't bust. To me, a 70-30 ratio makes doubling A-2 vs. 6 a dangerous double, so I do it only when necessary or when a loss doesn't mean a lot to my situation. Here are the numbers for other soft doubling hands, with "improves" meaning you end with 18 or more:

You can see that the best hand to double is A-7 because most of the time (a slim majority, to be sure) you'll actually improve the hand or at least not make it worse. Doubling A-10 (a "natural" as we call it here) in order to improve the payout from 3 to 2 up to 2 to 1 is an "iffy" proposition at best because you'll actually make it a worse hand about 70% of the time, so you really have to hope that the dealer busts. Now don't get me wrong; sometimes doubling your hand in the hope of a dealer bust is your only viable choice, so that's what you should do. But at least by becoming familiar with the numbers I've presented here, you can make an informed decision about your play. Just so you know, most "hard" doubles like 11 vs. 10 or 10 vs. 9 often don't need the dealer to bust in order to succeed, so I'm not covering them here, but I might discuss it in a future lesson.

Now let's talk about splitting pairs, which I've also placed in the "safe" and "dangerous" categories. While a lot depends upon which up card the dealer is showing, some pairs just beg to be split because they're a lousy hand otherwise. The prime example is, of course, 8-8, which is a 16 if left alone. To my way of thinking, the 8s are followed closely by A-A, which is a 12 that's magically transformed into two 11s when split. In the previous lesson I showed that just hitting A-A versus a dealer's 10 is a huge mistake from an expected value point of view, so make darn sure you're in dire straits before you choose to just hit them. My advice is to split Aces every time you get them, period. So, both Aces and 8s are in my "safe" category, which means you'll be much better off most of the time you split them. I also put 9-9 in that category, so long as the dealer isn't showing a 7, 10 or Ace. Basic Strategy says to split 9s versus 2 through 9, except for 7; otherwise stand and that's what you should do most of the time.

Don't forget that, unlike doubling, all hands created by splitting a pair (except Aces, of course) can take additional hits so splitting/not splitting is less of a problem when the dealer doesn't bust. That said, there are still some pairs where you're likely to need a dealer bust, which makes them "dangerous" to me. Pairs like 2-2, 3-3, 6-6 and 7-7 are both poor starting hands and poor splitting candidates. Naturally, we don't get to choose our starting hands, but whether or not to split them is our choice. In a tournament setting I almost always follow Basic Strategy when playing those pairs, but if an additional loss will hurt me quite a bit, I'll just hit or stand with them, depending upon what up card the dealer has. I seldom split 4-4 (even though it's proper Basic Strategy versus 5 and 6 when double after split is allowed) and never split 5-5 or 10-10, unless I'm desperate. For the life of me, I cannot understand the affinity for splitting 10s in these tournaments. As you can see in Lesson 3, it's a costly move from an expected value point of view, yet players do it all the time. I suppose I should just shut up and be thankful. With that, I'll shut up.

See you here next time.

There's nothing quite as exciting as a "Hail Mary" pass to end a football game or getting a blackjack when you've bet all of your chips on a hand, but both are acts of desperation that fail more often than they work. Prayer might work in a football game, but I know for sure that it doesn't work at Blackjack. Either that, or the Blackjack gods are ignoring me because I've called upon them too many times in the past. I know, because I get "blackjacks" (or 'naturals' as we prefer to call them around here) only about 1 hand in every 21, on average. Of course, that's the mathematical expectation for receiving a natural and, for the life of me, I haven't been able to improve on that probability. So, if you need a natural in order to survive, say, an elimination hand, your probability of success is less than 5%.

However, you might be able to improve your probability by making a bet that is less than all-in; what I call a bet with a choice. Unfortunately, such a bet has a cost associated with it. For example, if you have only T10,000 in chips (the "T" means tournament chips), bet it all and receive a natural, you'll have T25,000 in chips when the hand is finished. If you were to split your bankroll instead, then receive a natural, you'd have only T17,500 at the most when the hand is finished, unless you double the natural (which you can do in most Blackjack tournaments) in which case the most you'd have is T20,000, assuming you win the hand

By going all in on a hand, you're guaranteeing that you'll multiply your bankroll by 2.5 times about 5% of the time. Sure, it might be your only chance and if it is, you've got to go for it. But in my experience, it seldom comes down to such a desperate situation. In other words, most of the time you can give up the opportunity to get an all-in natural and still come out of the hand as a contender in the match. First, if you bet all of your chips and lose, you're out of the tournament, plain and simple. However, if you bet only a portion of your chips, you may still lose, but someone else might bet all of theirs and they'll go out, even if it's not an elimination hand. The problem is that you might still be in the match but you're basically crippled if you have only T1000 or T2000 chips left.

This situation leads us to an area of analysis that a lot of players new to the game miss. There's not a lot to be gained by surviving an elimination hand with just a few thousand tournament chips left, so you need to remember that you can't lose what you don't bet. Of course, if some or all of your opponents are using their secret bet on the hand, you cannot ever know for sure just how much to bet. But as you gain experience, you'll likely discover that many experienced players will bet as little as possible on an elimination hand because of two factors. First, they recognize that the odds of the game favor most of the players losing the hand and secondly, they do not want to end the hand as the short stack at the table. Unfortunately, there's no absolute here; the probability of the dealer getting a natural to wipe out the table is only the aforementioned five percent and even that won't happen all the time because some lucky stiff (not you or me, of course) will also have a natural and push. So, it's very likely that some of the players will win the hand, particularly if the dealer busts - something that will happen about 30% of the time - in which case everyone might win the hand. These numbers imply that it's not a smart move to bet the minimum (assuming you're more or less in the middle of the pack, chipwise) because you'll benefit against all of your opponents only when the dealer gets a natural and gain some benefit when you bust yourself (about 23% of the time when playing proper Basic Strategy, as I recall), although the latter case may still see you eliminated if others have taken the "low" or if they win their hands.

What's most likely to be the case is that you'll have to bet something more than the minimum in order to remain competitive. At the same time, you want to bet just enough to "squeek" by, thus not giving up too much ground should you lose the hand. If you bet no more than 50% of your chips, a lot of options are available - not the least of which is being able to split a pair. Oftentimes, pair splitting results in you winning one hand and losing the other if the dealer doesn't bust, so doubling is usually a better play than splitting if your cards permit. Of course, you're probably not going to double a hand of 10-10 because you can split them in order to get more chips on the table, but there are times when I'll double rather than split, even though I've bet no more than 50% of my chip stack. Take a hand like 4-4 versus a dealer's up card of 10 as an example. Naturally, hitting is the best play, but if I need to get more chips on the table, were I to split, there's a chance of me busting both hands but that cannot happen if I just double. Sure, I still probably need the dealer to bust, unless she has a 7 in the hole and I catch a 10 or Ace, but by splitting my expected value (EV) is to lose 61.89% and my EV from doubling is to lose 74.5%; not great, but at least I won't bust the hand, which really hurts when the dealer goes on to bust her hand.

Another good reason to bet no more than 50% of your chips is what I call the "confusion" factor. Let's say you're the low stack at the table, LB1 (see Part 2 of this series for an explanation of HB and LB) with T18,000 in chips and must bet first. Everyone else at the table will likely size their bets to cover you doubling up to T36,000, should you indeed bet your entire stack. But what if you bet only half, which is T9,000? Now, somebody's confused, I assure you. Most players will still figure you'll double, so they'll likely bet enough to end with more than T36,000 if they win the hand, but some will bet just their lead over you and others will bet enough to cover your total should you get a natural on the T9,000 bet. You see how this works? Bet all of your chips and it's easy for your opponents to calculate your probable ending total, plus you're out if you lose the hand. But if you bet only 50%, you can still bet your entire chip stack on the hand - either by splitting or doubling - but you can also surrender or perhaps survive elimination, even if you lose the hand.

I'll see you here next time.

When we're counting the cards, about 10% of the time we can vary the play of our hand according to the count, something we call "Basic Strategy Variations" (BSVs). Probably the best example is a hand of 16 versus a dealer's up card of 10. Basic Strategy says that's a hit, but if the count is above 0, the better play is to stand. Thus, the BSV for 16 v. 10 is to stand at any count above zero. Every hand in Blackjack has just one correct variation, like standing with 12 vs. 2 instead of hitting, doubling 11 v. A instead of hitting and, yes, splitting 10s v. 4, 5 or 6. But those plays should normally be made only when the count calls for it and the Blackjack tournaments played at Ultimatebet.com use 6 decks that are shuffled after every round of play, so counting the cards is of no use. (Darn it! The tournaments at Global Player Casino also use 6 decks, but they deal out 75% or more of the cards before a shuffle. I miss that a lot...sigh.)

But just because counting the cards isn't possible, it doesn't have to mean that a Basic Strategy Variation is never the correct play in a tournament. There may come a time when you need to get more chips on the table or cannot risk busting your hand and making a Basic Strategy "mistake" may be your only choice. Yes, I called it a mistake on purpose - if you make a BSV without having the count to justify the play, you're making a mathematical mistake, plain and simple. Of course, your entire tournament may be riding on the hand, so the benefit of winning will likely far outweigh the "expected value" loss of the play, but don't kid yourself - there is a cost associated with failing to play perfect Basic Strategy - and, while it may not show up in this tournament or the next one, or even next week's tournament - it will eventually be collected from you. What I'm trying to say here is that you should vary from proper Basic Strategy only when absolutely necessary or be prepared to pay the price.

You won't have to play very many Blackjack tournaments to discover that players just love to split 10s. Most would never do it in a "cash" game, mainly because it draws such a heated reaction from the other players - "You're messing up the order of the cards, man!" - but in a tournament, it's apparently a different case. (It's BS, of course; how others play their hand will have no long-term impact on your results.) I have even seen players in a tournament make weird plays like hitting a hard 18 because they thought their actions may cause the table to lose, but in reality, they're only hurting themselves. I never comment on it, but if I did, it would be only to encourage them to continue with their "sophisticated" play. Sure, a player might take the dealer's bust card and cause you to lose the hand, but in the long run, they'll help you as much as they hurt you - they might also take the dealer's 5 that would have given him or her a 21. Anyway, let's get back to splitting 10s. You need to remember this: By splitting 10s, you're not only giving up the very strong hand of 20, but are also betting more chips for the privilege. If you need to get more chips on the table, that's a good way of doing it, but there's a cost. How much? Glad you asked.

Your hand of 10-10 versus a dealer's up card of 6 has an expectation of winning 67.7% of all the $$$ you bet in that situation when you stand. If you split the 10s, your expectation drops to 25.25% on two hands, which totals 50.5% of your original bet. (Don't forget that you must make a bet equal to your original bet in order to split a pair.) So by splitting, you're giving up 17.2 percentage points or nearly 30% of your original expectation. Yes, I understand splitting the 10s may be your only choice to, say, survive the elimination hand or win the match, but to do it as a matter of course throughout a tournament is very costly. The only saving grace is that 10-10 vs. 6 is a hand you'll get only about 723 times in every 100,000 hands of play, so you don't get that many chances to split them. The corollary to that is, of course, if you get it so seldom, why mess it up? But don't tell the "splitters" that....let them continue to have their fun and reduce their chances of beating you.

You'll also see a lot of players just hit an 11 versus a dealer's up card of 10 and you should applaud their timidity. As you might guess, it's a mistake to not double here; this is a hand you'll get about 1.66% of the time, which doesn't make any statistics associated with it earth shattering, but a mistake is a mistake and we all make enough without trying, so why add to them? Sure, it might be that betting more on this hand and losing could cause you to fall behind the lucky stiff who was LB-1 and is now sitting there with a 20, but not doubling 11 vs. 10 on a regular basis is costing you 5.9 percentage points, which is about a third of the expectation of doubling. The expectation for hitting 11 versus a dealer's 10 is to win 10.7% of all the $$$ you bet in that situation, whereas by doubling, the expectation is 17.8%. The numbers I'm showing here are situations where you double for the same amount as the original bet (you may double for less) and are based upon the return on the original bet. In other words, the percentages recognize that you're doubling the bet, but in this case specifically, the return isn't two times 10.7% or 21.4%, mainly because you get only one card on a double, but it is 8.9% on each bet, which totals to 17.8%. Clear as mud? I'll explain.

When I speak about the percentages here, I say "percent of all the $$$ you bet in this situation" because that's the most accurate way to describe it. As an example, if you were to always bet $10 per hand in a "cash" game of Blackjack and you were always dealt a hand of 10-10 against a dealer up card of 6, you'd have an advantage of 66.7% over the house. (Hell, the "house" would soon be yours.) Your expected value would be $6.67 per hand, but you would win or lose $10 at a time - losing when the dealer hits to 21 and basically winning every other hand - which basically means you'll win 667 hands out of 1000, pushes ignored, and it's better expressed (for me, anyway) on a per-hand basis. But if you wish, you can think of it this way: If you stand with 10-10 versus 6, you'll win 66.7% of the time, but if you split the 10s, you'll win only 50.5% of the time. Remember, when you split 10s, sometimes you'll win one hand and lose the other, resulting in an overall "push" or you'll win both or lose both, lose one and push one or win one and push one, etc. Take all of those possible outcomes and your expectation is to win 66.7% if you stand and win only 50.5% if you split. When you split, you're creating at least one additional hand and those "extra" hands kind of mess up the equation, but you have to count them, regardless. The best way is to calculate everything off the original bet, rather than start trying to figure out just how many times you might split the 10s (you may split to create 4 hands at Ultimatebet.com), whether one hand will win and the other may push, etc., etc. This is probably no clearer than before, but I think you get the idea.

Perhaps this is a good place to introduce my "Tournament Basic Strategy Variations" matrix, which is attached here as a separate page that you may copy for personal use. What I've done is list most of the BSVs a card counter will use when playing a cash (non-tournament) game and calculated the cost of making that variation when the count does not justify it. For example, Basic Strategy says to always hit a hand of 10,2 versus a dealer's up card of 2. However, if one is counting the cards using the Hi/Lo count we teach here, the Basic Strategy variation is to stand on 12 vs. 2 when the True Count is 3 or more, so you can see that standing with 12 vs. 2 when you're not counting the cards is a mistake. If you hit 12 vs. 2, the expectation is to lose 25.2%, but if you stand the expectation is to lose 29.0%. No matter what you do with a 12 versus a 2, you're going to lose in the long run. But at least by hitting, you lose less. Now, understand that I hate 12s, but it doesn't affect the percentages - hit, lose less; stand, lose more. But, there may be a point in a tournament where you simply cannot afford to bust, so standing is your only option. If you do, it's costing you 3.8%, which is not a big deal on one hand, but if you do it all the time, in the long run it'll add up. So that's what I've done here - give you the cost of making a Basic Strategy variation when the count doesn't justify it.

In Lesson 1, I discussed some general principles of surviving the elimination hand and presented some rather simple strategies - simple, in that I showed you what can be done if you have a chip stack that's higher than the lowest stack at the table. It's usually very easy to play when you're in the lead, which is what makes it simple. This time, I want to discuss what's probably the worst situation, which is when you're the lowest stack at the table and, while it's still pretty simple - just bet everything and pray is the primary strategy - there are other little "tricks" that can apply in certain situations.

But before I do that, let me introduce some terminology that I'll be using throughout this series. When I speak of "chip stack", I'm of course referring to the total amount of chips you or your opponents hold prior to betting the current hand. In Blackjack, we typically call this our "bankroll", which is often abbreviated as BR, so the highest bankroll is BR-1, the next-highest is BR-2 and so forth. But in tournaments that have elimination hands, like the type played at Bet21.com, the lowest BR often plays a key role, so what I do is designate BRs as either high or low. In other words, BR-1 to me is HB-1 or "high bankroll" number 1, which is the chip leader at the table and HB-2 is the second-highest, HB-3 the third and so forth. The lowest bankroll at the table is LB-1, the next-lowest stack is LB-2, etc. Of course, a chip stack that is HB-3 might also be LB-2, depending upon your perspective and the number of players remaining at the table. So the ranking goes like this, from high to low for a 7-person table: HB-1, HB-2, HB-3, HB-4; LB-3, LB-2, LB-1. Just note that HB-4 could also be LB-4, if I were concentrating on more than three low bankrolls, which typically won't happen, but you never know. Clear as mud? Let's move on.

Okay, so let's say you're LB-1 and it's time to play hand # 8, which is an elimination hand. If you must bet first, there's very little choice except to go all-in, but you probably still have your secret bet available. The big question here is whether or not you're going to fool anyone by going all-in as a secret bet. Personally, I'd like to save it in case I survive the hand, but you might want to try making a minimum bet in secret, with the idea that most of the others will think you've gone all-in and will bet accordingly. I used this technique to win a single-table tournament (SnG) just the other day. My opponent had a big, but not substantial, lead over me - something in the T32,000 to my T26,000 neighborhood - and I figured that he'd figure I would bet at least half or T13,000 - so he he would bet T7500 (he didn't have a secret bet, but he did get to bet last), which would put him at T39,500 and me at T39,000 if, indeed, I bet half of my stack and we both won the hand. I gambled that he'd play it that way (and you think poker is the only game with a "he knows I know that he knows" aspect to it?), so I bet T500, which would put me at T25,500 and him at T24,500 if we both lost the hand, which is what the basic odds favor, anyway. As it turned out, the dealer obliged me by having a 'blackjack' so we both lost and I won the match. Of course I was toast if we both won the hand because even a double on my part wouldn't help me, but you can't have everything - luck and solid probability still plays its part.

The one thing you should try to avoid is betting in such a way where you must win the hand and your opponent (in the case of an elimination hand, the player who is LB-2) must lose in order for you to succeed. Naturally, that isn't always possible, especially when you're LB-1 on an elimination hand, but you need to think about some basic percentages that I covered in my series on Heads Up Blackjack Tournaments (Part 2, as I recall) before you act. The probability of both players losing the hand is in the 31% area, which obviously means there's nearly a 70% probability that both of you will not lose the hand. All that's left - other than pushes - is that you will win and your opponent will lose or you will lose and your opponent will win or you both will win. The probabilities here are about 30% that both of you will win the hand; 12% that you'll win and your opponent will lose and 12% that your opponent wins and you lose. As for pushes, the probability of both of you pushing is very small, hardly worth a number at all, and the probability of you pushing and your opponent winning (or vice-versa) is about 2%, so it's not a major factor. A case of you pushing and your opponent losing (or the other way around) is a little more significant - about a 5% probability, but it seldom makes a huge difference in an elimination hand, so don't spend a lot of time sweating it.

The really important numbers here are the probabilities of you both winning or both losing versus the probability of one winning and the other losing. It's roughly 30% - both win or lose - versus 12% that one will win while the other loses. Blackjack is a game of percentages and if you play tournaments, these are percentages you need to learn. I think most Blackjack players are optimists, so it shouldn't surprise anyone that most will play their hands with the idea that both will win. But sometimes, like when you are LB-1 in an elimination hand, you have to play it in an opposite manner in order to survive; which might mean making a minimum bet if that's your only chance - however slim - to make it through. Sure, I've "taken the low" (held back more chips than my opponent) and lost when the dealer busted with an Ace up, but that's how it goes sometimes. Stick with the percentages and in the long run they'll pay off.

Another factor you should consider when sizing your bet on an elimination hand is that you might actually survive the hand so betting as little as possible could serve you well. After all, what good is it to survive the elimination hand and be left with T1000 in chips? Sure, you might parlay that up to T25,000, but care to bet on it? Surviving the elimination hand only to go bust on the next hand doesn't make a lot of sense. I cannot give you any hard and fast rules here because each situation is different. But knowing the different choices available to you, as well as a rough idea of the probabilities for success will help you in the long run. In terms of general strategies for LB-1 on an elimination hand, most of what you can do is based upon your betting position and how far you're behind in the chip count versus your opponent(s). Here are some ideas:

LB-1 Betting First: You really have very little choice other than betting all of your chips and hoping for a decent hand. It's not likely that an opponent will hold back fewer chips than you, so you basically need to win the hand and hope that someone has made a bet that's not big enough to still beat you if you both win. Sadly, most will bet enough to "cover" you and since the probability that you'll get a 'blackjack' is only about 5%, you're really in a bad place. To survive, you usually need to win when someone else loses. As an aside, some players in this LB-1 situation will hold back T500 in chips so they can double for less, thus hiding their "hit" card, which may create some confusion on how their opponents should play the hand. Personally, when I see a desperate LB-1 double a 15 or higher, I figure they've busted and play accordingly. I seldom use that technique when I'm LB-1, but I do sometimes just split my BR and not use the secret bet, which can cause my opponents to under-bet their hands. Naturally, I then double any hand or split any pair, thus getting all of my chips in "the pot". The only thing I'm giving up is the 3 to 2 pay on a 'natural', but even then I'll double it. This works pretty well when you get a hand of 10-10, which can then be split. If an opponent bet his or her hand based upon you betting only 50% of your chips, they might be surprised. But in reality, this seldom happens in the $30+ entry fee tournaments - most of the players there will know what you're up to, although it's something to bear in mind.

The new Ultimate Blackjack Tour (tm), which is currently airing BJ tournaments on television (CBS on Saturdays) uses a format where the player who has the lowest chip count at the end of certain designated hands is eliminated. This approach to a tournament keeps the action lively and adds a certain amount of drama, which I find very appealing. Having played in literally hundreds of tournaments where the chip count after the final hand is all that matters, I think I can fairly say that watching or playing those events is very much like watching paint dry. I've done it myself plenty of times - make the minimum bet until one or two hands before the end, then let it rip. Well, most of the time that's the proper strategy so unexciting or not, it's certainly one way to win.

Now, with the addition of an elimination hand, one cannot just sit there and bet the minimum because you might very well find yourself in last place and gone in hand # 8 of a thirty-hand match. Consequently, you have to try and keep up with your opponents, especially the "rabbits", as I call them; the players who are seriously over-betting their chip stacks. This makes for some wild swings, and big bets are always exciting in a Blackjack tournament. A tip of the ol' GameMaster's hat to those that came up with the idea! Not only do elimination hands make the tournaments more fun to play, but they also make the tournaments harder to play.

Any advantage player prefers complicated games when competing against other players, because the average person will not take the time to learn or understand the nuances of it all. Most players would rather try to get lucky than put in the time and effort learn a proper strategy, which is why "normal" Blackjack games have continued to be available even after it was shown that most of them can be defeated by counting the cards. There are enough players out there who can only hope to win to pay for the players who know they can win. And it's no different for BJ tournaments in general and BJ tournaments with elimination hands in particular.

If you think about it, an elimination hand is really the final hand of a tournament where N-1 players advance, with "N" being the number of players in the hand. Let's say there are seven players at the table and this is an elimination hand; perhaps hand #8 of a thirty-hand match. That means six players will advance because one is going to be eliminated. The bet you should make on this hand is dependent upon several factors, like what position you're in (Will you bet first? Last? Somewhere in between?), the size of your chip stack, the size of your opponents' chip stacks, the minimum/maximum bet sizes and so forth. The goal is not so much that of coming out of the hand as the chip leader, but more one of coming out of the hand as something other than the low chip stack - the player who will be eliminated.

I'm currently doing a lot of simulation work on this topic and will, over time, present my findings. For this installment, I'll discuss some general approaches to playing an elimination hand where you are not the low-chip total at the table. Surviving the elimination hand is the priority; nothing else really matters and most players will think that way, which might allow us to improve our position at the risk of being eliminated and we'll discuss that in the future. Win or bust out trying to win is a general strategy that will always apply to BJ tournaments; there's nothing to gain by having a lot of chips and not advancing (or being paid, whichever is the case) and most players know that, so it's not exactly a big secret. But, at least in the 100 or so elimination-type of BJ tournaments that I've played in up to this point (some for $$$, most for play-money), I've noticed that my opponents are of two main types. The first is the "rabbit"; they bet all or at least half of their chips on the first hand in an effort to get way ahead of the pack - especially in the play-money tournaments - and when it works, they're usually in pretty good shape when the first elimination hand comes along on hand # 8. (This is a good time to mention that you can play elimination-style BJ tournaments for free at www.playubt.com/ until the cows come home. Because it does not offer real-money play, there should be no problem with this site, no matter what happens with the new legislation here in the U.S. But you can win the opportunity to appear in the next season of the Ultimate Blackjack Tour there, so it's worthwhile visiting. I play there under the name Aceten1, so if you see me, say hi.) The other major type of player is the one who bets only a small portion of his or her bankroll on each hand, which is what I'm inclined to do, especially in a real-money tournament. But when an elimination hand comes up, all bets are off, so to speak. What I'm going to do here is show you what I believe is the most important betting technique one should learn, because it will apply to probably 80% of all the situations you'll run into when playing elimination-type Blackjack tournaments. It's usually called:

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The Lock Out Bet

As I see it, there are three types of Lock Out Bets: the Guaranteed Lock Out (GLO), the Low-risk Lock Out (LLO) and the High-risk Lock Out (HLO), which are listed here in their order of preference. If you can make a GLO, that's better than making a LLO, which is better than making a HLO, as you'll see. Probably best explained by examples, these bets are not necessarily going to fit every situation every time, but I'll save more complicated situations for later chapters of this series. Let's go.

The Guaranteed Lock Out Bet - Regardless of your position for betting, if you have a big enough chip lead over the low stack at the table you can make a bet that guarantees you'll not be eliminated. For the moment, I'm going to ignore all of the other players at the table and focus only on the player with the least number of chips. Let's say you have T33,000 chips and the low stack has T12,000 in chips ("T" means tournament chips with no cash value). If the minimum bet is T500 and the maximum bet is T25,000, the very best that player can do is bet all of his or her chips and receive a 'blackjack' (or "natural", as I prefer to call it), which will leave him or her with 2.5 times T12,000 = T30,000 in chips. This obviously means you can bet any amount up to T2500 in total and, regardless of whether you win or lose, you cannot end with a total lower than the low stack. Notice that I said "T2500 in total", which means all of the bets you make on your hand. If you bet T2500 as your initial bet and then double an 11 versus the dealer's up card of 6, you'd be betting T5000 in total and could finish the hand as the low stack and be eliminated, should your opponent receive a natural when you lose. That's not a good thing, so plan your GLO bet accordingly; in this case I'd probably bet T500 and split or double if called for, but would not bet more than T2000 total if I split pairs and could double, etc. By keeping my total bets less than T2500, I am guaranteed to get through the elimination hand.

The Low-risk Lock Out Bet - The probability that any player will receive a natural on any one hand in a game that uses six decks (like those at playubt.com) is 4.5% or about 1 in 21, which makes this easy to remember. (Get it? "21" - BJ is usually called 21 by the casinos.) Okay, so let's say you have T29,000 in chips, the low stack at the table has T12,000 and you must bet ahead of that unfortunate soul. If you bet T1500, the only way the low stack can beat you is to bet all of his or her chips and receive a natural, while you lose your bet. If the low stack does get a natural, his or her final total for the hand will be T30,000 but you'll know that before you must play your hand, so you can at least double, in a desperate attempt to get to a total of T32,000 chips. If the low stack does receive a natural, but you win your hand, you'll have T30,500 chips to your opponent's T30,000. I call this a "low risk" bet because you're not guaranteed to stay in the match, but it's over 90% probability that you will.

The High-risk Lock Out Bet - If you do not have a big chip lead over the low stack, but are still ahead, then you'll need to gamble a bit, so this may not really be a "lock out" bet by the strictest definition. But it fits here and this is my article, so that's what I'm going to call it. Let's say you have T20,000 and the low stack has T12,000 in chips. If you must bet first, you have to guess what your opponent might bet and that's never a sure thing. But, you can make some reasonable assumptions and hope (prayer doesn't work at Blackjack - I know, I've tried it many times) that your assumptions are correct. First and foremost, you have the lead, so at a minimum you can bet in such a way that your opponent must win his or her hand in order to avoid being eliminated. If you bet T12,000 (not something I necessarily recommend doing, but it's not the worst bet you can make), your opponent goes "all-in" with a T12,000 bet and you both lose the hand, you will have T8,000 and your opponent will have zero chips. If you lose and your opponent wins one bet, s/he will have T24,000 chips to your T8,000, but if you win one bet and your opponent receives a natural, you'll be ahead, T32,000 to T30,000. Obviously, you would prefer to make a bet that allows you to remain ahead of your opponent even if s/he wins the hand and you lose it, but that's not possible in this situation, so you have to make a "high-risk" bet, which is only an attempt at locking out your opponent; it'll be up to the cards if that happens or not. If you assume your opponent will go all-in with a T12,000 bet, then your bet can be T5000, which will leave you with T15,000 if you lose and T25,000 if you win a single bet. Obviously, you have not protected yourself against the low stack receiving a natural, but if you were to make a T10,500 bet, even that situation would be covered. However, by betting less you'd cover a push by your opponent (leaving him or her with T12,000) and that's actually a better play - from a percentage point of view - than covering against a natural. The probability of pushing in Blackjack is 8%, the probability of one receiving a natural is, as we saw, about 5%, so guarding against a push is a slightly better deal. In this case, if you were to bet T7500, your total after losing one bet would be T12,500 so if you lose and your opponent pushes, you'll still avoid elimination. However, if the low stack goes all in, gets a natural and you win just one bet, you'll be eliminated, but you will advance if you both win one bet or lose one bet. You'll even advance if you win just one bet (ending with T27,500) and your opponent has bet in such a way that s/he can double (ending with T24,000). This brings us to another feature that we'll explore more in future chapters:

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The Secret Bet

In the tournaments offered at playubt.com, each player has the opportunity to make one secret bet at each table of the tournament, which means one at a sit & go match and one in each round of a multi-table tournament. This is a very powerful tool and a topic that I'll cover extensively as we go along in this series. In the situation we're discussing here - one in which you are not the low chip stack at the table - the secret bet is probably best saved so you can use it later in the match. One possible exception is when you'll be making a High-risk Lock Out Bet and must bet first in the hand. But bear in mind, that if you make the proper bet, the low chip player will really have very little choice but to go all-in, so be sure you know what you're doing before you burn up your secret bet.

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Practical Application of a Lock Out Bet

On the specially-designated elimination hands, the game at playubt.com allows you extra time to place your bet. While it's normally 30 seconds before a minimum bet will be placed for you, on the elimination hands, it's 45 seconds. If you take the general approch I've outlined here, it won't take you nearly that long to come up with a good bet - not necessarily the ideal bet - but a good, solid bet that'll work 80% of the time. It's really simple, even if you must bet first. Just multiply the low stack's chip count by 2.5 and subtract that total from your chip stack. If the remainder is more than 500, bet that amount, minus 500. For example, if you have T28,000 chips and the low stack has T10,000 chips, multiply 10,000 x 2.5 = 25,000. Subtract 25,000 from 28,000 = 3000. Subtract 500 from that = 2500, which is the maximum you should bet. You will not be eliminated, so long as you risk no more than T2500 on the hand.

If your stack is not at least 2.5 times that of the low-stack player, then do the same calculation, which will leave you with a negative number. For example, if you have T22,000 in chips and the low stack has T10,000, the result will be -T3000 and you cannot make a guaranteed lock out bet, (unless the low stack bets less than all-in, something to bear in mind if you're betting after him or her) so you have to gamble a bit here. My first choice is to bet enough to cover a double by the low chip stack, which would put him or her at T20,000 so your bet of T1500 is still a lock out to everything but a natural. So, if you get a negative number, multiply the short stack's chip total by 2, instead of 2.5 and subtract that number from your chip total. If the result is now a positive number, subtract 500 from that and you'll have your maximum bet.

Should your stack be less than 2 times, but still more in total than that of the low-stack player, then bet the same amount the low-chip player will bet if s/he goes all-in. By "correlating" your bet, you win if you both have the same result. Depending upon your actual chip totals, you might be able to finesse the bet a little to cover a natural by your opponent, should you win a single bet. For example, if you have T14,000 in chips and the low stack is at T10,000, a bet of T11,500 chips will put you on top, even if the low stack receives a natural. Of course, by betting first, you run the risk of the low stack holding back more chips than you, so this might be a good place to use your secret bet, if still available. If you've already used your secret bet, don't complicate matters; just bet as though the short stack will go all in.

Please remember that I've assumed you have a chip total higher than the low stack on this hand, even though you may not be the table chip leader, because the strategy will undoubtedly change if you are the low chip stack yourself. We'll cover that, plus a whole lot more in future parts of this series. By the way, I used a copy of Microsoft Excel that I programmed for Blackjack tournaments to calculate most of the numbers you see here. I also use it in online BJ tournaments and it seems to work well for me. If you'd like a copy, just send me an email with "Blackjack Calculator" in the subject heading, so I know it's not spam and I'll be happy to send you a copy. I'm at Aceten1@mindspring.com.

I'll see you here next time.