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Heads Up Blackjack Tournaments
Part 2

In the first part of what is now becoming a series, I discussed some general rules for how to bet on the last hand of a "duel" between you and one other player and promised to get more specific in the next article, which is this one. However, I think our time today will be much better spent if I discuss a tool that I use to help me with determining how much to bet on any hand, although it's of most use in sizing my bet on the next-to-last and/or last hand of a match. And, I should mention that this tool can also be used in other Blackjack tournaments, like full-table sit & gos where I have more than one opponent.

The tool is Microsoft's Excel that I have programmed to give me a good idea on how much I should bet at any given time. Now you need to remember that this tool isn't necessarily going to calculate the winning bet for you; whether or not your bet will be the winner depends upon what cards you get, what cards your opponent(s) receive, what cards the dealer gets and so forth. It also cannot predict how your opponents will play their hands - if one of them doubles on a 17 and catches a 4 when I have a three-card hand of 20 (something that happened to me recently), there's nothing I can do about that.

All I can really control is the size of my bet and the play of my own hand, but I can take into consideration the various probabilities of certain events and try to make a decision based upon those possible outcomes. For example, a player will, on average, lose 48% of the Blackjack hands s/he plays, will win 44% and push 8% of the time. So, if I wanted to stay with strict mathematics, I would always play my final hand with the idea that I and my opponent will lose. If only it were that simple. In reality, about the only time you can figure everyone will lose the hand is when the dealer pulls a 'blackjack' and neither you nor your opponent has one for a push. A dealer's blackjack (or "natural" as we call it here) will occur, on average, only 4.75% of the time in a 6-deck game, so for us to expect that to happen exactly on hand #15 of a match is wishful thinking, at best.

I won't bore you with the math, but the probability of both players losing the hand is 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, which I'll discuss in a bit - 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 win and your opponent loses 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 hardly 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. Now understand I'm not implying you should ignore pushes - in certain situations a push by one or the other could make the difference between winning and losing - so you definitely want to take that into consideration when sizing your bet. It's just that you cannot depend upon a push to win the match, for if you do, you're "drawing thin" as we say in poker.

When sizing your bet, you want to do it so that you take advantage of as many of the probabilities listed above as possible. In other words, there's very little percentage in sizing your bet so that you win only if you get a natural; it's a 5% probability at best. However, there's a very definite advantage in sizing your bet so that you'll win even if your opponent gets a natural and you just win a single bet; assuming you have enough chips to do so. It would be a crying shame to lose a match where you win your hand but your opponent wins the match because s/he got a natural. The same is true for doubling, splitting pairs and so forth. While you cannot predict what your opponent will do once the cards are dealt, the ideal situation is that you'll have enough chips to cover any contingency. That won't always be the case, of course, but at least knowing your opponent(s) options will be a big help to you.

Enter my Excel-powered "Blackjack Calculator" as I call it. Because 99% of all the Blackjack tournaments I play are online, I have the power of my computer at hand. And because I operate with a multi-monitor system, it's no big deal for me to have it available for instant use, although even a single-monitor system can use it as well, although perhaps not as quickly. I have used this tool for several years now, particularly in the monthly GMO tournaments at Global Player Casino, later in the 5-player SnG matches and now in the heads up duels they offer. Is it cheating? Obviously I don't think it is; the games are played on my computer and I'm using my computer to help me win, as anyone can. I also count the cards, as I've mentioned before and no one considers that cheating, even though not all Blackjack tournament players can count. In the case of my Blackjack Calculator, anyone can use it - your PC most likely has Excel on it somewhere and I'm about to show you how to program it - so one day everyone who plays a BJ tournament online will be using this or some version of it.

And that's a good point. I've programmed this to serve my needs, but you might want to do it differently. The programming possibilities are virtually infinite, so start with my version and let your imagination go wild. My only caveat is that it should be easy to fill in the information because in some matches time is a factor, although that's not typically the case in the Global Player Casino tournaments on the last hand. But, the simpler, the better as far as I'm concerned. So, I've tried to keep it simple, as you'll see. Before I show you the calculator, let me explain a little bit about how it works in actual use. I currently have it programmed to handle five-player tournaments, which obviously allows it to be used for two-player matches as well; the other three "spots" just go unused in that situation. If I were to begin playing, say, seven-player matches, it's easily expandable by using the "Insert" function after highlighting the bottom line. Anyway, what I do is enter the bankrolls of the players at the table in the order in which they will bet on that hand. So, if the first player to bet has T500 for example, I enter 500 in the top Bankroll cell and if I'm second to bet and have T250, I enter that in the line below. If the player to my left has T625, I enter that below my line and so forth. Because the bets will be placed in a specific order, it's easier for me to go down the column filling in the Bankroll amounts, then each player's bet, including my own. Of course if I have to bet first, I can only make certain assumptions about what my opponent(s) will bet and I'll cover more of that in Part 3.

Generally speaking, if I'm in a heads up match and must bet first, just how much I bet will be determined by my current bankroll in comparison with my opponent's. Should I have more chips than my opponent, I want to make a bet where I win the match if we both win the hand and also win the match if we both lose the hand - that's the ideal situation. Of course, my opponent will react to how much I bet and if s/he is a savvy player, one side of that equation will be taken from me; such is the power of position in Blackjack tournaments. But I can at least mitigate my poor position somewhat by making a smart bet, as you'll see on the example of the calculator I've posted here. Take a look and we'll discuss it below.

The Blackjack Calculator

I have entered some sample data to give you an idea of how this works, plus I'll show you the formulas that apply. Here, I'm first to act and I have a Bankroll total in cell A3 of T555 and have made a bet of T500 in cell B3, which is a maximum bet in this case. Obviously, this leaves me with T55. The formula in cell C3 is =sum(A3-B3), which gives us that answer. Column D is labeled "Bet # 2", which allows for the fact that a player may double for less in the Global Player Casino tournaments. This number is entered if and when such a bet is made. It can also be used in the case of pair splitting, but that of course may not be done for less. In order to split pairs, a player must bet an amount equal to the original bet, so in this particular case, neither I nor my opponent has enough chips to do that, but the software allows for it. Because the 2nd bet is entered manually, it can also be used if a player splits a pair, then doubles; even if s/he doubles for less. All you have to do is enter the total of any bets made after the original and the software will tell you what the total will ultimately be if all of the bets are won, shown in the "Win All" column or if all of the bets are lost, which will be the "Leaves #2" column. Of course a player might split pairs, then double one of them and win one while losing the other which makes for a very complicated calculation to program. I haven't done that on my version, but you might want to do it on yours. In my experience, it seldom comes down to a situation like that - most of the time the player wins them all or loses them all - so I just don't sweat it, but don't let me stop you from programming this to the hilt.

Moving on, the column of most importance is "Win 1", which calculates the total if you or your opponent wins the original bet in the usual manner. Most winning hands in Blackjack are where you get paid "even money", like when your 20 beats the dealer's 17 and so forth. You can see that my max. bet allows me to win if we both win the hand, but my opponent has countered me by "taking the low", which means s/he will win if we both lose the hand. That's significant, to be sure, but by betting the max, I've eliminated the possibility of my opponent splitting pairs, yet s/he will most likely be forced to double in order to win, plus I can surrender, which will give me the win if my opponent does not surrender, but loses the hand. I don't want to get ahead of myself here, because we'll discuss a lot of strategy in Part 3, but this demonstrates that the calculator is also a good training tool. The way I use it is by simply putting in various numbers and then run through what can happen in various situations. Let's move on. The next column, which is labeled "BJ" calculates what the result will be if I or my opponent gets a natural. In the heat of battle, so to speak, you need to remember to allow for this if you're behind or have just a small lead, but it's not the most important situation to worry about because as I mentioned earlier, the probability of getting a natural on any one particular hand is less than 5% and it applies to you, your opponent and the dealer alike. That said, you cannot afford to ignore the possibility, so I've included it here. The formula is: =sum(B3*2.5)+C3. Should your opponent choose to double his or her natural (which is permitted in the Global Player Casino BJ tournaments) you would just enter the amount in Bet #2 and the next column will give you the total. This is the "Win All" column, which uses the formula =sum(B3,D3)*2+E3. Because the game at Global Player allows late surrender, I've created a column for that, titled "Surr. Total". The formula is simple: =sum(B3/2)+C3, which shows that you may only surrender half of your original bet so you'll have half your bet plus whatever was left as your ending total. That can only change if you choose to take Insurance and then surrender.

Speaking of Insurance, while it's usually a bad bet in "cash" games (unless you're counting the cards), it can be a very effective tool in some tournament situations. As you undoubtedly know, Insurance is available only when the dealer's up card is an Ace. Should the dealer have a natural, then any Insurance bet is paid 2 to 1, which basically "insures" you against a loss, if you take full insurance, which is half of your original bet. But there's no law to stop you from insuring for less, either in a tournament situation or a cash game, so I made the Insurance column one where the amount bet is entered manually. If an opponent does take Insurance, you'd just enter the amount and Excel will calculate a variety of possible outcomes automatically when you hit "Enter".

Because Insurance is a separate bet than the one you originally made, there are a wide range of possibilities that can follow. If you lose the Insurance bet, which tells us the dealer did not have a natural, you might still win the hand. Your chip total will then be the amount in the column labeled, "If lost/win1"; and it has a formula of =sum(F3-J3), which is just another way of saying that the amount of the Insurance bet was deducted from the "Win 1" total. Now remember that the Win 1 total is 2 times the original bet, plus any chips left after making that bet. The amount left is the amount of Insurance you may take, up to half of the original bet, but all of that is accounted for if you just subtract the amount of the Insurance bet from the final total. In this example, I show an Insurance bet of T50, which is lost, but I win 1 bet so my total is T1005 after all is said and done. But I might also take insurance, lose it, then double and win, so that resulting total is shown in the column labeled "If lost/win all". The formula for that cell is: =sum(H3-J3), which just subtracts the amount of the Insurance bet from the "Win All" total.

If the dealer does have a natural and I've taken Insurance, but do not have a natural myself, my result will be the total in the next column, "If paid/lose". This means the Insurance bet was paid 2 to 1, but I lost my original bet (and therefore any doubles don't count), so my total will be 3 times the Insurance bet plus any amount in the "Leaves" column, minus the Insurance bet. Let me walk you through it, because I was confused myself as I was putting this together. Bear in mind that the only way I can win an Insurance bet is if the dealer has a natural, which means I automatically lose my hand if I don't have a natural also. My original bet was T500, which left me with T55 in chips. I then bet T50 on Insurance, lost my T500 bet when the dealer flipped the "snapper", but got paid T100 on the Insurance bet, plus I get the T50 back. At that point I had only T5 left, so 100+50+5 = 155, which is the total in the "If paid/lose" column. The formula here is: =sum(E3-J3)+3*J3.

On the other hand, I might have a natural myself but can still elect to take Insurance if the dealer's up card is an Ace. If I take insurance for the full amount - 50% of my original bet - it's what's known as "taking even money", which guarantees I'll win my original bet if the dealer does have it, but I'll forego the bonus one gets on the 3 to 2 payoff. Winning just one bet may or may not suit my purposes, but the option is there, if you have enough remaining chips. But in this example, I have only T55 left, so I bet T50 on Insurance and voila! the dealer had a natural, so my original bet pushes. But my T50 Insurance bet now returns T150, which gives me a total of T705 (555 +150 = 705), which is shown in the column labeled "If paid/push." I kept the formula simple here: =sum(3*J3)+A3.

Okay, one more possibility and we'll wrap this up. Another permutation of Insurance is that you can make an Insurance bet and still surrender your hand. Because I count the cards and because Insurance is a profitable bet at certain counts (a True Count of 3 or more in a 6-deck game), the ability to win some chips is out there, especially since you may make an Insurance bet of any amount up to 50% of your original bet. Naturally, if the TC is 3 or higher and I have enough chips, 99% of the time I'll insure for the full amount - that has won me more than one tournament, I don't mind telling you - but I might not want to do it that way for a variety of reasons: I'm way behind, so I don't want to risk losing both the Insurance bet and my original bet (like when the dealer has a 9 under the Ace and I have 19) or the count is fairly high, say TC2 and I have yet another 15 versus the dealer's Ace. Sure, it's a bad bet, but I might be able to salvage some chips by making a small insurance bet of 25% of my original bet, because I'm certainly going to surrender 15 against an Ace. Should the dealer have a natural, I'll lose my entire bet because this is "late" surrender, but I'll win the Insurance bet so my total will be shown in the "If paid/lose" column, however if the dealer does not have a natural, I'll lose the Insurance bet, but my surrender will be valid and my total will be that which is shown in the "If lost/surr." column. The formula there is: =sum(I3-J3).

You can see that I've done a bit of color-coding to remind me where to look for my answers. If a 2nd bet, which is marked in blue is used, the resulting total will appear in the "Win All" column, which is also marked in blue. I used green for the original bet and surrender because of their relationship, as well as the Insurance/surrender column. I did this so that it's easy for me to get an answer quickly; it may or may not work for you, but it's something to consider.

By the way, if you have Excel on your hard drive and would like a full-functioning copy of this, just send an email to me and I'll ship it out asap. Please put "BJ Calculator" in the subject line and send it to Aceten1@mindspring.com/

I'll see you here next time.