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The GameMaster's Secrets:
Final Hand Problems

I play Blackjack tournaments in much the same way I play poker: tight and conservative. Sure, I've lost plenty of times to players who bet 15 or 20 percent of their bankroll on nearly every hand (what I call "rabbits"), but I guarantee that I've beaten them more than they've beaten me. When it comes to Blackjack, aggressive play has limited value, in my not-so-humble opinion because the very nature of the game dictates that even the best player will lose more hands than s/he will win.

Depending upon the rules of the particular game, the player who uses perfect Basic Strategy can expect to win about 44% of the hands, push on 8% and lose 48%. Of course, the casino doesn't have a four percent edge over this player, as the numbers imply, because the player may double, split pairs and will receive a 3 to 2 pay on a "blackjack". Those player options, when properly used, will cut the house edge to about one-half of one percent in a game with typical rules. But in a tournament situation, it's not the casino's edge that really matters - it's the 44, 8, 48 that matters the most - because you're not playing against the casino; you're playing against the other players. That being the case, if you were to bet just one percent of your bankroll on every hand and all of your opponents were to bet 20% of their bankroll on every hand, in a match of, say, 200 hands, you'd win probably 95% of the time.

Unfortunately, most Blackjack tournaments are composed of 100 hands or less, so "luck" (or as I prefer to call it, variance) plays a big role in the outcome. In the single-table Sit & Go tournaments I've been writing a lot about lately, only 15 hands are played, which means luck is a huge factor and the so-called rabbits can do very well, at least for a while. However, even the luckiest of the rabbits usually discovers that 20 or 30 matches, which one can easily play in a week's time, is just too many hands for their luck to hold out. At that point they either change their style of play or give up; I've seen both happen quite a few times. But, we still need to remember that in any one, particular 15-hand match, almost anything can happen and usually does. Luck cannot be eliminated but its impact can be reduced quite a bit by playing a lot of tournaments skillfully, which to me, means not trying to win the match on hand number 5 but rather trying to still be in contention on the last hand. If I make it to hand 15 of enough matches, I'll win my fair share and, if I play that last hand more skillfully than my opponents, I should win more than my fair share.

So for the moment, let's concentrate on winning that last hand. How well you do on the last hand is a function of many variables: how big your bankroll is, how much you bet, how big your opponents' bankrolls are and how much they bet; your position at the table, what cards you get, what card the dealer is showing and so forth. You as a player have very little control over any of those, other than how much you bet and how you play your hand, so it's not surprising that bet size and playing strategy are key items to your success. Sometimes even the "perfect" bet and the proper play aren't enough to get the victory for you, but most of the time they'll work and that's all we can hope for, to be correct most of the time.

As an example, let's say you have 1235 chips left and another player has 1230 chips and must act before you; all other competitors are basically out of the running at this point. Talk about an ideal situation! You are a huge favorite to win here and your opponent knows it. Regardless of what your opponent bets, you can just simply match it and if you both win the hand, you win and if you both lose the hand, you also win. Of course, if your opponent gets a 'blackjack', s/he will beat you, but that's about a 5% probability, so you're "only" a 95% favorite. I'll take those odds all day long. So, let's say your opponent makes a maximum bet of 500 chips and you then match it. The cards are dealt and your opponent gets A-6, while you get 10-10 and the dealer shows an 8. Again, how sweet it is!

Then, your opponent doubles and catches an Ace for at total of 18. S/he now has 1000 chips bet with 230 remaining while you have 500 chips bet and 735 remaining. So, should you match your opponent's bet by splitting your 10s? I'm ruling out doubling here because of the high probability of busting, but splitting is a very viable strategy because if the dealer busts you would be the winner. Decisions, decisions. Well, like most decisions in Blackjack, the mathematics involved can steer us to an answer. Your opponent has 18 versus a dealer's 8 and, for the moment, you have 20. As things stand now, if the dealer busts or ends with 17, your opponent will win. The probability of a dealer bust when showing an 8 is about 24% and the probability of the dealer having 17 is 13%. That totals to 37%, so you have a 63% probability of winning if you stand on your 20. Being better than 50%, standing is the way to go.

Nice numbers, but where did they come from? No secret here; they can be found at Ken Smith's site, www.blackjackinfo.com/ in the tournament section. You should go there and get a copy of the proper "Dealer Outcome Table" for the game you play, which is 6 decks, dealer stands on all 17s, if you participate in the Sit & Go tournaments at Global Player Casino. Having that chart handy, if not exactly committed to memory will prove to be very helpful in the future.

But there is another possibility for your play and that's splitting your 10s, thus assuring you'll win if the dealer busts. We already know the dealer will bust roughly 24% of the time when showing an 8, but what do you give up by splitting the 10s? Obviously nothing if your hit cards are 10s and Aces, but there's no guarantee of that. While you could cycle through all of the various possibilities, an easier approach is to use our old friend, "expected value" (EV) to help us find an answer. We know that the EV for 10-10 vs. a dealer's 8 is +.790 (Appendix E of Professional Blackjack by Stanford Wong), in other words we'll win 79% of all the $$$ we have bet in that situation, which is a fancy way of saying we'll win 79% of the time, if it were just us against the dealer. The same table shows that our EV drops to +.389 if we split the 10s and that can get a little confusing if you try to work that into our tournament example.

The way the tables are presented in Professional Blackjack recognizes the fact that you must place a bet equal to your original bet when splitting pairs, but in order to keep things simple, the EV is based upon the original bet only (Page 299). So if you had, say, a bet of $10 when you got a hand of 10-10 versus an 8, your EV for standing is 79% of $10 or $7.90. If you split the 10s, your EV is +.389 or $3.89; that is, about $1.95 per hand. You can quickly see that you'll give up about half of your expected value in this situation by splitting the pairs. Naturally, that's because you have no control over what cards you'll receive, so while you might hit one 10 with another 10, you might get a 6 on one of them, hit it and bust. As a general rule in tournament play, splitting pairs is less desirable than doubling, because split pairs often lead to an overall "push" - you win one hand and lose the other. That's not to say there aren't times when splitting pairs is your best play, it's just that splitting is not as desirable as doubling in the overall scheme of things.

Let's look at a variation of our original example for more insight on splitting pairs. Say you have the same 1235 chips, your opponent has 1230 and must bet before you; s/he bets 500 and you match it. The cards are dealt and your opponent gets A-6, while you get 10-10 and this time the dealer shows a 6. Your opponent correctly doubles and catches an Ace for a total of 18. Your opponent will win if the dealer busts or ends with 17, which from the charts I mentioned earlier is now a 59% probability. Thus, your probability of winning has dropped to 41%. Is it time to split those 10s? The EV for standing with 10-10 versus 6 is +.703 and for splitting, it's +.567. That EV has no actual meaning for you in a tournament situation, because we already know how you can win the hand - it's if the dealer has 18, 19, 20 or 21 only - but the EVs can give us a quick way of making our decision to split or not split. In the first example we lost quite a bit of EV by splitting the 10s, mainly because we could be turning a 20 into two 13s, which do us no good. Plus, the dealer is less likely to bust when showing an 8 (24%), as opposed to when showing a 6 (42%). Because of that higher busting percentage, not as much EV is lost by splitting the 10s when we're facing a dealer's 6. So, while we might hit both 10s with lousy cards, we can just stand "stiff" and pray for a dealer bust, which will give us the win.

But what do the numbers say? Now remember, by standing, our opponent will win if the dealer busts or makes a 17, which will happen 59% of the time the dealer is showing a 6. Thus, our probability of winning by standing is 41%, which is less that the breakeven point of 50%, so some action is indicated. If we stand with 10-10, our EV is +.703 and if we split, it drops to .567, which is roughly a 20% reduction. That reduction in EV is directly associated with the dealer making some sort of hand, because now if s/he (it?) busts, we win. But the only way we can get really hurt is if the dealer makes a 17 and our split 10s are 17s or less. Also, if the dealer ends with 18, our opponent will push and if our split 10s are 17 or less, we'll lose two bets and that'll cause us to lose. The probability of the dealer ending with 17 or higher (which will likely cause us to lose) is roughly 41%, but by splitting we've eliminated the fact that a bust will allow our opponent to win. By splitting, we've moved our expectation up to 59% and if we factor in the 20% drop in EV, which accounts for all those horror stories I mentioned above, our probability is just about 47%, which is a definite improvement over 41%. The numbers say "split".

Here's another example with everything remaining the same, except the dealer is now showing a 4. The dealer will bust 40% of the time and make a 17 thirteen percent of the time, so our probability of winning is 47% if we stand with 10-10. The EV for 10-10 versus a 4 is +.658 and the EV for splitting 10s vs. 4 is +.484, which is a 27% reduction. The probability of the dealer ending with 17 or higher when showing a 4 is about 59%, which means we have a 41% probability of winning if we split the 10s. Reduce that by 27% and we get 30%, which is less than the 47% probability of winning by standing with 10-10. Thus, the numbers say to stand.

It's probably no surprise that the dealer will bust less often with an up card lower than 6 and, the lower it gets, the better it is for us to stand with 10-10. The same is true as the dealer up card gets higher, of course. Consequently, you'll want to give some thought to splitting 10s unless it's really the only way you can win. For whatever reason, a lot of players in tournaments love to split 10s; I suppose it's because they'd incur the wrath of everyone at a "real" table, but have heard it's sometimes a viable strategy in a tournament. The key word is "sometimes." Just remember this: the closer you adhere to the basic mathematics of the game - even in a tournament setting - the better you'll do long term.

I'll see you here next time.

  

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