Obviously, no hand of hold ’em poker is played in isolation; you will always have at least one opponent and the community cards that are dealt on the flop, turn and river can change the value of your hand and that of your opponent(s) in a dramatic way. That’s really the “puzzle” part of this game, which is why I enjoy it so much (not to mention the $$$ that can be made) – if you’re good at solving puzzles, you’ll probably also be good at winning poker tournaments. Puzzles of all kinds – be it a Rubik’s Cube, a Sudoku game, Free Cell or the New York Times crossword puzzle – have a basic element of logic about them that is often grounded in mathematics (well, maybe not the crossword puzzles), which often means a “key” exists that allows you to solve the puzzle.

Poker is grounded in rather simple mathematics that most players – probably 90% or more – don’t care about. They kind of understand it’s a game of skill but after a few instances of pushing all in after the flop and seeing their opponent(s) fold, it’s no longer a game of math to them – it’s now a case of “playing the opponent”, rather than playing the cards. I love that expression: “Playing the opponent”, which is another way of saying “Raise with junk and most of the time the others will fold.” And it’s true – most of the time the others will fold, but when your opponent has a “real” hand (one that is mathematically justified in calling your raise), you’re going to get called and will likely lose. Naturally, if you’re doing the calling with, say, a pair of 7s against the raiser’s J-3 suited, a Jack will be the first card out on the flop and two things will happen. First, your opponent will congratulate him or herself on being such a successful “aggressive” player and you will think it sucks that J-3s can beat 7-7 so easily. And, if it’s happened two or three times in a row, you’ll become more and more convinced of it.

Let me switch to Blackjack for a minute to give you an insight on what’s happening here. You may or may not play BJ, but you don’t need to in order to understand my explanation. It’s just that Blackjack has fewer hands overall to deal with, so the numbers from it are easier to grasp. For example, if you ignore suits and treat hands like 5-4, 6-3 and 7-2 as a 9 and call all Tens, Jacks, Queens and Kings just 10s, there are a total of 34 starting hands for the player: fifteen “hard” two-card totals of 5 to 19, not using an Ace or pairs; nine “soft” hands, which includes A-2 up to A-10 and ten sets of pairs (remember, 10-10 is a 20; don’t count it twice). Okay, against those 34 player hands, the dealer can show one of ten possible up cards (2 through A, but counting the 10s and face cards as just 10s), which means there are only 34 x 10 = 340 possible starting hand “situations” – a player’s two-card hand versus a dealer’s up card – for a Blackjack player. Hell, there are 1326 distinctive two-card starting hands just for the player in a hold ’em game, let alone all of the permutations made by a three-card flop.

Hopefully you get my point that Blackjack outcomes are easy to calculate accurately. For example, if you hold a hand of 17 versus a dealer’s up card of 5 in the average Blackjack game (6 decks, dealer hits soft 17), your expectation is to win 19.9% of all the $$$ you bet in that situation, assuming you stand. This basically means you’ll win with 17 vs. 5 19.9% of the time, in a reasonable sample. In other words, you’re not going to win with 17 vs. 5 every time, nor are you guaranteed to win six times out of the next ten times you have this situation (which is a 20% win rate). But, if you played 1000 hands of Blackjack and somehow were to get 17 vs. 5 every time, you’d find that you won about 600 of them. This is called “expectation” and the “expected value” of 17 vs. 5 is +.199. Consequently, if your average bet was, say, $100 per hand for those 1000 hands, you can reasonably expect to show a profit of about $2000, which is 19.9% of all the $$$ you bet in that situation. If you’re varying your bet from, say, $50 to $400, (but the average is $100 per hand), rather than flat-betting $100 per hand, the resulting win could be slightly larger or smaller, due to “variance” (which is what most people call luck), but it’ll still be pretty close because the sample size is fairly large.

Now, take a poker hand like the aforementioned 7-7 versus J-3 suited, preflop. The numbers show that 7-7 will win roughly 66% of the time. But does that guarantee you’ll win the very next time you run into this situation? Of course not. You have an expectation of +66%, but only after enough “trials”, as we call these, will you see your results trending toward the +66% figure. But just because we cannot predict what will happen on the next hand does not mean we cannot gain from such plays. In the “long run”, it’s generally profitable to call with 7-7 versus J-3s. I say generally, because if you have to bet $10,000 versus your opponent’s $1000 bet to make this play, it’s obviously not worth making. But, in most hold ’em poker games all you need to do is match your opponent’s bet, so you’re getting 1 to 1 odds on the call, which makes 7-7 vs. J-3s wildly profitable, even more so when you figure in the blind bets or bets made by players who subsequently fold (“dead money”).

Naturally, you hope to win the hand, but even if you don’t, you experienced a “positive expected value” (+EV) that goes into a sort of “bank” as a deposit. Weird? Not really. Let me go back to my Blackjack example. If you bet “N” $$$ on every hand at Blackjack where you have a 20% +EV, it’s easy to see that it’s only a matter of time before you become quite wealthy. Unfortunately, it doesn’t work that way in reality – sometimes you’ll have a bet out where you have 16 versus a dealer’s Ace (-58% EV) or 13 vs. 9 (-38.3% EV) – so you have to take the good with the bad. In Blackjack, just as it is in poker, you win or lose one bet at a time. If your bet is always $100, your bankroll goes up and down in $100 increments (ignoring the 3 to 2 pay on a “natural”, doubling and splitting for the moment), so if you lose four hands in a row, your bankroll will be lower by $400. But what if all of those hands somehow were our 17 versus 5 example where we know we hold a +19.9% EV? Yes, you’re still down by $400, but you have a “built up” EV of $80, which is about 19.9% of all the $$$ you bet. It’s just that you haven’t collected on it yet. And “yet” is the operative word here. Sure, if you stop playing Blackjack for the rest of your life at this point, you’ll never get that $80, plus your $400 back. On the other hand, if you continue to play, one fine day all of those $$$ will come rolling in.

It’s the same in poker. You will win some hands and lose others, but so long as you’re playing with an advantage – and you continue playing – the $$$ you have “banked” in these +EV situations will eventually come back to you, even though you may have actually lost the hand this time. If you play more +EV hands than -EV hands, you’ll eventually win, if the bets you make are the same. Of course that doesn’t happen in poker like it does in Blackjack, so you have to make more profitable bets than losing bets in order to show a profit. Any bet can be profitable, just as any bet can be unprofitable; it all depends upon what cards you hold, what cards your opponent holds, what cards come on the flop, etc., etc. Would it be that we knew our opponent’s cards, but poker wouldn’t exist if that were the case – you don’t know her cards, but she doesn’t know yours, either. So, we have to basically make guesses as to whether or not our hand is better than our opponent’s hand; maybe you can look into the soul of your opponent to see their hole cards but I can’t, so what I do is figure the odds involved.

The odds you’re being offered to take a bet is the logic that I referred to earlier, which will allow us to solve the problem of: Can I win this hand? Because the title of this lesson is “All in on the Flop”, it means we and our opponent are going to get to see all of the cards in the hand, which are the turn and river cards – two more cards to help us win. It then follows that we need to calculate some odds in order to see if making the bet is worthwhile. With two cards to come, calculating our odds of success is easy, if we can define “success”. I think it’s fair to say that a set of Trips will win most hands of hold’ em poker, but that obviously doesn’t apply if our opponent made a Full House at the same time. But, because we don’t really know the cards our opponent holds, a reasonable guess is needed in order to determine what will win the hand. That “guess” might be accurate 80% of the time, but it’ll probably never be accurate 100% of the time. I throw that idea out because I’m trying to fine-tune my game in situations like this. In other words, the pot may be offering me $4500 for a $1500 bet (3 to 1 odds) against a 25% probability of winning, which appears to be a hand where I’ll win as much as I lose – breakeven in the long run – but when you factor in the possibility that my idea of what the winning hand will be might be wrong 20% of the time, it really isn’t a breakeven proposition.

Breakeven plays really do nothing for you in the long run, other than to increase the up-and-down swings of your chip stack. That said, in a tournament situation if you have the opportunity to knock out an opponent, a breakeven bet is usually worth making. Not only will you add to your chip stack if you win, but you may also move up in the prize money standings, so there are some intangibles to consider when you call an all-in bet. Do these intangibles outweigh the fact that you might be mistaken about what cards will win the hand? There is no one correct answer here, but at least consider the question before you make the play. Personally, I like to have a 20% “cushion” on my odds if I’m relatively short-stacked myself (which is usually the case) or if I feel the player going all in is a “tight” player that may be doing so only with a premium hand. For example, if I hold J-10 offsuit, the flop comes A-9-Q and my opponent goes all in, I have an open-end Straight draw and two cards to catch a K or 8. If the pot totals 2000 with my opponent’s bet and it’s 1000 to me, I’m being offered 2 to 1 pot odds. Because my probability of making an open-ended Straight is 31.5%, I really need pot odds of 2.2 to 1 for this to be a break-even call. The question I have to ask is whether or not a Straight will win the hand. First of all, I’ve got to take into account the probability that my opponent can make a Flush or a higher Straight. The suits of the flop cards will give me an insight on that – some of my 8s or Ks might be “dead” because they’ll give my opponent a Flush – so making a 20% reduction isn’t unreasonable. If the flop is “rainbow”, the Flush is less of a threat. However, my opponent may have gone all-in with K-10 and if she gets a Jack on the turn or river, it’ll give her an Ace-high Straight. But I’ll also have an Ace-high Straight, which will cause us to split the pot, but doesn’t add to my risk – so making a 20% reduction is probably not necessary. My play on this hand would be to fold if there are two or more cards of the same suit on the flop and to call if there aren’t. I’m not getting the full 2.2 to 1 odds I really need, but it’s close and the “intangibles” add something, so I probably would call if it appears a Flush is not imminent.

This is a good time to show you the chart I use to help me in situations like this. Take a look and we’ll discuss it below:

Of course, the outs you have depend upon what you’re holding after the flop. But remember – just because you have outs, it doesn’t automatically mean you’re going to win the hand if you hit one or two of them. However, if the pot odds meet or exceed the minimum odds shown here, it’s a bet you should consider. Take a look at the entry for 6 outs, which is two overcards to the flop. What this means is that you have a hand like A-10 offsuit, the flop has come 2, 7, 8 “rainbow” and your opponent now goes all in. Let’s say the pot is now 1400 and it’s going to cost you 500 to call, which translates into 2.8 to 1 pot odds. From strictly an odds point of view, this is a fold, because you need odds of 3 to 1 minimum, if you think that pairing either your Ace or 10 will win the hand. However, a low-card flop like that may well mean your opponent missed hitting anything just like you and it might come down to who has the highest pocket cards. Well, you have an Ace and a decent, if not great, kicker. You might well be “dominated” (see Lesson 25, “Is My Ace Dominated?” for more on this), but it’s only about a 3% probability if you’re up against just one other player. While the math is important, you must also consider some of the intangibles before deciding to fold – Is your opponent acting with a very short stack, like 6 times the Big Blind or less? Do you have an above-average chip stack? Will the elimination of this player move you up the money ladder? Will losing leave you with fewer than 8 Big Blinds or some other number that will make you nervous? There’s nothing wrong with adhering to the math 100% of the time – it will virtually guarantee that all of your decisions are +EV plays – but it won’t necessarily guarantee that you’ll always end up at the final table, where the big $$$ are handed out. Some intelligent “gambling” can really make a big difference in your overall final standings, if you can live with the idea of “final table or bust”.

Okay, now look at the entry for 12 outs. If you flopped a four-card flush and have a card that’s higher than all three community cards, you need pot odds of 1.2 to 1 in order to call. In most cases, you’ll automatically be getting at least 1 to 1 odds, because all you have to do is match your opponent’s bet – the blinds and other “limpers” who fold may increase that to the 1.2 number or higher. But this scenario assumes a pair higher than anything showing on the board will win the hand if you miss the Flush. It might look like this: You hold Ah, 7h and the flop comes 2h, 9h, 10s and your opponent goes all in. The pot is now 1500 and you must call 1200 to stay in. That conveniently works out to be 1.25 pot odds, so it’s a call from a strictly mathematical point of view and I would make it if I had the Ace, which will give me the “nut” Flush and a pair of Aces might win the hand should I miss the Flush. I’d be less inclined to make it if I held Qh, 7h because I might make a Flush lower than my opponent and a pair of Queens might not win the hand. That’s where the column “20% Reduction” comes in. With a high card of less than an Ace, I want better odds to make the call. Since it shows I need 1.5 to 1 odds, the pot should be 1800 if I must call a 1200 bet. That cushion, so to speak, might be worth ignoring if I believe my opponent will go all in with basically any two cards, or it might not be big enough if I have a reading that my opponent is a very tight player. Sadly, nothing is absolute in a situation like this, but at least I go into it with my eyes wide open.

I think the rest of the chart is pretty much self explanatory, but if you have any questions, please email me at Aceten1@mindspring.com/ and I’ll get back to you as soon as possible.

See you here next time.