Poker Ace Count As 1
In the last couple of years, as theoretical understanding of poker has galloped forward, an entire new vocabulary has emerged. I mean, when I was playing limit hold'em in San Jose 25 years ago, had you said, 'minimum defense frequency,' they'd have thought you were talking about the 49ers.
It pays 2:1 (meaning that the player receives two dollars for every dollar bet) and is available when the dealer's exposed card is an ace. The idea is that the dealer's second card has a fairly high probability (nearly one-third) to be ten-valued, giving the dealer blackjack and disappointment for the player.
- An ace can be high or low, but not both in hold'em. So AKQJT is the highest straight, A2345 is the lowest straight (called 'the wheel'), and a wrap-around like 32AKQ is worthless. Note that many players overvalue starting hands like A4 or A5. Because of this, 76 and 65 can win some big money, because, with 543 on the board, 76 beats A2.
- Yes, the ace can count as the lowest card in a straight and function as a '1' when combined with 2-3-4-5. Is JQKA 2 a straight? A straight cannot go 'around the corner', the Ace can only be either the highest or the lowest card, not a card in the middle. So no, J-Q-K-A-2 is no straight in poker.
One of the words that you hear most frequently now is 'combinations' or 'combos.' Once you accept the concept of an opponent (or yourself) having a range of hands, the next interesting question is, 'Well, how many hands are in that range?' The way you answer that is to figure out how many 'combinations' there are of the hands that make up the presumed range.
Counting Combos: Pocket Pairs
Let's try one. Suppose you are playing $1/$3 no-limit hold'em and before the flop, you raise to $12 in early position with a pair of jacks. A straightforward and uncreative player in late position reraises you to $40. It folds back around to you. Based on your knowledge of this player, you expect her to three-bet with only a pair of queens or better, and all of her ace-kings. So her three-betting range is Q-Q, K-K, A-A, and A-K. How do your jacks fare against her presumed range?
Well, there are six combos of every pocket pair. To determine that, we see that we can randomly pick any of the four queens in the deck, and now have three remaining queens with which to make a pair. So that's 4 x 3 = 12. However, if we pick the first, and then the , that's no different than picking the first and then the . So we must divide by two to get a total of six.
Another way of skinning the same cat: pick the and see that you can then pick the , , or to make a pair. That's three. Now pick the first, leaving just the and to pair. Two more. Finally, the has only the to pair it. One more. 3 + 2 + 1 = 6. Math is beautiful.
So, six combos for each pocket pair. For Q-Q / K-K / A-A, that's a total of 18 combos. So far so good.
Counting Combos: Non-Paired Hands
What about A-K combos? If we give the villain all of the ace-king combos, then she can make one by taking any of the four aces and crossing them with any of the four kings. 4 x 4 = 16 and that's the number of combos.
Of course, if she restricts herself to suited ace-kings, then pretty clearly there are just four of those — , , , .
Calculating Our Equity
We'd agreed that she would three-bet all of her ace-king combos plus queens, kings, or aces, so we conclude she has one of 34 possible hands: 18 pocket pairs and 16 ace-kings.
The 18 pocket pairs are 81-to-19 favorites against us, while we are a 57-to-43 favorite against the 16 ace-kings. To determine our equity against her, we weight each combo by its share of the range pie, compute our equity against that slice, and then sum them up.
For this example, we can compute our equity as follows:
- Against the higher pairs, we have 0.18 (18%) equity. The higher pairs make up 18 / 34 of the villain's presumed range. So our equity for that piece = 0.18 x 18 / 34 = 0.10 or 10% (0.095 to be closer).
- Against the ace-king combos, we have 0.57 (57%) equity. The ace-kings make up 16 / 34 of the villain's range. Our equity against that piece is 0.57 x 16 / 34 = 0.27 or 27%.
- Summing the two, we get 0.10 + 0.27 = 0.37 or 37% equity against her presumed range.
The good news is that there are programs such as Pro Poker Tools and the like that let you ask questions such as 'How much equity does a pair of jacks have against a range of Q-Q / K-K / A-A / A-K?' But it's useful to know how those things are calculated.
Using Combos to Improve Decision-Making
What to do with that information is beyond the scope of this article, but as an example, if the villain were all in for her $40, we'd know exactly how to proceed.
Setting aside rake for the moment, there's $12 + $40 + $1 + $3 = $56 in the pot. It costs us another $28 to call. Conveniently enough, we're getting exactly 2-to-1 odds to call, so we must have at least 33.3% equity to call her shove. We have a hair above that (37%), so we shrug, slide in the extra $28, and ask the dealer to run out the board.
By the way, I had suggested that we ignore the rake for simplicity. Note that in this case once we take the rake into effect, this could turn into a fold. If you don't see that, subtract the rake ($5 or whatever) from the pot and redo the pot odds calculations, remembering that you still need to call the full $28.
Conclusion
I grant that counting pairs and ace-king combos is relatively simple. But suppose in the heat of battle, a flop comes down and you believe that your opponent could have (among other possible hands) any of the heart flush draws that are two suited Broadway cards, plus all of the ace-high flush draws. How many flush draw combos does she have? (See the answer below.)
Not surprisingly, the best way to get better at this is to practice in the lab (a.k.a. 'your kitchen table'). Go over common situations and learn the arithmetic. Eventually, you'll be as comfortable with the important ones as you're sure that jacks have 37% equity against a range of {QQ+, AK}.
This stuff is not trivial and if you're not used to working with numbers, it can be a bit daunting. But at least some of your opponents are already doing it, and once you get the hang of it, you might even enjoy the mental gymnastics.
P.S. Your villain can have the suited-in-heart combos of A-Q, A-J, A-T, A-9, A-7, A-6, A-5, A-4, A-3, A-2, Q-J, Q-T, J-T, for a total of 13.
Lee Jones can help you count combos and then count your winnings. Go to leejones.com/coaching and schedule a free coaching consultation. Lee specializes in coaching live cash game players.
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At a Maryland casino poker room, I was busily typing notes into my phone. In the background, two players announced 'all in,' pulling my attention back to the table at which I was sitting.
The board read and both players tabled flushes. A hot wave of red flashed across my face as I realized I had folded on the flop when it had become clear my bottom pair was no good. Not only did the large pot go to another player, I also missed out on a $1,000 high hand jackpot.
Many players have a story like this. If only.. I would have..
Jackpots are exciting, providing big payoffs for high hands, bad beats or royal flushes. They draw players into poker rooms and keep them seated longer. The room buzzes when a jackpot is paid, and players agonize over near misses.
But are jackpots worth chasing? Should you adjust your play to try to win a jackpot?
The 'House' Point of View
Jackpots are funded through a dollar or two taken out of each pot and kept separate from the rake. The rake belongs to the house. Jackpot money belongs to the players and strict accounting for these funds is required of public casinos.
When you win a jackpot, the house neither wins nor loses — they merely handle the money. So in one sense the house doesn't really care about paying out the winners.
Yet looking at it another way, the house actually cares very much. With fixed jackpots (for example, $1,000 for the highest hand in the room every hour), the house wants lots of winners. More winners creates more buzz and more word-of-mouth advertising that helps attract new players.
Other jackpots are progressive, growing every day there is no winner. Like the multi-state Powerball lottery, the buzz comes when the jackpot gets bloated and 'hey, somebody's got to win that thing!' The house wants progressive jackpots to grow as large as possible, with palpable anticipation as more players enter the room.
Most of all, the house cares deeply about players chasing jackpots. As soon as you enter a pot solely because of the allure of a jackpot, the house wins. More players means more chips in the pot which means a higher likelihood of maximum rake.
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Adjusting Preflop Ranges
Before considering any adjustments, take a moment or two to consider why you play poker. Here in the strategy section of PokerNews, we mostly tend to assume every poker player always strives to make the most money possible. While that's laudable, many poker players are at the table for other reasons.
For those who play poker primarily because they like to gamble, enjoy the social experience, have time to kill, or some other reason that makes losing over the long run acceptable, it's perfectly fine to loosen up preflop ranges to improve the chances of winning a jackpot. Possible jackpot hands include all pocket pairs and all suited cards with no more than three gaps. Feel free to limp or call modest raises with these hands from any position. (While you're at it, don't forget to buy some Powerball tickets, too!)
But if you play poker to make money, tune out the jackpots and don't adjust your ranges at all. A starting hand that isn't worth playing still isn't worth playing when there are jackpots to be won! You simply won't win a jackpot often enough to recoup the value leaked by unnecessarily putting yourself in difficult, unprofitable situations.
Perhaps the most important preflop consideration is whether other players are chasing jackpots. If so, you may need to put some additional hands in their ranges.
Postflop Adjustments
Make sure you know the qualifying rules, which tend to vary from one poker room to another. Sometimes the flop will give you a draw to a jackpot qualifying hand, or even better will get you there right away. Even if you made no preflop adjustments, you'll want to be prepared.
Here are a few examples of possible postflop adjustments to make:
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High Hand with vulnerable kicker — You have in the big blind and no one raised. The flop is , giving you quads. The display monitor shows the current high hand is quad 9's and there are five minutes remaining until a $500 high hand jackpot is paid. If the rules require you to use both hole cards, but do not require you to have a pocket pair for your quads to count as a high hand, you should go all in right away. Your kicker is vulnerable and won't play if a jack, king or ace comes on the turn or river.
Flopped set of aces — You have and get an ace-high flop. Is the current high hand already quads or better? If not, aces full will often hold up for a high hand jackpot. On most boards, you should play passively to make sure you see the turn and river cards. With a wet board and multiple opponents, however, a continuation bet should get called by at least one opponent.
Poker Ace Count As 1 4
A bad beat jackpot could occur if the final ace appears and you either lose to a straight flush or beat a lower four-of-a-kind. As rare as this is, you probably don't need to adjust your play. The player who flops a lower set or a straight flush draw isn't going anywhere.
In Poker Can Ace Count As 1
Other flopped sets — When you flop a set lower than aces, your only chance to win a high hand jackpot likely requires making quads. You have one out. You will improve to quads approximately 4% of the time, so you can add 4% of the jackpot amount to the EV of playing passively. Let the texture of the flop be your guide. With wet boards, don't let the jackpot lure you into a passive approach where the potential value to be gained by betting is far greater.
Straight flush draws — Look at the texture carefully to see if two straight flushes are possible. If you have 8-7-suited and the flop includes the J-T, J-9, T-9, 6-5, 6-4 or 5-4 of your suit, filling a straight flush could win a high hand jackpot, and there's also a chance of another player making a straight flush to trigger a bad beat jackpot. With such long odds, note that playing more passively than you otherwise would is going to be a negative EV approach. And try not to lose all your chips if you make a regular flush and run into a higher flush or full house!
Royal Flush draws — Royal Flushes are rare and special. I've been fortunate to make four of them in live Texas hold'em play, though I know many players who are still waiting on their first Royal. No one will ever blame you for chasing a Royal Flush, and you'll enjoy telling the story of your first Royal Flush for years to come.
Conclusion
While jackpots are exciting, chasing them leads to weaker preflop ranges and passive postflop play. You usually miss and the chase is costly.
When the flop brings jackpots into play, be sure you know the qualifying rules and adjustments to make to maximize these opportunities while minimizing the EV leakage along the way.
David Bass mostly plays in live no-limit hold'em cash games and has been writing about poker since 2012. You can follow him on Twitter @KKingDavidPoker or enjoy his blog, They Always Have It.
The photo above comes from a crazy $1/$2 cash game hand played at the Casino Del Sol in Tuscon, Arizona, which you can read about here: 'Bad Beat on the Bad Beat Jackpot: Straight Flush over Quads over Quads.'
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