Poker hand probabilities

poker hand probability chart


Spades strategy

IMG_0029_edit Spades is one of those games with fairly simple rules but can have a complex strategy. While we can’t possibly share all there is to know about Spades strategy, here’s a few tips that will give you something to think about next time you play.

Are bags really such a bad thing?

Most people will be pretty cautious about collecting too many bags, due to the hefty 100-point penalty assessed for collecting ten of them. But it’s worth remembering that in some situations capturing a bag or two can be a decent strategy, if you have a good reason for doing so.

The reason for taking bags that is easiest to spot is when your opponents are at risk of breaking contract. If it’s the end of the hand, you’ve made your contract, and your opponents are still a few tricks away from making theirs, it is generally a good idea to set them by denying them those last few tricks, ensuring they score zero for the hand, even if it means taking in a few bags.

If your opponents are within a few bags of getting that 100-point penalty, it may be a good strategy to risk taking a few bags yourself to try to trick them into going over the edge. Aggressive play at the beginning of the hand can put your opponents in a frame of mind where they’re worrying about making their contract, causing them to play even more aggressively and potentially take in tricks they don’t need.

On the other hand, keep your number of bags in mind. If you have more than seven or so bags, it’s probably not a good option to risk taking the bag penalty unless your opponent will be taking it with you.

In some games, you don’t need to worry about bags at all. In games played to only 200 or 300 points, chances are you simply will not have enough time to accrue ten bags. Longer games, such as 500-pointers, make the bag penalty more dangerous.

Card counting

Since Spades is only played with one fifty-two card deck (like Denexa 100% Plastic Playing Cards), players with a good memory can easily keep track of what cards have been played and what haven’t. You don’t even need to remember every card; just keep track of those that are important to your hand. If you hold the Q♦ and you know the K♦ and A♦ have not been played, you know that it’s more likely that your queen will be beaten. Of course, no matter what your hand is, it’s usually a good idea to keep track of the spades that have been played, since those cards can be used to trump most any card in your hand.

When you have a lot of spades

Holding a lot of spades opens up a few new opportunities to a player. Naturally, you know that there will be fewer spades in the hands of your opponents, and you can trump many more tricks. You can lead spades, and the other players will be forced to follow suit. This can give you useful information; if you lead spades and someone plays a different suit, you know that they will be less likely to overcome your non-spade cards. Repeatedly leading spades can force players to sacrifice all of their spades to follow suit, leaving them unable to use them to capture tricks.

The importance of position

Where you’re sitting can be as important in Spades as it is in poker. If you are the second to play, that is, right after the lead, playing a spade to try to take the trick can be a bad move, because your opponent to the left may simply play a higher spade, and your partner will have to play an even higher spade to win the trick. It is often better to play conservatively and use the opportunity to burn off a less valuable card.

On the other hand, when you are in the third seat (your partner is the leader), it is usually appropriate to play to lock down the trick. The only times you might not want to are when your partner leads with a nigh-unbeatable card.

Remember your partner

And above all, try to keep tabs on what your partner’s doing. If you notice that they appear to have no cards in a suit, but you’re long in it, you may want to lead that suit repeatedly so that your opponent can take the opportunity to play whatever they wish and potentially win the trick with spades.

Keep their bid in mind too. If your partner made a very high bid, they likely have an exceptionally powerful hand, so you should let them use it and try to stay out of their way. Likewise, if they made a very low bid, they probably have a weak hand, so you will have to be the one scoring the tricks for your partnership.


The gambler’s fallacy

A roulette wheelThe gambler’s fallacy is the mistaken belief that after a series of random events occur, a certain outcome is “due” to happen, so that the series of outcomes is corrected to better match the odds of each outcome.

The simplest example is a coin flip. A perfectly fair coin will have a 50% chance of landing on heads and a 50% chance of landing on tails. It is unlikely, but possible, for the coin to land on heads five or even ten times in a row. If a coin lands on heads ten times in a row, what are the odds for the eleventh flip? Someone operating under the gambler’s fallacy would say that tails is almost certain to come up—but the odds are exactly the same; 50% for tails and 50% for an eleventh heads.

Another place where it’s easy to see the gambler’s fallacy is on the roulette wheel. A modern roulette wheel has eighteen red spaces, eighteen black spaces, and two green spaces. The odds are approximately 47% for red, 47% for black, and 5% for green. In 1913, an incident occurred at the Monte Carlo Casino where the ball landed on a black space twenty-six times in a row. Gamblers rushed to bet millions of francs on red, believing a bet on red to be almost a sure thing after such a long string of spins landing on black. Most of this money was lost to the casino.

Keep in mind that the gambler’s fallacy only really applies when each trial (a spin, a coin flip, and hand of cards, etc.) is an independent event. This is not always true in card games; the odds will vary as cards are distributed from the deck. In Blackjack, for instance, as aces are dealt from the shoe and discarded, blackjacks become progressively less likely. But it remains true that you are not “due” a win after any number of losing hands, meaning that betting systems that rely on this, like the martingale, are fundamentally flawed.

Another caveat is that the fallacy only applies in situations that are truly random. In the case of something like the stock market, there are human factors at play, meaning that outcomes are not based purely on probability alone.


Signals in Cash (a.k.a. Kemps, Kent)

Four aces.In the card game Cash, also known as Kemps or Kent, the majority of the game’s opportunities for strategy are found in the signals used in the game. The most important rule in choosing a signal is to choose something that works for your partnership! Not all players notice or react well to the same same thing, so get to know your partner and learn what works and what doesn’t.

Keep in mind that part of a successful Cash game is fooling your opponents. Turn the pitfalls mentioned here around on your opponents—watch them to see if they are committing these errors, or commit them yourself with a phony signal to trick your opponent into calling “Counter cash!”

Verbal signals

Verbal signals (a spoken word used as a signal) are the easiest to successfully communicate and are therefore also the easiest for your opponents to detect. Most of the time, you will be able to use a verbal signal only once. For this reason, it can be pretty much anything, because even if it’s something that you would obviously never say unless it was a signal, like “shark putty”, all you have to do is call “Cash!” before your opponents can call “Counter cash!” and you’re good.

But if you do want to reuse a verbal signal, you can attempt to camouflage it. You can use a single word and bury it within a longer sentence, for instance. Make sure it’s a word that is common enough that it won’t stick out like a sore thumb, but not so common that you will say it on accident. It should also be something that doesn’t force an awkward change in subject—you don’t want to be talking about your grandmother’s cookies, then suddenly bring up Breaking Bad because that’s your signal word. Something that can help camouflage a signal is deliberately waiting for a few moments before calling “Cash”, in the hopes of keeping your opponents from associating the signal with you winning.

There is some merit in pretending an already-used signal is your code word, when in reality you have since changed your signal. The reason for this, of course, is to trick your opponents into losing by calling a bogus “Counter cash!” If that’s what you’re trying to do, re-read that last paragraph, and do everything it tells you not to!

Non-verbal signals

With non-verbal signals, many of the same rules apply. You will want something natural enough that your opponents will not notice, but conspicuous enough that your opponent will. Practically anything will do—taking a drink, fanning your cards out wider or narrower than usual, fiddling with your watch, slowly swaying your chair side to side. Just don’t pick anything like scratching your head or rubbing your eye—you are guaranteed to get a sudden itch in that spot when the hand starts!

One thing to watch out for is that you don’t fixate on wherever your partner’s signal will be coming from. If your partner will signal by adjusting their glasses, don’t stare at their glasses! Your opponents may notice and start staring too, and will call “Counter cash” whenever they notice anything amiss.

And remember, just because non-verbal signals have a higher shelf-life, it doesn’t mean they have an indefinite shelf life. You should still probably use the same signals for no more than three hands. Your opponents are bound to catch on eventually.


High hand jackpots

Casino poker rooms usually run lots of promotions to get people at their tables and away from those of their competitors. They help to spice up the game and give the players a chance to win a little extra money. One common promotion that is easy to add to a home game is a high hand jackpot.

What is a high hand jackpot?

A high hand jackpot is merely a jackpot awarded to a player for going to the showdown with the highest hand within a defined period. In a busy casino, the jackpot might be paid out as often as once per hour. In a home game with only one table running, you will probably want to award the jackpot at the end of the night as your players are cashing in their chips.

In the casino, the purpose of the jackpot is to get people in the door, so the money is being paid out of the casino’s marketing budget. While your players will think it’s very generous of you if you give them free money to play at your place, you probably don’t want to do that. Instead, you can collect an extra amount from each player when they buy in (it is best to make participation optional; players who do not contribute simply can’t win the jackpot). Set chips equal to this amount of money aside. Keep track of who has the highest hand as the night progresses. When it is time for the jackpot to be awarded, give the chips in the jackpot to the player to cash in with their winnings. It’s that simple!


Well, not exactly. There are still some details to iron out. How much should each player’s contribution to the jackpot be? Will wild cards count? (We recommend that hands with wild cards be treated as their natural values for the purposes of the high hand jackpot, since it’s easy to create ludicrously high hands with wild cards.) What happens if two players tie—does the first player to get the hand get the entire jackpot, or is it split? What happens if a player holding high hand leaves before they get a chance to collect? As host, it’s your responsibility to come up with a fair set of rules for all of these situations. Put it in writing so there’s no question as to fairness later. (You should probably consult with your players as you write the rules, so they have a hand in deciding what works best for your group.)

Don’t forget the law

Before starting a high hand jackpot for your home game (and before starting a home game, really), check your local laws to make sure that it is legal. Running a jackpot like this may cause your house to be legally considered a casino, and chances are it’s not licensed as one. Adding bells and whistles to your home game isn’t worth it if the next game you get dealt into is behind bars.



Gin Rummy strategy

On Wednesday, we posted the rules of Gin Rummy. As simple as the game is, its strategy is complex. While we can’t cover every one of the ins and outs of Gin Rummy strategy, this post will hopefully give you a few things to think about during your next Gin game. There has been a great deal more written about Gin Rummy strategy over the years, including in the classic Scarne on Cards by John Scarne (1965), which contains an excellent analysis of Gin Rummy (as well as many other games such as Hearts, Red Dog, and Pinochle).

Watch the discards

The chief skill that will help with Gin Rummy is a good memory. It is very important to remember what has been discarded, and by whom. First of all, it keeps you from chasing after unlikely melds. If you are going after a meld of fours, and a four is in the discard pile, your chances of getting your meld are diminished by 75%. Likewise, if you have the 5♣ and 6♣, your chances of making a meld of them are halved if the 7♣ is in the discard pile.

It is also vital to keep track of what your opponent is discarding, what they are not discarding, what they are taking from the discards, and what they are passing up. Keeping track of draws and discards helps you form a picture of what your opponent is shooting for. For instance, it is dangerous to discard a six if you have not seen any sixes in the discards—it’s possible that your opponent is hoarding sixes. If you see them pick up the 8♠, there are two possibilities—either they are trying for three or four eights, or for a run of spades. If you know that they discarded the 9♠ earlier in the hand, you know it’s likely that they are going for 8s.

Watch the score

When the scores are approaching 100, it is important to keep an eye on exactly how far away your opponent is from ending the game. If possible, keep your unmatched card count low enough that if your opponent knocks, the game goes on.

Keeping a reserve

It’s generally a good idea to keep a few low cards in your hand, preferably three or four with a total value under ten. These cards will become your deadwood when you are ready to knock. Otherwise, you may be ready to knock, but get stuck with a succession of high unmatched cards to deal with before you can get your deadwood down to where you can knock.

High or low?

There are advantages and disadvantages to going after melds with high cards like 9s, 10s, and face cards. Because of their high point totals, they are more dangerous to keep around; you might get stuck with them should your opponent knock before you can form them into a meld. On the other hand, because of this danger, your opponent will likely be discarding them more frequently, making it easier to form melds out of them.

In general, don’t have a strict policy one way or another about playing high cards. It’s in your best interest to not play too predictably, since a savvy opponent will take advantage of that fact.

Choosing discards

Of course, the best card to discard is one that helps neither you nor your opponent. Watching the discards helps you determine which cards those are.

Kings and queens in particular are often good discards. Since they are the highest cards in the game, their usefulness is comparable to other cards only in melds of kings and queens. When it comes to runs, each king can only be used in one three-card run, that being J-Q-K. Queens fare a little better, since they can be part of 10-J-Q and J-Q-K. But all other cards can form three different three-card runs: a jack can be part of J-Q-K, 10-J-Q, and 9-10-J. Queens and kings are also worth ten points each, making them undesirable to keep around. Aces and twos have the same disadvantages as kings and queens respectively, but represent a far lesser liability against your hand due to their low point values.

As far as melding is concerned, the most valuable cards are 5s, 6s, 7s, 8s, and 9s. These cards can be used in six possible three-card melds and five possible four- and five-card melds. The 7 in particular is valuable, because it is present in all seven of the possible seven-card melds (not that you will have seven-card melds that frequently).

It’s usually safe to discard a card of the same rank as an opponent’s prior discard. But be careful—a good player may discard a card of the same rank that they need in some other suit to complete a run, in an attempt to trick you into throwing it their way.

Choosing melds

Sometimes you will have a card which will go well with two different completed melds, such as 6-7-8-9♦ and 9♠-9♣-9♥-9♦. Which should you put the 9♦ with when you lay down your hand? The answer is always with the 9s—your opponent cannot lay off cards to a four-of-a-kind meld, and the absence of the 9♦ stops them from laying off the 10♦ onto the run.

Likewise, you can choose your last discard prior to knocking carefully to prevent your opponent from laying off a card on your meld. For example, suppose you have 4-5-6-7♠. You haven’t seen the 8♠, so you suspect your opponent might be hanging onto it, knowing of your meld and hoping he can lay off on it. You might consider discarding the 7♠ as your final discard before knocking, so your opponent is left hanging onto the 8♠ and the eight extra points in deadwood.


Hearts strategy

In our last post, we discussed the game of Hearts. Now that you know the rules of the game, here’s some tips that might help your game.

Choosing what to pass

In may card games, what you’re dealt is what you’re stuck with. Not so in Hearts—you have the opportunity to shape your hand somewhat by choosing to pass cards to the next player.

The gut reaction of most players is to pass the Q♠ when she has been dealt to them. This is not always the best play; sometimes, it’s easier to avoid capturing the Q♠ when you can control when she comes out. A good time to hold the queen is when you only have a few cards in some other suit—when you run out of that suit, you can play the Q♠, and you will be immune to capturing her because you did not follow suit. If you are considering holding the Q♠, make sure you have some other spades to play when some other player leads with spades—otherwise you may be trapped with only the Q♠ as a valid play.

The two spades higher than the Q♠, the K♠ and A♠, should be treated with nearly as much care as the Q♠. You do not want to be forced into playing one of these cards early in a trick and have the Q♠ come out after you. If you are short on spades, pass them.

High hearts are almost always a good option to pass, unless the spades situation is more pressing.

If you have a lot of cards of a particular suit, you might consider passing some of them on—if you’re running long, at least one of the other players is guaranteed to be running short, so they will be using tricks of that suit to unload their undesirable cards. You don’t want to be forced to lead that suit over and over again because of a lack of anything else to lead with.

Remember what you passed, and to whom. Since most of the time, you will be passing on higher, undesirable cards, knowing who holds them can be useful. In particular, if the player holding the Q♠ has already played to a trick, you know there is no way she can be played to the trick.

If you are playing the Jack of Diamonds variant, consider passing the J♦ if there is nothing more pressing to pass. The J♦ is seldom won by the player holding him, since three other cards can be played to collect him.

Play of the hand

A good portion of a winning Hearts strategy involves discovering the most opportune times to ditch cards you don’t want to get stuck with. The easiest method to ditch a card is to run out of a suit—if that suit is lead, you can burn off an undesirable card with no risk that you will end up capturing it. This is an excellent way to get rid of the Q♠ and her accomplices, the K♠ and A♠, as well as high hearts.

Being the last to play to a trick gives you the advantage of knowing what the trick contains. If you see that the trick has no point-scoring cards, you can play a high card and capture it, allowing you to both burn off a high card and choose what the next suit to play is (which might be helpful to get rid of the last few cards of your short suit). If it’s a spade trick, and the Q♠ isn’t in it, you can play the K♠ or A♠. Likewise, if someone has played a high card, you can play a slightly lower card which might cause problems on down the road (e.g. if someone plays the A♥, it’s an excellent time to get rid of the K♥).

If you don’t have the Q♠, it can be a good option to lead spades repeatedly in an attempt to force the Q♠ to show herself, hopefully sending her back to where she came from.

Naturally, keep track of whether the Q♠ has been played. If she’s out of the picture, the K♠ and A♠ are considerably less harmless, and you can ditch them with much less risk.

Keep the lower cards, like twos and threes, around unless you have a specific reason to play them. These cards can be used as exit cards, meaning you can use them in uncertain situations, like leading a trick or being the first after the lead to play, to avoid taking the trick. The 2♥ and 3♥ are particularly useful, since they let you dodge tricks that are often worth up to 4 points.


Seven Twenty-Seven strategy

On Wednesday, we posted the rules of Seven Twenty-Seven. Today, we’re going to take a deeper look into the game and share some Seven Twenty-Seven strategy tips that will hopefully improve your skill at the game.


Seven Twenty-Seven is a game where it’s important to keep track of the probability of particular favorable or unfavorable outcomes. For example, you know that twelve of the fifty-two cards in the deck—about 23%—are face cards, and thus worth half a point. This can come in handy to keep in mind when attempting to determine what other players have, and whether drawing is or isn’t a good idea. For example, if a player is showing a 6 and is acting as though they are going low, it is far more likely that their count is actually 6½ rather than 7.

However, each draw is not an independent event; the probabilities change as the hand progresses. Keep an eye on other players’ hands—if you see lots of 10s and 9s already out, you’re less likely to bust. Likewise, watch out if a good chunk of the face cards have already come out! It means that the deck is composed of a greater percentage of higher cards.

The importance of being low

The winner of the low half of the pot is known fairly early on in most cases. Some players will be dealt hands with a count higher than 7 to begin with, and still others will find themselves overshooting 7 in an attempt to get closer to it. Usually, after one or two drawing rounds, there is only one player left standing under 7. This player knows they can’t lose, so they will be the one driving the betting by raising to the limit at every opportunity, and those going for high will have no choice but to call if they want the other half of the pot.

Therefore, you want to be that low player as often as possible. Obviously, if you are dealt a hand lower than seven, go for low. Even if you have a count of 8 or 9 (or 10½!), you may still be able to bluff low if the card that is showing is lower than 7. Wait a round or two before taking any cards, since standing, followed by betting, will be interpreted by your opponents as consistent with with going for low, and you should see some of your opponents fold naturally as they try to get nearer to 7 and overshooting or find that they have mid-range totals that aren’t good for either half of the pot. With aggressive betting, you may even be able to force any competitors for low, with low totals like one or two, to believe you have 7 or 6½, which will cause them to hit to get closer to 7 or simply fold. (This can be painful when they do end up with a total of 7.)

The most problematic thing that occurs when going low is when someone else is doing the same thing. Here, you will have to take into account their play history and probability to deduce what their count is. Obviously, if you are bluffing low, you should consider getting out of there, since attempting to force them out with aggressive betting can be expensive if it’s not successful. If you have a count less than 5 or so, consider taking a card to try to get closer to 7. If you overshoot, fold immediately—going for high with a starting total of 7½ puts you considerably behind the other players, and you will be milked for chips by your former low competitor the whole time.

If you find yourself as the only low player, take care in betting. Betting too high too early does nothing but scare players with marginal hands away. Keep the betting sane at first. Don’t break out the maximum bets until everyone is likely over 20 or so—at this point, players become attached to their hands since they are potentially one card away from 27.

Remember, the game ends when everyone declines to take a card. Also, you don’t have to have a count below 7 if you’re the only one going low. Therefore, if you’re the only low player, and the game shows signs of winding up, you can extend it a little, and get more chips in the pot, by taking a card. Players will virtually never fold at this point, because they are happy with their hands, so it’s essentially free money toward your half of the pot.

Folding vs. going high

If you’re showing a 7 through 10, you have no choice but to go high. But just because you have a count greater than 7 doesn’t mean you should go high. Folding early is an attractive option with a count of 8 through 14 or so. With counts this low, you will have to take several cards to get near 27 (think of all the face cards you might draw), and the low player will be betting the entire time, as well as any other players who get close to 27 before you.

15 through 17 is an excellent count for high, since a single 10 could put you at 27. Above 17 should obviously go for high, although the risk of busting is now present.

How close is close enough?

Unlike in Blackjack, where getting 17 (four away from 21) is considered good, you have to get considerably closer to 27 to win. Counts below 25 will seldom win without all other players busting. 25 is about the minimum you should stand on. If the hand is competitive, you may want to try to draw to 26 or greater. 26½ will rarely lose the hand.

Likewise, for low, if you have another player going low in the same hand, a count below about 5 or so may need to be hit. 6, 6½, and 7 are all very good totals to end on.

When you reach a total that is worth standing on, you should probably follow the low player’s lead and start trying to milk the players going for high that have not yet reached a total they’re satisfied with. They may fold, or even better, bust, and then you and the low player can split the proceeds.