- Players hoping for a royal flush, straight flush, or four of a kind could be waiting a long time, with probabilities of less than 0.001 percent, less than 0.002 percent and 0.02 percent, respectively. If a player refuses to switch out any cards in the draw, or starts making noises about these hands, you can use this to assess their credibility.
- A good rule of thumb I always use for a flush draw is multiply outs(13 spades - 4 spades) with 4 on the flop and 2 on the turn. This ways it's much easier to remember and you aren't that far away from the correct percentage. That is: On the flop = number of flush outs x 4 = (13-4)x 4 = 36%. On the turn = number of flush outs x 2 = (13-4)x 2 = 18%.
In the third part of the Paul Phua Poker School series on poker odds, Paul Phua gives tips on predicting the future to improve your present strategy
Would it not be wonderful to have the power to predict the future? It would certainly be easy to make money at betting! Film-lovers will recall how using a sports almanac from the future made Biff Tannen a rich man in the second Back to the Future film.
We can’t all have a DeLorean time machine, but in poker we have the next best thing. We have the ability to predict what is likely to happen in the future, and to change our strategy accordingly.
In the first two parts in this mini-series on poker odds, I gave tips on why odds are important, and how to calculate them using a simple magic formula. We have seen already how knowing our likelihood of winning will affect how much we bet. Now here is an interesting application in practical play:
In hold em, the probability you hit a royal flush by the flop is the same as in draw poker. However, we can compute an upper bound for the probability that you hit a royal flush by the river. If we make the assumption that you will play any two suited cards 10+, and that you always see 5 board cards, then the probability is.
How to play a nut flush draw
As I said in my video on the best pre-flop hands, a suited Ace has great potential as a starting hand, even if your kicker is low. An Ace on the flop often gives you the best hand, though be prepared to fold to opposition if your kicker is weak. And if you flop a flush draw, you are in a very powerful position – more powerful than many people realise.
Let’s take the starting hand shown in my video: A4 of diamonds. The flop comes K5 of diamonds, with a 9 of spades. Another player bets. First, do what you should always do when someone bets: work out what hand they are likely to hold.
There’s no strong straight draw out there; if he has a flush draw it’s worse than yours; sets are uncommon. You can’t put him on AK, as he didn’t seem that strong in pre-flop betting, so you reckon he has a K: maybe KQ or KJ. So he likely has top pair, and you have nothing – yet! But you have great potential. Let’s work out how much.
Count up your “outs”
There are nine diamonds left to come that complete our flush, plus three Aces to give us a higher pair: that’s 12 “outs”. Using our magic formula for calculating the odds, that gives us 12 x 4 = 48% chance of winning by the river. [Mathematicians say the real figure is 45% –the magic formula isn’t perfect, but it’s close enough.]
That’s a nearly 1 in 2 chance of winning the pot! Pretty good odds. But the great thing about poker is it’s not all cold, hard math. It takes strategy and psychology to decide how to play those odds.
Your instinct here will be to call, and hope to hit. That’s a reasonable strategy, and the more people who are in the hand, the better it is. You will likely take all their money if you hit your nut flush – thus being paid several times your investment.
But let’s look at another, more advanced strategy, one that is particularly valuable if only one other player is in the hand.
Re-raising for “fold equity”
Unless you are keen to keep a number of people in the pot, a great tactic against a single opponent is to re-raise rather than call. Re-raising gives you “fold equity”. That’s a fancy way of saying it gives you an extra chance at winning: if they get scared and fold, congratulations! You’ve won the pot with the worst hand. And if they call, you’re still a coin-flip to win by the river.
To have fold equity, your bet should be big enough to make them fold. Simply doubling their bet is almost never enough. Even a weak King is likely to call and hope you are semi-bluffing with a flush draw (which you are!), or that they hit two pair on the turn.
So how much do you raise? That calls for psychology: is this player a holder or a folder? Some people are “calling stations” who will call almost any bet with a pair. With a person like this, you may need to raise bigger. Either way, do it confidently. If you are relatively short-stacked, you can even shove all-in. Don’t worry! You are nearly 50-50 to win even if they call.
If they do call – what next?
Maybe they realise you’re on flush draw. Maybe they’re just stubborn. Whichever, your opponent calls you, and the turn card is a blank – it doesn’t help. What now?
Usually now you have no fold equity: if they called a re-raise on the flop, they will often feel committed to call a bet on the turn. And now you have only one card left to come, not two, so your chances of winning are halved to than 1 in 4.
Unless you are a very experienced player with a strong read that your opponent may fold, it’s not worth inflating the pot with what are now poor odds of winning. You want to check. The good news is, your opponent will be wary of you and will usually also check, so you get a “free” card to see the river.
To sum up: when you re-raise on the flop, you have maybe a coin-flip chance of them folding to give you a small pot; and a coin-flip chance of them calling, in which case you then have a coin-flip chance of winning a big pot. Three quarters of the time, therefore, you are winning with a re-raise!
Other flush draws
Let’s just look quickly at other flush draw combinations that you might not be aware of.
Two more outs: Let’s say there was a 4 on the flop rather than the 5, giving your A4 of diamonds a small pair. Now you have two additional outs (either of the two 4s still to come would give you three of a kind to beat his pair of Kings), so you are even better than 50%.
Three more outs: Or let’s say the flop came K52. Now with your A4 you additionally have an inside straight draw, giving three extra outs. (There are four 3s that would make a straight. One of these is a diamond and you’ve already counted that out in your flush draw, hence three extra outs not four).
Three fewer outs: The flush draw to beware of is where you have no extra outs, just the nine cards for your flush. The magic formula tells us that your chances then are just 9 x 4 = 36%, ie 1 in 3. It’s a big leak in less experienced players’ strategy to chase this kind of flush draw against a single opponent.
In my next article on poker odds and strategy…
I hope the above example shows how knowing the odds – our own probability time machine that lets us peer into future likely outcomes – helps dictate our present strategy. In my next article, I will give you a useful chart of the most common. Learn it well! Read the next article.
The odds of flopping a straight flush with a premium suited connector such as T9s is 0.02% or 1 in 4,900
Definition of the Straight Flush –
Five cards of consecutive rank, all of the same suit.
Example – 5d6d7d8d9dThe Ten to Ace Straight Flush is the strongest hand in poker and is referred to as the “Royal Flush”.
Odds of Making a Straight Flush on the Flop
Flopping a Straight Flush seldom happens in poker. We specifically need to start out with two suited connected cards for this to be possible.
The odds of flopping a Straight Flush are so unlikely (0.02% or less) that the majority of poker equity calculators don’t even show the precise odds.
We’ll need to do some maths of our own.
Calculation of Straight Flush Odds
Let’s start with a very specific example -
We hold A2s. What are the odds of flopping the Ace to Five Straight Flush?
Why do we choose this example? It’s the easiest one because it provides only one way of making the Straight Flush. The flop has to come down precisely Three, Four, Five of the correct suit.
So, how likely is this?
In order to calculate, we’ll first need to know how many combinations of three cards are possible on the flop.
Basic Combinations and Permutations
Firstly, how many different combinations of three cards can be dealt on the flop? Assuming we care about the order of the three cards (and that our two hole cards are already known), the answer is 117,600 (50 * 49 * 48).
In statistics, this type of calculation is referred to as a permutation and accounts for the order of the flop cards.
Of course, in Hold’em, the order of the cards on the flop doesn’t matter (i.e. a 3,4,5 flop is the same as a 5,3,4 flop, for all intents and purposes). What we are interested in is the number of possible combinations of three cards.
A combination is similar to a permutation but doesn’t account for the order. Since there are 6 possible ways of arranging three cards, we can simply divide our number of permutations (117,600) by 6 to establish the number of possible three-card combinations on the flop.
117,600 / 6 = 19,600 possible combinations of three cards on the flop (given two cards are known)
In other words, there are 19,600 different possible sets of three cards that may fall on the flop given that our two hole cards are already known.
Guess what?
To make the exact Straight Flush in question, only one of these 19,600 combinations will do the job.
Armed with that information, we can now establish a range of different probabilities.
Odds of flopping the Straight Flush with A2s = 1/19,600 = 0.00005 or roughly 0.005%
That’s an insanely small likelihood!
Thankfully, the odds with different types of starting hands are usually a little better.
It all depends on the number of different combinations of three cards that provide a Straight Flush.
For example, think about T9s.
How many different ways are there to make a Straight Flush with 9Ts?
Ways of making a Straight Flush with T9s
JQK
QJ8
J87
678
So that’s four different ways. We are hence four times as likely to make a Straight Flush with 9Ts as we are to make a Straight Flush with A2s.
Odds of flopping the Straight Flush with 9Ts = 4/19,600 = 0.0002 or roughly 0.02%
Ways of making a Straight Flush with T8s
QJ9
J79
679
Odds of flopping the Straight Flush with T8s = 3/19,600 = 0.00015 or roughly 0.015%
Ways of making a Straight Flush with T7s
J89
689
Odds of flopping the Straight Flush with T7s = 2/19,600 = 0.0001 or roughly 0.01%
Only suited connectors (or gappers) can make Straight Flushes on the flop. All other holdings such as pocket-pairs and off-suit combos can never flop a Straight Flush.
We are, naturally, more likely to flop a Straight Flush draw as opposed to the Straight Flush itself. To see examples of calculating the odds of hitting a Straight Flush draw on the flop, check out the 888poker article on Royal Flush odds in poker.
Odds of Making a Straight Flush on the Later Streets
There will be two primary types of Straight Flush draw we’ll flop. The gutshot Straight Flush draw and the open-ended Straight Flush draw.
Gutshot Straight Flush draws have 1 out in the deck, while open ended Straight Flush draws have 2 outs in the deck.
Odds of Hitting on the Turn or River
Odds of catching the gutshot Straight Flush on the turn 1/47 = 0.0213 or roughly 2.1%
Odds of catching the open-ended Straight Flush on the turn 2/47 = 0.426 or roughly 4.3%
Odds of catching the gutshot Straight Flush on the river 1/46 = 0.0217 or roughly 2.2%
Odds of catching the open-ended Straight Flush on the river 2/46 = 0.0435 or roughly 4.4%
Odds of Hitting by the River
To calculate the probability of hitting by the river, we’ll employ the trick of calculating the possibility of not hitting and then subtracting from 100%.
Odds of not catching the gutshot Straight Flush on the turn 46/47
Odds of not catching the open-ended Straight Flush on the turn 45/47
Odds of not catching the gutshot Straight Flush on the river 45/46
Odds of not catching the open-ended Straight Flush on the river 44/46
Odds Of Royal Flush
Odds of not catching the gutshot Straight Flush on the turn or river = 46/47 * 45/46 = 0.9574 or roughly 95.7%
Odds of not catching the open-ended Straight Flush on the turn or river = 45/47 * 44/46 = 0.9158 or roughly 91.6%
Poker Odds Royal Flush
Odds of hitting the gutshot Straight Flush by the river = (100- 95.7%) roughly 4.3%
Odds of hitting the open-ended Straight Flush by the river = (100 – 91.6%) roughly 8.4%
Implied Odds Analysis of a Straight Flush
A Straight Flush always carries excellent implied odds when hitting. This is because our opponent is usually forced into stacking off with very strong worse hands such as worse flushes and full houses.
Straight Flushes made with two of our hole cards always carry better implied odds than Straight Flushes made with one of our hole cards.
When using just one of our hole cards, it means there will be four cards to the Straight Flush already on the board. This decreases the chance that our opponent will pay us off with worse holdings.
Although Straight Flushes should hardly ever be folded, their implied odds are the best when no higher Straight Flush is possible on the board.
Basic Strategy Advice
It’s basically the nuts. Play aggressively and make big bets! Even if a higher Straight Flush is possible, it’s usually just a cooler if we are beat. We’d have to be really deep to find an exception.
Odds of Making Straight Flush | |
Method (Straight Flush) | Probability (%) |
Flopping the Straight Flush with A2s | 0.01 |
Flopping the Straight Flush with T9s | 0.02 |
Flopping the Straight Flush with T8s | 0.02 |
Flopping the Straight Flush with T7s | 0.02 |
Catching the Straight Flush Gutshot from flop to turn | 2.13 |
Catching the Straight Flush open ender from flop to turn | 4.26 |
Catching the Straight Flush Gutshot from turn to river | 2.17 |
Catching the Straight Flush open ender from turn to river | 4.35 |
Catching the Straight Flush Gutshot from flop to river | 4.30 |
Catching the Straight Flush open ender from flop to river | 8.42 |