- \n
- The basics when playing a drawing hand
<\/i><\/li>\n- Shifts in equity and semi-bluffs
<\/i><\/li>\n- Differences between being in and out of position \t
<\/i><\/li>\n<\/ul>![\"\"](\"https:\/\/www.pokerstrategy.com\/download\/content\/bilder\/ps_trennlinie.jpg\")
<\/div>This article will teach you the best way to play strong draws. A strong draw is defined as a hand with more than 8 outs (for a strong hand) and no showdown value.<\/p>
We will look at playing with strong draws from a mathematical standpoint. This isn't always easy; you will almost never be getting the right pot odds to call with a draw. The implied odds, however, are usually much higher than the pot odds you would need to call.<\/p>
The fact that you can vary the size of your wager also allows semi-bluffing to be very effective. You can often generate enough fold equity to make semi-bluffs a very profitable part of your game.<\/p>
The next section will give you a systematic walk-through in playing with strong draws and provide examples of how to play in concrete situations.<\/p>
The basics<\/h1>
Implied odds<\/div>The implied odds are naturally much higher in NL Hold'em than FL Hold'em. You can often expect to get a pot size bet (PSB), or at least a half pot size bet (HPSB), in the coming betting round(s).<\/p>
Always keep an eye on the stack sizes. If yours or your opponent's is too small, you won't be getting good implied odds. You can only win what you and your opponent both have.<\/p>
EXAMPLE<\/div>Assume there are 12 BBs in the pot and you have a nut flush draw with 9 outs (the board is not paired). Your opponent bets 8 BBs. The pot odds are at 1:2.5; you need 1:4.22 pot odds to make a correct call with a 9 outer (calculated as follows: [1-(9\/47)]\/(9\/47))<\/p>
When you assume that your opponent will usually bet 1\/2 pot on the next street, your implied odds for calling are much higher.<\/p>
Calculating the implied odds:
Pot on flop: 12 BBs
Size of opponent's bet: 8 BBs
Pot on turn after calling: 28 BBs (12 BBs+8 BBs+8 BBs)<\/p>Implied odds for calling on the flop: 1 : [(\"Pot on flop\" + \"Opponent's bet\" + \"Expected profit if you hit on the next street\") \/ (\"Opponent's bet\") <\/i><\/p>
Implied odds = 1 : [12+8+28\/2)\/8] = 1 : 4.25 <\/i><\/p>
As we said, you need 1:4.22 pot odds to make a correct call. Your implied odds for calling are 1:4.25, enough to justify staying in the hand.<\/p>
You will not, however, always bet getting very good implied odds with a drawing hand. In fact, you often won't have very high implied odds at all after hitting. This is the case when your previous action makes your completed draw too obvious.<\/p>
The more obvious your draw (esp. flush draws and one card straight draws), the more realistic and pessimistic you must be when estimating your implied odds. Your implied odds are, in part, defined by the way your opponent interprets the flop texture.<\/p>
Shifts in equity when holding a strong draw<\/h1>
In order to really understand playing with strong draws, you have to know how your equity shifts on the turn when you miss. You should already know that your equity is always higher on the flop, since you have still have two chances (turn and river) to complete.<\/p>
You only have one more chance to complete once you're on the turn. This results in a loss in equity. The following chart should make this very clear:<\/p>
\n\n
\n ![\"\"](\"https:\/\/www.pokerstrategy.com\/download\/content\/bilder\/ps_icon_tabelle.gif\")
<\/td>\n\n Equity shift from flop to turn<\/p>\n
<\/p>\n
\n\n
\n Your hand
<\/b><\/td>\nOpponent's hand
<\/b><\/td>\nFlop
<\/b><\/td>\nEquities on flop
<\/b><\/td>\nTurn
<\/b><\/td>\nEquities on turn
<\/b><\/td>\nRelative loss in equity
<\/b><\/td>\n<\/tr>\n\n A ![\"\"](\"https:\/\/cdn-origin.pokerstrategy.com\/smileys\/heart.png\")
7<\/td>\nT ![\"\"](\"https:\/\/cdn-origin.pokerstrategy.com\/smileys\/spade.png\")
9![\"\"](\"https:\/\/cdn-origin.pokerstrategy.com\/smileys\/diamond.png\")
<\/td>\nT 92<\/td>\n36.46:63.54<\/td>\n 3 <\/td>\n20.45:79.55<\/td>\n 43.9%<\/td>\n<\/tr>\n \n K Q![\"\"](\"https:\/\/cdn-origin.pokerstrategy.com\/smileys\/club.png\")
<\/td>\nJ T<\/td>\nJ T2<\/td>\n32.83:67.17<\/td>\n 3 <\/td>\n18.18:81.82<\/td>\n 44.6%<\/td>\n<\/tr>\n \n K Q<\/td>\nJ T<\/td>\nJ T2<\/td>\n53.32:46.68 <\/td>\n 3 <\/td>\n34.1:65.9<\/td>\n 36.1% <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table> These three situations show how your equity with a strong draw shifts from flop to turn. You have to complete an obvious flush\/straight draw, or hit runner runner two pair to win the hand.<\/p>
As you can see, a blank card on the turn results in an equity loss of 36.1-43.9%. The simple conclusion from this is that you should be more willing to go broke with a draw on the flop than on the turn, since you will always have more equity on the flop if you are behind and have to hit to win.<\/p>
The logic can be applied to made hands, as well. You should be more willing to go broke against a draw after a blank card on the turn than on the flop.<\/p>
Bet\/raise, call or fold?<\/div>Unfortunately, it isn't easy to say whether you should play your draw aggressively or passively (or even if you should simply fold). So far all you know is that if you're going to go broke with a drawing hand, you should do so on the flop in order to maximize your equity against made hands.<\/p>
A mathematical analysis on playing with strong draws is very complex and doesn't give us any exact answers, since there are so many unknown variables. You will usually have to adapt your play to your opponent's playing style and can't really develop any standard line for playing strong draws. We will start by establishing general guidelines and look at examples of how they can be put to practice.<\/p>
When should you fold?<\/div>You should fold when ...<\/p>
- \n
- ... you do not have sufficient implied odds to call and when semi-bluffing is out of the question. <\/li>\n
- ... you are too likely to already be drawing dead. This can be the case, for example, when you have a flush or straight draw on a paired board and risk running into a full house. <\/li>\n
- ... you have a strong draw but are still often dominated. This can be the case when you are not drawing for the nut flush or when your hole cards are on the bottom end of an OESD. <\/li>\n<\/ul>When should you call?<\/div>
You should call when ...<\/p>
- \n
- ... you cannot generate sufficient fold equity by semi-bluffing but do have sufficient implied odds to call. This is often the case when a passive opponent suddenly bets the flop.<\/li>\n
- ... your opponent is too likely to re-raise your semi-bluff and force you to fold (either because the odds are too poor or because you're too much of an underdog). This is often the case when an aggressive opponent is protecting a made hand on a draw heavy board.<\/li>\n<\/ul>When should you bet\/raise (semi-bluff)?<\/div>
You should bet\/raise when ...<\/p>
- \n
- ... you can generate high fold equity and when there is already a fair amount of money in the pot. <\/li>\n
- ... you have so many outs that you have very good equity against made hands. <\/li>\n
- ... you are in position and your opponent is likely to let you take a free card on the turn. <\/li>\n
- ... you are heads up against an opponent who overplays one pair hands and often takes them to the showdown on principle. This is a good spot to build up the pot so that you can make big value bets on later streets. <\/li>\n<\/ul>How large should a semi-bluff be?<\/div>
This answer can be based on empirical observations which hold true in most situations.<\/p>
- \n
- Minraises rarely generate high fold equity. They are rarely effective as semi-bluffs.<\/li>\n
- A pot size raise often gives you a very good price-performance ration with respect to the fold equity it generates. Pot size raises generate significantly more fold equity than minraises. <\/li>\n
- Overbets usually generate even more fold equity than pot size bets, but there is a catch: the higher you overbet, the worse your price-performance ratio.<\/li>\n
- The fold equity you generate does not increase linearly with the size of your bet. Strong, thinking opponents may not be impressed by a very big bet; they will ask themselves if you would bet\/raise the same amount with a set, for example. If they interpret your (too) large bet as a sign of a drawing hand, they will call with somewhat more marginal made hands.<\/li>\n<\/ul>
As you can see, you have to select your bet size based on the opponent you are facing. You should also keep in mind that minraises very rarely generate enough fold equity to semi-bluff with +EV.<\/p>
How important is your bet sequence when semi-bluffing?<\/div>Semi-bluffs are usually only +EV when you generate enough fold equity with your bet\/raise. You have to select the right betting sequence to convince your opponent.<\/p>
You will usually be the one going all-in, as this also allows you to generate the highest amount of fold equity possible. But remember: You can't generate much fold equity when your opponent is already committed.<\/p>
You can also use this against your opponent. If, for example, you have a nut flush draw on an otherwise dry board, you can choose a betting sequence that induces your opponent to semi-bluff all-in with a weaker flush draw.<\/p>
This allows you to create very profitable situations in which your opponent is often behind on the flop. The important thing to remember is who you are playing. This won't work on an opponent who never semi-bluffs with a non-nut flush draw on the flop.<\/p>
How much emphasis should you place on balancing your hand range?<\/div>Balancing is often very over-rated in micro limit and low limit games. There is no need to worry about your own hand range when your opponents aren't paying any attention to it, either.<\/p>
You can play your flush draws like flush draws and your sets like sets. Most of your opponents at these limits won't be asking themselves what kinds of hands you might have in your range; they are only interested in their own hand and seeing if they are ahead or not.<\/p>
But the better your opponents get, the more you have to start thinking about balancing your range. You will find yourself in situations in which you make a much larger bet than you normally would with a set to make it look like a flush draw, and vice versa.<\/p>
The same idea applies to your betting sequence. Balancing your betting sequence makes it more difficult for your opponent to put you on a type of hand, which means he will make mistakes when playing against your monsters \/ strong draws.<\/p>
As we said, balancing is only an issue when you are playing against good, attentive opponents. Don't overestimate this aspect too early. You are usually better off playing for maximum value in the micro limits and low limits.<\/p>
We will conclude with a few thoughts to keep in mind when estimating your implied odds:<\/p>
- \n
- Implied odds vary from draw to draw. A flush draw usually has lower implied odds than an OESD. This is because possible straights don't look as dangerous as possible flushes. Three cards of the same suit stand out more than three cards (especially when they are not in sequential order) to a straight. <\/li>\n
- Implied odds vary from opponent to opponent. You can expect an opponent with a very high WTSD stat to pay you off more often when you complete your draw than an opponent with a low WTSD stat. <\/li>\n
- Implied odds vary from board to board. A straight draw on a single suited board looks much more dangerous than a straight draw on a rainbow board. The implied odds sink accordingly. <\/li>\n
- Implied odds vary based on effective stack sizes. You can't win more than your opponent and you yourself have.<\/li>\n<\/ul>
Applying the theory to your game<\/h1>
You are out of position<\/div>Two problems arise when you are OOP:<\/p>
- \n
- It will be hard to extract value if you do hit, since it will usually be fairly obvious when you bet into him upon completing. An attempt to check\/raise is not very promising. A lot of NL players check behind after a possible draw may have completed.<\/li>\n
- Seeing the next card can be very expensive. You will rarely be given a free card. <\/li>\n<\/ul>
You can often avoid these two problems by choosing a betting sequence on the flop that leads to an all-in. This is one way of dealing with your positional disadvantage and the shift in equity that will occur if you miss on the turn.<\/p>
Of course, your betting sequence should lead to you being the one who goes all-in, for reasons we have already discussed. This is usually a very profitable way of playing very strong draws (12+ outs). You don't need to generate much fold equity in the end for such a move to be profitable with so many outs.<\/p>
You are OOP in a raised pot<\/div>YOU HAVE INITIATIVE<\/div>NL 2\/4 Dollar<\/p>
Villain1 (Button) ($400)
SB ($350)
BB ($420)
Hero ($600)
MP ($500)
Villain2 (CO) ($350)<\/p>Pre-flop:<\/b> Hero is MP3 with K<\/b>
, Q<\/b>
1 fold<\/font>, Hero raises to $12<\/font>, CO calls $12, Button calls $12, 2 folds<\/font>.<\/p>Flop:<\/b> ($42) T<\/b>
, J<\/b>, 3<\/b> (3 players)
Hero bets $35<\/font><\/p>You make a standard 3 BB pre-flop raise with KQs from MP3. Two opponents call. On the flop you have an OESD + overcards. You decide to semi-bluff for the following reasons:<\/p>
- \n
- You showed strength before the flop. You will usually be able to take the pot down with a contibet when both of your opponents missed. <\/li>\n
- If you do get called, you have 8 safe outs for the nuts.<\/li>\n<\/ul>
Scenario 1:<\/b><\/p>
Hero bets $35<\/font>, Villain2 (CO) raises to $105<\/font>, Villain1 (Button) calls $105, Hero calls $70.<\/p>
In this scenario your opponent raises to $105. You call for the following reasons:<\/p>
- \n
- After you showed strength before the flop you got a raise and a cold call. At least one of your opponents is sure to have a strong hand, which means you would generate very little fold equity by re-raising\/pushing.<\/li>\n
- You are getting good pot odds to call (1:4.1). This isn't enough to call with your OESD (8 outs require app. 1:4.875 pot odds), but you can assume that your implied odds are very high, since at least one of your opponents is sure to have a strong hand.<\/li>\n<\/ul>
Your decision on the turn will be easy with such a large pot. If you miss, you have to check, since you will only be able to generate low fold equity.<\/p>
There are $357 in the pot on the turn. If an opponent bets (1\/2 would be enough), you will be getting too poor of odds to call and won't be able to count an any implied odds, since the stacks are so small in relation to the pot. An easy fold. If you complete, you can check\/raise or bet directly, depending on the opponent you are facing.<\/p>
Scenario 2: <\/b><\/p>
Hero bets $35<\/font>, Villain2 (CO) calls $35, Villain1 (Button) calls $35.<\/p>
Turn:<\/b> ($147) 4<\/b>
(3 players)
Hero checks, Villain2 (CO) checks, Villain1 (Button) bets $110<\/font>, Hero folds<\/font><\/p>In this scenario a blank shows up on the turn. You check after having gotten two calls on the flop. It is very unlikely that both opponents have a weak made hand or a draw. Another semi-bluff would not generate much fold equity.<\/p>
Villain2 checks behind and Villain1 bets $110 with $147 in the pot. If Villain2 folds, you will be getting 1:2.3 pot odds. This is clearly not enough to call with your 8 outer (you need app. 1:4.875).<\/p>
The implied odds are the decisive criterion when it comes to calling. If you assume you can get the rest of his stack ($193) on the river if you complete, your implied odds would be 1:4.1. This isn't enough to justify a call, so you fold your hand.<\/p>
YOU DO NOT HAVE THE INITIATIVE<\/div>NL 2\/4 Dollar<\/p>
Button ($250)
SB ($200)
Hero ($240)
UTG ($180)
MP ($140)
Villain (CO) ($300)<\/p>Pre-flop:<\/b> Hero is BB with T<\/b>
, A<\/b>
2 folds<\/font>, Villain (CO) raises to $12<\/font>, 2 folds<\/font>, Hero (BB) calls $8.<\/p>Flop:<\/b> ($25) 6<\/b>
, 9<\/b>, 7<\/b> (2 players)<\/p>You have ATs in the Big Blind. You pick up a nut flush draw + gutshot (12 outs) on the flop. Your overcard outs will even be good sometimes. This is a hand you would like to push all-in with on the flop.<\/p>
You are clearly ahead against your opponent's range (steal raise from CO). When facing a normal opponent, you should select a betting sequence that allows you to be the one who pushes all-in. If you are facing an opponent who likes semi-bluffing the flop with weak draws, you can use the betting sequence from the following scenario:<\/p>
Scenario 1:<\/b><\/p>
Hero checks, Villain bets $20<\/font>, Hero raises to $60<\/font>, Villain raises to $180 <\/font><\/p>
You can clearly see why this betting sequence would be sub-optimal against a normal opponent. You let him be the one to make the decisive raise. If you push now, you won't be able to generate much fold equity, since your opponent would be getting 1:2.9 pot odds.<\/p>
Your opponent's raise allows you to limit his hand range to the following hands:<\/p>
- \n
- He has an overpair and wants to protect against draws. <\/li>\n
- He has two pair and wants to protect against draws. <\/li>\n
- He has a set and wants to protect against draws.<\/li>\n
- He has a completed straight. <\/li>\n
- He has a strong draw and is semi-bluffing. <\/li>\n<\/ul>
How does your equity compare?<\/p>
- \n
- Against an overpair (other than AA): 53% <\/li>\n
- Against a straight: 40% <\/li>\n
- Against two pair: 40% <\/li>\n
- Against a set: 33% <\/li>\n<\/ul>
You are obviously ahead against a draw. You have to either push or call in this situation due to your high equity. You can also see: The more often your opponent has a draw, the higher your overall equity against his entire hand range.<\/p>
This would not be the best way to play against a normal, aggressive opponents, since it requires you to go all-in with the fold equity being on your opponent's side. The next scenario offers an alternative betting sequence for such a situation.<\/p>
Scenario 2:<\/b><\/p>
Hero bets $20<\/font>, Villain raises to $65<\/font>, Hero raises All-In <\/font>[$228]
In this scenario your opponent raises to $60. This can mean a number of things:<\/p>
- \n
- He may have hit a strong made hand (two pair or better) and want to protect.<\/li>\n
- He may have a weak\/medium strong made hand (TP, overpair) and want to protect. <\/li>\n
- He may have a draw as well and be semi-bluffing. <\/li>\n
- He may be bluffing. <\/li>\n<\/ul>
Now for a few thoughts on equity. Your equity compares to his range as follows:<\/p>
- \n
- Against a set: 33% <\/li>\n
- Against a straight: 40% <\/li>\n
- Against two pair: 40% <\/li>\n
- Against an overpair (other than AA) or TP (with A kicker): 53% <\/li>\n
- Against a pair (without A kicker): 60% <\/li>\n<\/ul>
You have app. 42% equity on average (this is pessimistic - bluffs and semi-bluffs are not yet included). You would be getting 1:2.45 pot odds to call, for which you have more than enough equity. The only question is whether or not a raise would be better.<\/p>
If you just call, you could run into the following problems:<\/p>
- \n
- You are OOP. If you do hit, it is very unlikely that you will be able to get any more value out of your opponent. A hit would also be pretty obvious to your opponent, since the board will either show three cards of the same suit or 4 numbers in sequential order (with a T or 5 completing the straight). Your opponent will often fold if you bet and take a free card if you check.<\/li>\n
- If you miss on the turn and check, your opponent will usually bet again. You will then have to fold, since you won't be getting the right odds and will lose a fairly large pot.<\/li>\n<\/ul>
Let's look at your other option: a raise. If you decide to raise, the first thing you have to do is decide how much to raise. If, for example, you make a pot size raise and your opponent pushes all-in, you will have to call due to the (correct) odds. For this reason, pushing all-in yourself is a better option.<\/p>
As we said before, you should bet the amount that generates the highest amount of fold equity. An all-in usually generates the greatest amount of fold equity in the lower limits where the opponents aren't thinking too hard. Pushing in this situation is +EV very often.<\/p>
This is due to your high equity and the large pot you are playing for. The following formula shows you how to calculate the EV of a push.<\/p>
We'll start with the abbreviations:<\/p>
Pfold<\/sub> = The probability that your opponent will fold
Pot = Size of pot before you push all-in
Stack = The size of the smaller stack (yours or your opponent's)
Dead money = Money that was put in the pot by players who are no longer in the hand
Costs = The cost of your semi-bluff<\/p>Your total profit when pushing is calculated as follows:<\/p>
Profit<\/i> = Pfold<\/sub> * Pot + (Stack + Dead money + Stack - Costs) * Equity * (1 - Pfold<\/sub>)
Loss = Costs * (1-Equity) * (1 - Pfold<\/sub>)
Total profit = Profit - Loss
<\/i><\/p><\/i>Example<\/b> 1: Fold equity = 0%<\/i><\/b><\/p>
Costs<\/i> = $208
Pot = $110
Dead money = $1 (from the Small Blind)
Stack = $240
Equity = 0.4 <\/i><\/p>Note<\/i>: Your equity has changed slightly (from 42% to 40%). This is because your opponent will not call your all-in push with all the hands in his range. He will call with a set, straight and, now and again, with two pair or an overpair.<\/p>
Total profit = $109.2 - $124.8 = - $15.6 <\/i><\/p>
<\/i>Example 2: Fold equity = 25%<\/b><\/p>
Total profit<\/i> = $109.4 - $93.6 = $15.8
<\/i><\/p><\/i>Example<\/b> 3: Fold equity = 50%<\/b><\/p>
Total profit<\/i> = $109.6 - $62.4 = $47.2 <\/i><\/p>
Example<\/b> 4: Fold equity = 100%<\/b><\/p>
Total profit<\/b> = $110 - $0 = $110
<\/b><\/p><\/b>The trend is easily seen: As your fold equity increases, so does your total profit. With just 25% fold equity (your opponent must fold 1 in 4 times) you make a (long term) profit.<\/p>
In conclusion, we can say that you almost always push profitably, assuming you have enough fold equity, when you have a draw with 12 or more clean outs and there is already a fair amount of money in the pot.<\/p>
To get a better feeling for when a push would be +EV, you can play around with the parameters in the example. Try varying the following terms in the equation to see how it affects the outcome:<\/p>
- \n
- Costs <\/li>\n
- Pot <\/li>\n
- Fold equity <\/li>\n
- Dead money <\/li>\n
- Stack<\/li>\n
- Equity (based on # of outs) <\/li>\n<\/ul>
Look for the points at which your total profit is highest\/lowest. You can also plot various relations (for example, fold equity in relation to equity) with a program of your choice.<\/p>
OOP in an unraised pot<\/div>NL 2\/4 Dollar<\/p>
Button ($550)
SB ($300)
BB ($420)
Hero ($430)
Villain (MP) ($800)
CO ($290)<\/p>Pre-flop:<\/b> Hero is BB with 8<\/b>
, A<\/b>
1 fold<\/font>, Villain (MP) calls $4, 1 fold<\/font>, Button calls $4, 1 fold<\/font>, Hero checks.<\/p>Flop:<\/b> ($14) 3<\/b>
, 6<\/b>, 4<\/b> (3 players)
Hero bets $12<\/font><\/p>In this example you have A8s in the Big Blind and pick up a nut flush draw (9 outs) on the flop. You decide to bet a little less than the pot, since your opponents will rarely have a strong hand in an unraised pot (no one showed any strength pre-flop), which means your bet should generate a lot of fold equity.<\/p>
Scenario 1:<\/b><\/p>
Hero bets $12<\/font>, Villain (MP) calls $12, Button folds<\/font><\/p>
In this scenario MP calls and the BU folds. MP's call can only mean one of the following:<\/p>
- \n
- He is slowplaying a strong made hand (set, straight) and is not worried about protecting. <\/li>\n
- He has a weak\/mediocre hand (pair, overpair) and wants to wait and see what you do on the turn.<\/li>\n
- He also has a draw. <\/li>\n<\/ul>
Turn:<\/b> ($40) J<\/b>
(2 players)
Hero bets $30 <\/font><\/p>The turn card is not likely to have helped your opponent. An overcard to the board also weakens his weak made hands, assuming he didn't pick up two pair.<\/p>
You decide to semi-bluff again. If he has a weak\/medium made hand or a draw, he will fold very often. If he calls, you still have quite a few outs.<\/p>
If your opponent does call, you should be cautious on the river. If you hit, bet 1\/2 pot - pot; if you miss, your line is simple: check\/fold.<\/p>
Scenario 2:<\/b><\/p>
Hero bets $12<\/font>, Villain (MP) raises to $35<\/font>, Button folds<\/font><\/p>
In this scenario MP raises to $35 and the BU folds. MP's raise can mean several things:<\/p>
- \n
- He hit a strong made hand (two pair or better) and wants to protect.<\/li>\n
- He has a weak\/medium made hand (TP or overpair) and wants to protect.<\/li>\n
- He also has a draw and is semi-bluffing.<\/li>\n<\/ul>
This is not a good spot to push all-in. Your effective stack is $414, and there are only $61 in the pot. Your opponent will only call an overbet with hands that have you clearly beat in terms of equity.<\/p>
Your equity against his range is as follows:<\/p>
- \n
- Against a set: 26%<\/li>\n
- Against a straight: 34%<\/li>\n
- Against two pair: 36%<\/li>\n
- Against an overpair: 45% <\/li>\n
- Against a pair (without A kicker): 52%<\/li>\n<\/ul>
Now assume you will have app. 35% equity on average against your opponent's calling range. We can now determine how high Pfold<\/sub> must be for your total profit to be positive:<\/p>
Condition: Profit > Loss<\/i>
Profit = Pfold<\/sub> * Pot + (Stack + Dead money + Stack - Costs) * Equity * (1 - Pfold<\/sub>)
Loss = Costs * (1-Equity) * (1 - Pfold<\/sub>)
Pfold<\/sub> > [-Equity * (2 * Stack +Dead money) + Costs] \/ [-Equity * (2 * Stack +Dead money) + Costs + Pot ]
with A = -Equity * (2 * Stack +Dead money) + Costs
<\/i><\/p>Pfold > A \/ (A + Pot)<\/i>
<\/b><\/p>With:
<\/b>Pot = $61
Stack = $430
Dead money = $6 (SB + Button's limp)
Equity = 0.35
Costs = $414<\/p>The result is:
Pfold<\/sub> > 0.6451%
<\/i><\/p><\/i>Example with Pfold <\/sub>= 70%<\/b><\/p>
Total profit<\/i><\/b> = $9.43
<\/i><\/p><\/i>A push is +EV when your opponent folds 65% of the time or more. Whether or not you have this much fold equity depends, of course, on your opponent. But even if you are absolutely certain that he will fold to a push, one question remains: Would calling be even more profitable? The fact that you have to overbet the flop to win a relatively small pot suggests that a direct push is not the ideal move in this situation.<\/p>
A mathematical analysis of the EV of calling is, unfortunately, not very easy. This is due to the many variables that come into play, including the difficulty in estimating your implied odds with two open streets, the possibility of seeing a free card, etc. We can, however, start with an analytical look at a very simple situation: You call with the intent of folding on the turn if you do not improve.<\/p>
You are getting 1:2.65 pot odds to call. You can assume that you will usually be able to get another pot size bet out of your opponent on a later street if you hit, since your opponent has shown so much strength. This gives you 1:6.3 implied odds, which is, of course, more than enough to justify calling with a nut flush draw (you need 1:4.22 to call with a 9 outer).<\/p>
Your total profit is therefore:<\/p>
Total profit<\/i> = Profit - Loss
(of the 47 remaining cards, 9 are helpful, 38 are not)
Profit = 9\/47 * $61 + 9\/47 * $84 (estimated implied odds: PSB = $84) = $27.76
Loss = 38\/47 * $23 =18.59
Total profit = $9.17 <\/i><\/p><\/i>Of course, this is all very hypothetical. You can assume that you can generate 70% fold equity with a push. An increase in fold equity results in an increase in profit when pushing.<\/p>
But most of all, this example should give you an idea of how such formulas work. Changing a few small parameters can have a big impact on your equity. In this example, the key parameter was your fold equity. When it comes to calling, the implied odds are decisive.<\/p>
Developing a feeling for the right decision in a given situation is extremely important, since you will not be able to perform any of these calculations during live play.<\/p>
You are in position<\/div>You have a number of advantages when you are in position:<\/p>
- \n
- You have a much better chance at taking down the pot with a semi-bluff.<\/li>\n
- You have better chances at being able to take a free card.<\/li>\n
- Your informational advantage gives you better chances at taking down the pot with a busted draw. <\/li>\n
- You can extract max. value from your opponent when you complete your draw.<\/li>\n<\/ul>
You have every possibility when you are in position. A betting sequence that allows you to push all-in on the flop is rarely the best option, since usually does not allow you to extract max. value. Keep in mind: You lose your positional advantage at the moment you go all-in. At that point you can not make any more decisions; you can no longer count on your post-flop edge and must depend entirely on your hand's performance.<\/p>
You are IP in an unraised pot<\/div>YOU HAVE THE INITIATIVE<\/div>NL 1\/2 Dollar<\/p>
Button ($400)
Villain (SB) ($600)
BB ($160)
Hero ($300)
MP ($480)
CO ($120)<\/p>Pre-flop:<\/b> (5 players) Hero is UTG with J<\/b>
, A<\/b>
Hero raises to $7<\/font>, 2 folds<\/font>, SB calls, BB folds<\/font>.<\/p>Flop:<\/b> 4<\/b>
, 7<\/b>, 2<\/b> ($16, 2 players)
Villain (SB) bets $16<\/font>, Hero raises to $56<\/font>, SB calls $40.<\/p>Turn:<\/b> 9<\/b>
($128, 2 players)
Villain (SB) bets $56<\/font>, Hero calls $56<\/p>River:<\/b> J<\/b>
($240, 2 players)
Villain (SB) bets $180<\/font>, Hero folds<\/font><\/p>A typical situation: You raised with suited broadway cards from early position. Only the SB calls. You pick up a nut flush draw + overcards on the flop and the SB donks with a pot size bet. His bet can mean any of the following:<\/p>
- \n
- He has a monster (set) and wants to get raised. <\/li>\n
- He has nothing and wants to steal the pot. <\/li>\n
- He has a middle pocket pair and wants to find out where he stands with his hand. <\/li>\n
- He has an overpair or TP (perhaps A7) and wants to protect against draws. <\/li>\n
- He also has a draw and is semi-bluffing. <\/li>\n<\/ul>
Scenario 1:<\/b><\/p>
No reads.<\/p>
In this case, a semi-bluff raise is a very good option. Your fold equity will be very high for the following reasons:<\/p>
- \n
- You are the PFA and in early position. Your pre-flop action demonstrated a lot of strength.<\/li>\n
- Your opponent is not likely to have hit the board. There aren't any broadway cards to be seen and no draws are possible, either (another flush draw is unlikely since you have two diamonds yourself). <\/li>\n
- Your opponent will usually fold every hand other than a monster or an overpair. You also have good fold equity even against an overpair (other than QQ-AA). <\/li>\n<\/ul>
Other reasons for semi-bluff raising include the possibility of taking a free card on the turn and the opportunity to build up the pot. You may even be able to stack your opponent upon completing.<\/p>
Your opponent calls your raise in our example hand and a blank card shows up on the turn. Your opponent donks again, but this time his bet is fairly small (less than 1\/2 pot). This can mean any of the following:<\/p>
- \n
- He has a monster and wants to try to induce a raise once again (and is not worried about protecting). <\/li>\n
- He also has a draw and is trying to buy a free card. <\/li>\n
- He has an overpair or TP and is trying to keep the pot small (and is not worried about protecting). <\/li>\n<\/ul>
Reasons for not semi-bluffing again are:<\/p>
- \n
- You would have to invest at least $200 to raise and would practically be all-in. <\/li>\n
- The probability that he has a monster or an overpair is much more likely after he called on the flop, which results in a big decrease in fold equity.<\/li>\n
- You are getting very good odds to call (1:3.3). You can also count on even better implied odds, since, as we just said, the probability that your opponent has a good hand is now very high. <\/li>\n<\/ul>
You call in our example hand. An interesting card shows up on the river. You hit top pair and your opponent bets 2\/3 pot. After reviewing the previous action (opponent calls pre-flop, donks flop, calls flop raise, donks turn, large bet on river) you can be pretty sure that he already had a very strong hand on the flop (possibly a set). The only thing left to do is to fold your hand.<\/p>
Scenario 2: <\/b><\/p>
Your opponent is very passive.<\/p>
Unlike in Scenario 1, semi-bluffing in this spot would be wrong. You signaled strength before the flop and now have a passive opponent betting into you. This is a clear sign of a strong hand.<\/p>
You are getting 1:2 pot odds to call on the flop. Your implied odds, however, are very high, since your opponent has signaled that he has a strong hand. With so little fold equity and such high implied odds, this is an easy decision: call.<\/p>
YOU DO NOT HAVE INITIATIVE<\/div>NL 1\/2 Dollar<\/p>
Button ($150)
Villain (SB) ($350)
BB ($420)
UTG ($200)
MP ($500)
Hero (CO) ($200)<\/p>Pre-flop:<\/b> Hero is CO with J<\/b>
, T<\/b> . SB posts a blind of $1.
2 folds<\/font>, Hero raises to $8<\/font>, Button calls $8, Villain (SB) raises to $20<\/font>, 1 fold, Hero calls $12, Button calls $12.<\/p>Flop: <\/b>($62) 9<\/b>
, 4<\/b>, Q<\/b> (3 players)
Villain (SB) bets $25<\/font>, Hero ...?<\/p>You raise first in with JTs from the CO. You get one cold call and a re-raise, which you call. You pick up an OESD on the flop; your opponent bets a little under 1\/2 pot. This can have the following reasons:<\/p>
- \n
- He missed the flop and is trying to buy the pot. <\/li>\n
- He hit a monster (perhaps top set) and wants to get raised (and is not worried about protection). <\/li>\n
- He has an overpair and is trying to extract value, once again without worrying about protection. <\/li>\n<\/ul>
The last two are the most likely given the pre-flop action, assuming you don't have a read on your opponent (pre-flop squeezer).<\/p>
Your opponent re-raised after a raise and a cold call pre-flop. This usually indicates a strong hand. You should usually refrain from semi-bluffing (without a good read) for the following reasons:<\/p>
- \n
- You can generate little fold equity; your opponent has signaled that he has a strong hand.<\/li>\n
- You are getting good odds to call (1:3.48) and have good implied odds, since your opponent is likely to have a strong hand. <\/li>\n
- You risk getting re-raised on a draw heavy board if you do semi-bluff.<\/li>\n<\/ul>
Scenario 1:<\/b><\/p>
Villain (SB) bets $25<\/font>, Hero raises to $80 <\/font><\/p>
This example should show why you should not raise when the risk of getting re-raised is high. This is often the case when your opponent has signaled that he has a strong hand that he probably won't be giving up.<\/p>
If your opponent has a strong hand, he will rarely slowplay on such a draw heavy board, but rather 3-bet directly. And considering the stacks sizes, this 3-bet is a gateway to an all-in.<\/p>
If your opponent pushes all-in, you will be getting 1:3.22 pot odds to call, which you would have to do based on equity (30%, assuming you will see two more community cards, which requires just 1:2.33 pot odds). Calling is technically +EV, but only because you more or less committed yourself with your raise.<\/p>
Of course, you would prefer to see your opponent just call on such a draw heavy board. This is not very likely, but it would allow you to see the turn and then decide what to do.<\/p>
Scenario 2:<\/b><\/p>
Villain (SB) bets $25<\/font>, Hero calls $25, Button folds<\/font>.<\/p>
Turn:<\/b> 2<\/b>
($112, 2 players)
Villain (SB) bets $80<\/font>, Hero folds<\/font>.<\/p>In this scenario you are getting good pot odds on the flop and call to see the turn. A blank card shows up and your opponent bets app. 2\/3 pot. You have to fold for two reasons:<\/p>
- \n
- Your draw did not complete. Your opponent is signaling a strong hand, which means your fold equity is very low and a semi-bluff is not likely to take down the pot. Your opponent will not be folding an overpair or better, especially since you would be giving him 1:4.6 pot odds to call an all-in. <\/li>\n
- You are only getting 1:2.4 pot odds to call. If you do call, you will only have $76 left in your stack, so even if you hit, you can't win any more than another $76. This gives you just 1:3.35 implied odds; you need 1:4.875. Calling would clearly be a mistake. <\/li>\n<\/ul>
We haven't even talked about discounting yet. With an OESD on a suited board you only have 6 clean outs. You could complete and still lose the hand, which has a negative impact on your implied odds.<\/p>
You are IP in an unraised pot<\/div>NL 1\/2 Dollar<\/p>
Button ($150)
SB ($350)
Villain2 (BB) ($420)
Villain1 (UTG) ($150)
MP ($500)
Hero (CO) ($200)<\/p>Pre-flop:<\/b> Hero is CO with 5<\/b>
, 6<\/b> . SB posts a blind of $1.
Villain1 (UTG) calls $2, 1 fold<\/font>, Hero calls $2, 2 folds<\/font>, Villain2 (BB) checks.<\/p>Flop:<\/b> ($7) J<\/b>
, 4<\/b>, 7<\/b> (3 players)<\/p>You limp in from the CO and pick up a straight flush draw on the flop. You can usually count on 15 clean outs, though it is possible that someone has a better flush draw.<\/p>
Your equity compares as follows:<\/p>
- \n
- Against a set: 42% <\/li>\n
- Against two pair: 50% <\/li>\n
- Against a pair: 55% <\/li>\n
- Against a random hand: 66% <\/li>\n<\/ul>
You have more than 50% equity on average; you usually won't be able to fold this hand on the flop.<\/p>
Scenario 1:<\/b><\/p>
Villain2 (BB) bets $5<\/font>, Villain1 (UTG) raises to $15<\/font>, Hero calls $15<\/p>
In this scenario you are confronted with a bet and a raise. You should call instead of raising for the following reasons:<\/p>
- \n
- Two opponents are showing strength in an unraised pot. Hardly anyone risks their stack for an unraised pot if they don't have a good hand. <\/li>\n
- A direct push would probably only isolate you against better hands (perhaps two pair or a set). You will usually take down a small pot or be the underdog in a big one. <\/li>\n
- Raising leaves the door open for an opponent to re-raise all-in. You would then have to call with so many outs. <\/li>\n
- If you call and Villain2 re-raises, you might get the chance to push. You would obviously prefer to see your opponent(s) fold than call, since you would then get all the money already in the pot, but even if you do get called, 50% of the pot is yours based on equity.<\/li>\n
- You have position, which allows you to extract max. value if you complete your draw. If you miss, you can try to see the next card at a cheap price, or possibly even take a free card.<\/li>\n<\/ul>
Scenario 2:
<\/b><\/p>Villain2 (BB) checks, Villain1 (UTG) checks, Hero bets $6<\/font><\/p>
In this scenario both opponents check. You can semi-bluff for the following reasons:<\/p>
- \n
- No one is likely to have hit in an unraised pot. If this is the case, the pot will be yours. <\/li>\n
- You want to build up the pot, since your equity is probably over 50%. <\/li>\n
- A bigger pot on the turn means you can make a larger value bet when you hit without giving your opponents too poor of pot odds to call.<\/li>\n<\/ul>
In this scenario Villain1 calls and Villain2 fold:<\/p>
Villain2 (BB) checks, Villain1 (UTG) checks, Hero bets $6<\/font>, Villain2 (BB) folds<\/font>, Villain1 (UTG) calls $6.<\/p>
Turn:<\/b> 2<\/b>
($19, 2 players)
Villain1 (BB) checks, Hero bets $15 <\/font><\/p>Villain2 checks again on the turn. You decide to semi-bluff again. We'll start with a look at your equity on the turn:<\/p>
- \n
- Against a set: 30% <\/li>\n
- Against two pair: 32% <\/li>\n
- Against a pair: between 32% and 55% <\/li>\n<\/ul>
Your equity falls to app. 37% when your opponent hits. Your fold equity, however, is fairly high. Your opponent has been playing as if he had a weak hand or a draw. He's checked to you twice, both on the flop and on the turn. Betting also allows you to build up the pot (and to make a larger value bet when you hit on the river).<\/p>
This hand could play out as follows:<\/p>
Turn:<\/b>
- Shifts in equity and semi-bluffs