gmanko
03-04-2005, 09:22 PM
This is a follow-up to my original post:
http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1776899&page=0&view=c ollapsed&sb=5&o=&fpart=1
*** PLEASE NOTE THAT SOME OF THE CALCULATIONS IN THE ORIGINAL POST ARE INCORRECT ***
*** WHICH AFFECTS SOME OF THE RECOMMENDATIONS IN THE EXAMPLES ***
*** PLEASE READ ALL OF MY POSTS IN THIS THREAD ***
which did not cover what adjustments needed to be made if there was a possible straight or flush draw (or possible made straight or flush) aganist you.
Also, these posts cover top pair with a weak kicker, middle pair with a good kicker, and middle pair with a poor kicker. Since overcards are treated thoroughly in SSHE I will not go over them here.
Now what about those draws?
Excluding the cards which you hold in your hand, when two cards of a suit appear on the flop, there is approximately a 5% chance per opponent that they will have a flush draw (11/47 x 10/46). If you hold one of that suit the odds are closer to 4%, and if you have two of that suit you no longer have a marginal hand, but we will use 5% for these examples.
When three cards of a suit flop, there is only a 4% chance that someone has a made flush, but if you do not have a high card of that suit, you know what to do.
Straights draws are a little trickier, and I am only going to consider 2-way straight draws using both hole cards for the purposes of this analysis. The chances of having a certain 2-card combination of ranks is approximately .75% (4/47 * 4/46). However, there is more than one way that 2 cards can mesh with the flop to make a straight draw:
Assuming the flop is T92 - QJ, J8, and 87 form a 2-way straight draw
Assuming the flop is T82 - J9 and 97 form a 2-way straight draw
Assuming the flop is T72 - 98 forms a 2-way straight draw
Assuming the flop is 58J - 97 forms a 2-way straight draw (double-gutted)
I hope I am not double-counting, but in the first example it looks like there is a 2.25% chance (3 x .75%) that each opponent has a straight draw. Going out on a limb, (please correct me if I am wrong), there are 7 possible ways to make a 2-way straight draw, and 4 possible types of flops, so I am going to make a wild guess and say that there is a 1.3% chance on average per opponent that they have a straight draw when one is possible.
Note that on extremely raggedy flops such as 742 you may want to discount the chances that someone is on a straight draw, but in very loose games or vs. the blinds no combination can be completely excluded.
When a made straight is possible the odds for each combination are still the same (4/47 * 4/46). And I think that the chances that someone will have a made straight the same as well, but it is Friday night and my math brain cells are resting up for the tables tomorrow.
So what does this mean?
Well, in order to be 50% certain on average that someone is even on a draw, there must be 10 opponents for a flush (50%/5%), and 22 for a straight (50%/2.25%) if the flop contains two connecting cards. Even if my math on straight draws is completely messed up and there is a 10% chance per opponent that they are on a straight draw, none of the guidelines for playing these types of marginal hands can stand more than 4 opponents.
The end result is that the chances that any opponent is even on a draw is rather low. In fact, this is true even when many players see the flop. The good news is that you should not constantly be afraid of draws when you play. By the river the nuts is usually at least a straight, but it is rare that someone actually has a straight. Even if a draw appears to come in, there is only a 4% chance that someone actually has made the flush, or a 2.25% chance for a straight (again, if I did my math right, and even if not it is not very likely). I there is 3 flush and a possible straight on the flop, or a four straight or flush later on, don't be too aggressive though.
Even though a possible draw increases the likelihood that a bet or raise is coming from a player that you currently have beat, I would NOT increase any of the recommendations for maximum number of opponents. For example, if there is no draw and you have top pair with a weak kicker against four opponents, I would recommend folding. If there is a possible draw I would not play vs. five opponents, you could still get raised by someone behind you who does have you beat (even if you have four opponents you should fold if bet into, the chances are still better that you are beat than the player is on a draw).
Also, when you DO have a > 50% chance of having the best hand with a possible draw on board, you should almost always bet or raise (consult the original thread for how to determine this based on your holding and the number of opponents). You cannot afford to give anyone a free card. If you have the bettor beat you may knock out a draw. If the bettor is on a draw you may knock out a slightly better hand (in a three-way pot, if you have middle pair with a strong kicker and two opponents, your raise may fold top pair with a weak kicker behind you). Of course, if you are reraised it may be time to pack it in and save some bets.
Conclusions:
With or without a draw, the primary factor in determining whether a marginal hand is playable is the number of opponents. In fact, personally I would play these types of hands (top pair with a weak kicker, middle pair with a strong kicker, and middle pair with a poor kicker) as aggressively as strong ones (if I have a > 50% chance of having the best hand, and there is not too much pushback or action in front of me).
In multiway pots I feel that it is probably best to release these hands quickly on the flop, if other players show aggression because of the negative implied odds if you have to call multiple bets on later streets. Even if you are still ahead and your opponent is indeed on a draw, I feel that it is better save these battles for when you have a stronger hand. Heads up you may need to slow down, but folding is probably a mistake (especially with top pair), see the section on heads-up play in the original post.
If you have been betting and a draw appears to have come in, continue betting unless one of your opponents will often bluffraise in this situation, as the probabilities show the chances of someone actually having that particular draw are slim.
Notes:
As always, if during the course of betting, if you had intended to fold but are getting proper odds to draw to two pair or a backdoor draw when the action gets to you, by all means do so.
I have just started to apply these strategies, and although they seem to work for me so far (at least better than betting middle pair into 5 opponents was, which is why I started investigating this topic), they need to be proven over the long run.
Playing in the manner described will result in raising or folding the great majority of the time, which is tight and aggressive. The good thing is that it will be hard for opponents to read your hand (they will not be able to put you on top or middle pair based on if you raise vs. just call, since you would either raise or not play). The bad part is that when you just call you will most likely be on some type of draw, whcih they may pick up on.
On the other hand, even if opponents know you are on a draw, they will not now what type of draw you are on - just overcards, drawing to two pair, straight, or flush. When a 4 hits on a Q82 flop, they will never guess that you called with Q4s in the small blind when you had 12-1 on the flop.
Also, you will also often just flat-call when you are slowplaying or want to raise on a later street, which should slow some of your opponents down. So in general, here is what this style would look like:
- Raise (strong hands, strong draws, and marginal hands when played)
- Bet (strong hands, strong draws and marginal hands when played)
- Call (monsters [rare], strong hands that you want to raise on the turn, weak to medium draws)
Check (trash, marginal hands that do not justify betting, check-raising hands)
- Fold (trash and nonplayable marginal hands)
http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1776899&page=0&view=c ollapsed&sb=5&o=&fpart=1
*** PLEASE NOTE THAT SOME OF THE CALCULATIONS IN THE ORIGINAL POST ARE INCORRECT ***
*** WHICH AFFECTS SOME OF THE RECOMMENDATIONS IN THE EXAMPLES ***
*** PLEASE READ ALL OF MY POSTS IN THIS THREAD ***
which did not cover what adjustments needed to be made if there was a possible straight or flush draw (or possible made straight or flush) aganist you.
Also, these posts cover top pair with a weak kicker, middle pair with a good kicker, and middle pair with a poor kicker. Since overcards are treated thoroughly in SSHE I will not go over them here.
Now what about those draws?
Excluding the cards which you hold in your hand, when two cards of a suit appear on the flop, there is approximately a 5% chance per opponent that they will have a flush draw (11/47 x 10/46). If you hold one of that suit the odds are closer to 4%, and if you have two of that suit you no longer have a marginal hand, but we will use 5% for these examples.
When three cards of a suit flop, there is only a 4% chance that someone has a made flush, but if you do not have a high card of that suit, you know what to do.
Straights draws are a little trickier, and I am only going to consider 2-way straight draws using both hole cards for the purposes of this analysis. The chances of having a certain 2-card combination of ranks is approximately .75% (4/47 * 4/46). However, there is more than one way that 2 cards can mesh with the flop to make a straight draw:
Assuming the flop is T92 - QJ, J8, and 87 form a 2-way straight draw
Assuming the flop is T82 - J9 and 97 form a 2-way straight draw
Assuming the flop is T72 - 98 forms a 2-way straight draw
Assuming the flop is 58J - 97 forms a 2-way straight draw (double-gutted)
I hope I am not double-counting, but in the first example it looks like there is a 2.25% chance (3 x .75%) that each opponent has a straight draw. Going out on a limb, (please correct me if I am wrong), there are 7 possible ways to make a 2-way straight draw, and 4 possible types of flops, so I am going to make a wild guess and say that there is a 1.3% chance on average per opponent that they have a straight draw when one is possible.
Note that on extremely raggedy flops such as 742 you may want to discount the chances that someone is on a straight draw, but in very loose games or vs. the blinds no combination can be completely excluded.
When a made straight is possible the odds for each combination are still the same (4/47 * 4/46). And I think that the chances that someone will have a made straight the same as well, but it is Friday night and my math brain cells are resting up for the tables tomorrow.
So what does this mean?
Well, in order to be 50% certain on average that someone is even on a draw, there must be 10 opponents for a flush (50%/5%), and 22 for a straight (50%/2.25%) if the flop contains two connecting cards. Even if my math on straight draws is completely messed up and there is a 10% chance per opponent that they are on a straight draw, none of the guidelines for playing these types of marginal hands can stand more than 4 opponents.
The end result is that the chances that any opponent is even on a draw is rather low. In fact, this is true even when many players see the flop. The good news is that you should not constantly be afraid of draws when you play. By the river the nuts is usually at least a straight, but it is rare that someone actually has a straight. Even if a draw appears to come in, there is only a 4% chance that someone actually has made the flush, or a 2.25% chance for a straight (again, if I did my math right, and even if not it is not very likely). I there is 3 flush and a possible straight on the flop, or a four straight or flush later on, don't be too aggressive though.
Even though a possible draw increases the likelihood that a bet or raise is coming from a player that you currently have beat, I would NOT increase any of the recommendations for maximum number of opponents. For example, if there is no draw and you have top pair with a weak kicker against four opponents, I would recommend folding. If there is a possible draw I would not play vs. five opponents, you could still get raised by someone behind you who does have you beat (even if you have four opponents you should fold if bet into, the chances are still better that you are beat than the player is on a draw).
Also, when you DO have a > 50% chance of having the best hand with a possible draw on board, you should almost always bet or raise (consult the original thread for how to determine this based on your holding and the number of opponents). You cannot afford to give anyone a free card. If you have the bettor beat you may knock out a draw. If the bettor is on a draw you may knock out a slightly better hand (in a three-way pot, if you have middle pair with a strong kicker and two opponents, your raise may fold top pair with a weak kicker behind you). Of course, if you are reraised it may be time to pack it in and save some bets.
Conclusions:
With or without a draw, the primary factor in determining whether a marginal hand is playable is the number of opponents. In fact, personally I would play these types of hands (top pair with a weak kicker, middle pair with a strong kicker, and middle pair with a poor kicker) as aggressively as strong ones (if I have a > 50% chance of having the best hand, and there is not too much pushback or action in front of me).
In multiway pots I feel that it is probably best to release these hands quickly on the flop, if other players show aggression because of the negative implied odds if you have to call multiple bets on later streets. Even if you are still ahead and your opponent is indeed on a draw, I feel that it is better save these battles for when you have a stronger hand. Heads up you may need to slow down, but folding is probably a mistake (especially with top pair), see the section on heads-up play in the original post.
If you have been betting and a draw appears to have come in, continue betting unless one of your opponents will often bluffraise in this situation, as the probabilities show the chances of someone actually having that particular draw are slim.
Notes:
As always, if during the course of betting, if you had intended to fold but are getting proper odds to draw to two pair or a backdoor draw when the action gets to you, by all means do so.
I have just started to apply these strategies, and although they seem to work for me so far (at least better than betting middle pair into 5 opponents was, which is why I started investigating this topic), they need to be proven over the long run.
Playing in the manner described will result in raising or folding the great majority of the time, which is tight and aggressive. The good thing is that it will be hard for opponents to read your hand (they will not be able to put you on top or middle pair based on if you raise vs. just call, since you would either raise or not play). The bad part is that when you just call you will most likely be on some type of draw, whcih they may pick up on.
On the other hand, even if opponents know you are on a draw, they will not now what type of draw you are on - just overcards, drawing to two pair, straight, or flush. When a 4 hits on a Q82 flop, they will never guess that you called with Q4s in the small blind when you had 12-1 on the flop.
Also, you will also often just flat-call when you are slowplaying or want to raise on a later street, which should slow some of your opponents down. So in general, here is what this style would look like:
- Raise (strong hands, strong draws, and marginal hands when played)
- Bet (strong hands, strong draws and marginal hands when played)
- Call (monsters [rare], strong hands that you want to raise on the turn, weak to medium draws)
Check (trash, marginal hands that do not justify betting, check-raising hands)
- Fold (trash and nonplayable marginal hands)