Most of the players in seven-card stud have made a habit to call on fourth-street because it is usually a small bet in a spread-limit game and only a half-bet wager in a structured-limit game. This is absolutely wrong.
You should continue playing your hand because it warrants it, not just because it's cheap. Now let's go further for our poker knowledge.
If you have started with trips and haven't improved, you will want to stay till the end. (The improvement with three-of-a-kind would be to make it four-of-a-kind.) You still have the best hand. You are first to act, how would you play? You should bet – maximum in a spread limit game. You want to discourage player who have made four-straights or four-flushes from drawing to those hands. They will stay anyway but make them pay for the draw. Never them a free chance to beat you. Free cards are good to get but not good to live.
If someone has bet in front of you, just call, unless there are two or three players to act after you who look like they have made four-straights or four-flushes
If this is the case, just raise. Try to knock them out and limit the field. While it is true that you do have a good chance of making a full house and winning a big pot if they also make their hands, it is also true that, with several of them drawing to hands, you get a higher chance of being beaten if you don't fill up.
If you are the high board but not showing a face card with your trips here at fourth-street, bet more and more. You don't want to miss any bets here. You won't be tipping the strength of your hand. If there are small trips and you raised at third-street, your rivals will likely have put you on a big pair at third-street and because they see no improvement at fourth-street, will figure that a big pair is still your maximum holding. Remember, most players are going to call at fourth-street unless they have drawn a worse card.
If another player has a pair showing whose rank is higher than your trips, your work is to identify if he has trips, two pair, or has added a pair to his drawing hand. What action did he take at third-street? Did he raise showing a card bigger than your trips? He has trips larger than yours. Do you want to chase him?
Of the three possibilities, two will be bad for you. If neither of you improves, he wins. If you both improve to full house, he wins. If you improve and he doesn't you win. Out of the three possibilities one would be in your favor.
If two or more players have paired their doorcards the ranks of which are higher than your trips, you are beaten in at least one spot. If lot of action takes place, you should better throw away your hand – a tough thing to do, but if you are beat, you are beat. It is a judgment call that you learn from studying the game, getting to know your rivals, and gaining experience.
With the same situation as the one above, if your trips are higher than the ranks your rivals are showing, raise – and don't stop raising until the maximum amount of raises has been reached or until you run out of chips. You have the nest hand and the ability to knock out the straight and flush draws. If you win at fourth-street it is fine. If the other trips stay with you, it is also okay. Either way, you have the best of it.
You should play trips aggressively at fourth-street unless you find a particular reason of playing it
In seven-card stud in fixed-limit games, a player showing a pair at fourth-street has the opportunity of making a single fourth-street bet, or of making the double fifth-street bet. For example in a $5-$10 game, you could bet either $5 or $10 on fourth-street with an open pair. Many players will do one or the other, the same way each time. Good poker players tend toward making the double bet. Don't you tend toward anything – think first and then act.
If you pair your doorcard and now have four-of-a-kind, whether you check, bet, or make it the double-bet depends on various factors: the value of your cards, (how big or small they are), how many players you are against; who those players are (good, bad, aggressive, solid, tight, loose) and on what action will look obvious.
If you were the low card on third-street showing a three in an un-raised pot, and have caught another three here on fourth-street, it would be obvious to check. Your rivals will assume that you hold only the two threes you are showing which, if that's all you have, you wouldn't bet. Your slow-play looks more obvious.
Many players especially the good player who know what a long shot four-of-a-kind is, will be much more likely to put on trips than on quads. If you check into large field you will probably get a bet from someone. Even if you don't, you have given all these players a chance to catch up and make something so that you can make some money.
If you have raised at third-street with your small trips, or just called a raise, and have now caught another card of your rank at fourth-street your rivals will put you on big pair or on small trips. Whether you bet the single or double bet still depends on the factors stated above.
For example, you started with big trips, three kings and have caught the fourth king here at fourth-street. Now your board shows a pair of kings. Is it a single bet or double bet?
In this case, what seems obvious can cost you money
The obvious move would be the double bet, announcing that you are trying to win now. But you are not. You want players. To bet any amount would knock out those players. But to check would appear that you are trying to trap them – this is what you are doing. But that's your only alternative. Give them a free card and expect someone catches up enough to give you a play.
For example, you did start with a pair of fours and now catch a third three four at fourth-street. Play the same as if you had started with trip fours and haven't improved on the fourth-street. Against more number of players, bet or raise the maximum and try to eliminate the players. You want to knock out any rival who is considering staying with a medium pair. You won't be able to get a large pair out, but get out those you can chase out with aggressive betting.
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