Question on SSHE, Equity, How # of players affect decisions

J. Stew · #1 10-08-2005, 04:50 PM

Straight out of Hand Quizzes -- Flop Play SSHE

"You have 7[img]/images/graemlins/club.gif[/img]6[img]/images/graemlins/club.gif[/img] in the big blind. The player under the gun raises, and three players cold-call. You call (10.5 small bets). The flop is K[img]/images/graemlins/club.gif[/img]8[img]/images/graemlins/heart.gif[/img]4[img]/images/graemlins/club.gif[/img], giving you a gutshot and a flush draw. What should you do?

Answer: Check with the intention of raising a bet from early position." pg. 274-275 SSHE

Hypothesis: The number of players in the pot determines whether you should check-raise or check-call.

So you check with the intention of raising and believe you need to hit one of your 13 outs (four 5's and nine [img]/images/graemlins/club.gif[/img]'s) to win. The pf raiser bets, but all three cold-callers fold and it is back to you (11.5 small bets). You'll hit an out on the turn 28% (13/46) of the time but you have a chance to hit the river as well so you have a 29% chance (13/45) to hit the river if you don't hit the turn.

Question #1: How do these two percentages (28%, on the flop for the turn and 29%, on the turn for the river) combine to give you an estimate of how often your draw comes in when you are on the flop? I think this might be simple but I'm kinda stoopid. [img]/images/graemlins/tongue.gif[/img]

Question #2: Say this percentage, that your draw will come in by the river, is 42%. Is this number your equity in the hand?

Back to the hand . . .
There are 11.5 small bets in the pot and the action is back to you, head up with pf raiser who bet the flop. If your equity is 42%, his must be around 58% barring the chance of a split pot.

Question #3: Assuming there is no chance the pf raiser is going to fold to a raise calling is the best option because you are getting 11.5-1 and you will make your draw 42% of the time or about one in 2.4 times or 2.4-1. You should call because your equity (42%) is less than his (58%)???

Now, say one of the pf cold-callers called the pf raiser's flop bet and the action is back to you (12.5 small bets) and you believe he has a pair of tens or a hand that you can beat if your draw comes in.

Question #4: Assuming your equity is above 1/3 or 33%, you should raise when the action is back to you because you have an edge in equity here, while when you were heads up with the pf raiser you did not???

Conclusion: In this hand, the addition of one player changed our flop action from a check-call to a check-raise.

Thanks for any input or swear words you guys can give.

jrz1972 · #2 10-08-2005, 04:57 PM

When you flop a flush draw, you have something like 35% pot equity. The number of players in the hand doesn't change your equity much. Basically, if you hit your flush you are going to win. If you miss your flush, you won't.

That's why the standard line is to pump your flush draws on the flop vs. two or more opponents. You win more than 1/3 of the time, so your flop bets and raises are for value.

ubercuber · #3 10-08-2005, 05:23 PM

You're numbers are off a bit, counted 5c twice, and should be 12/47, 12/46. I believe the way to calculate pot equity is to muliply your outs by 4 on the flop and by 2 on the turn. So here, assuming 12 outs(small flush, not sure if you should discount that some or not) 48% for you, 52% for your opponents. The rest of your questions I think can be answered by this: compare your pot equity to the number of people in the hand. 4 players, before dealt cards, have a 25% equity in the pot each. You are now at 48% and if you still have 3 opponents you are getting more than youre share. You want to be putting in 25% of the bets and take the pot 48% of the time and you will make money. So raise it up. If you are down to heads up, you are getting less than your share...50% to your 48% so you are calling if the pot odds are there, but taking free cards if they are there. There are probably some nuances to this that I don't understand. or forthat matter I be a moron and have the whole thing wrong, hopefully not.

J. Stew · #4 10-08-2005, 05:31 PM

I accidentally posted up in small stakes first, here's what Jason T said for anyone that is interested:

[ QUOTE ]
Question #1: How do these two percentages (28%, on the flop for the turn and 29%, on the turn for the river) combine to give you an estimate of how often your draw comes in when you are on the flop? I think this might be simple but I'm kinda stoopid. [img]/images/graemlins/tongue.gif[/img]

[/ QUOTE ]

Mathematically, the solution is

(13/46) + (33/46) * (13/45) = 48%.

The draw other hits on the turn (with probability 13/46) or it doesn't (with probability 33/46). If it doesn't hit on the turn, there is a 13/45 chance that it hits on the river. There are no other possibilities.

You can obtain a rough estimate via the calculation (number of outs) * 4. In this case we'd obtain that our draw will hit rougly 13 * 4 = 52% of the time.

[ QUOTE ]

Question #2: Say this percentage, that your draw will come in by the river, is 42%. Is this number your equity in the hand?

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It's a rough estimate of your equity in the hand. Your equity could be lower if a higher flush draw is out or if someone has a set.

[ QUOTE ]
Back to the hand . . .
There are 11.5 small bets in the pot and the action is back to you, head up with pf raiser who bet the flop. If your equity is 42%, his must be around 58% barring the chance of a split pot.

Question #3: Assuming there is no chance the pf raiser is going to fold to a raise calling is the best option because you are getting 11.5-1 and you will make your draw 42% of the time or about one in 2.4 times or 2.4-1. You should call because your equity (42%) is less than his (58%)???

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Yes. If you ignore the size of the pot, you are losing money postflop with each bet you put in.

[ QUOTE ]
Now, say one of the pf cold-callers called the pf raiser's flop bet and the action is back to you (12.5 small bets) and you believe he has a pair of tens or a hand that you can beat if your draw comes in.

Question #4: Assuming your equity is above 1/3 or 33%, you should raise when the action is back to you because you have an edge in equity here, while when you were heads up with the pf raiser you did not???

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Correct. However you should take into consideration things such as how likely the pf raiser is to 3-bet and the caller to fold to that 3-bet.

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