equity and pot odds on draws

[thegoingoforit]

In limit hold em I always hear about raising on the flop with top pair to cut down on the pot odds of someone on a draw, but from what I understand about equity is that if your odds of winning are more than your fair share then you should raise. If you were four handed you would be giving 25% of the money with a 35% chance of catching the flush. So according to equity you should raise but according to pot odds you shouldn't because it cuts your odds in half. What am I missing?

[SplawnDarts]

This isn't a pot odds question really. If you raise, and 3 people call, your EV goes up. That's good. If you expect 2 callers, you'll break even on the raise itself, but it's still probably a good idea because it will grow the pot and thus make it harder for your opponents to fold if you do make the flush, so it may help you win bets down the road. It also adds some deception to your hand.

If you thought you were going to get zero callers a high percentage of the time, raising on the bluff would make sense. But zero callers is unlikely.

If you thought you would get exactly 1 caller, getting more money into the pot at less than 1:1 and risking a 3-bet is dumb obviously. So you would either call or fold depending on pot and implied odds.

Pot odds area tool for determining if you want to call. It doesn't have much to say about whether you should bet or raise.

[UtzChips]

If someone limps in and I raise with AQs, the SB folds and you call in the BB with 76s, there are 6.5 bets in the Pot, if the other player calls.

If you flop a flush draw and check and the next guy bets, there are now 7.5 bets in the Pot. So, if I fold, you would be getting 7.5:1 on your money to call on a 4.2:1 draw to the Flush. If I call, you're getting 8.5:1.

However, if I raise, you have to call two bets and are only getting 4.75:1; 5.75:1 if the other guy calls.

So, by my raising on the Flop with my TPTK, I've reduced your Pot Odds considerably, which in turn, reduces your return on your investment.

I don't decrease your chances of making the Flush, I just decrease your overall return on your investment (ROI) long-term, and increase my potential ROI when I have the best hand on the Flop.

You don't mind, however, as you are getting Pot Odds greater than your odds of catching a Flush on the Turn. So, even though your ROI is less, it is still a profitable call.

It's still good for me to raise, even though it doesn't make your calling an unprofitable play, because it reduces your ROI (since you would prefer to get 7.5:1 on your money instead of 4.75:1), while increasing my profit those times I win, which will be the majority of the time.

Looking at it in the context of this taking place on the Turn, you're a 4.1:1 Dog to catch your Flush.
Same amount of bets in the Pot, but they're big bets.

19.61% of the time, you'll make your Flush and collect 9.5 big bets in profit (assuming the other player folded to my raise). More if he calls or someone calls you on the River.

80.39% of the time, you'll miss, losing 2 BB's

.8039 * 2 = 1.6078
.1961 * 9.5 = 1.863

Net return: .2552 * 100 = 25.52 BB's long term, when the 3rd guy folded and I didn't call you on the River.

Now if I don't raise the Turn and neither one of us calls you on the River when you make your Flush:

.8039 * 1 = .8039 lost
.1961 * 8.5 = 1.6669 won

Net Profit = .8630 * 100 = 86.30 BB's long term.

[UtzChips]

You have 35% against 3 player, so you're putting in 25% of the money, giving you an overlay. If there were 4 bets in the Pot Preflop, you're putting in 12.5% of the total money in the Pot, but if you raise, you're putting in 2 bets and getting 3 more in the Pot, making the potential profit 10:2 or 5:1.

When you didn't raise, you were getting 7:1 on your money.

HOWEVER: You must look at it this way:

If I call, I'm getting 7:1 on my money with 35% equity.
I have 3 players though, so on top of the 7:1 on my call, I'll raise and get 3:1 on my 2nd bet (the raise) with 35% equity, which is 1.86:1.

Here, you are getting a greater return on your raise, than the odds of making your hand. This is different from my first post, where you had to call 2 bets.

Let's say you don't raise here, and nobody calls you when you make your hand:

.35 * 7 = 2.45 BBs won long term
.65 * 1 = .65 lost.

Net Profit = 1.80 * 100 = 180 BBs.

Now you raise:

.35 * 10 = 3.5 BBs won
.65 * 2 = 1.3 BBs lost.

Net Profit 2.20 * 100 = 220 BBs.

You're overall profit is greater than just calling, because your money odds on the raise when three opponents called the raise, are greater than the odds of you making your hand.

The person with the best hand doesn't mind you raising, as he'll take the Pot the majority of the time, unless the cummulative outs of his opponents makes him a money underdog.
So, if you both knew what you had, and could get the other two to call four bets, you would both love capping it here, as you both profit long term.

[Njursparven]

very good posts utz.

[UtzChips]

Thank you.

[thegoingoforit]

no, thank you

[KipBond]

[ QUOTE ]
.8039 * 2 = 1.6078
.1961 * 9.5 = 1.863

Net return: .2552 * 100 = 25.52 BB's long term,

.8039 * 1 = .8039 lost
.1961 * 8.5 = 1.6669 won

Net Profit = .8630 * 100 = 86.30 BB's long term.

[/ QUOTE ]

[ QUOTE ]
.35 * 7 = 2.45 BBs won long term
.65 * 1 = .65 lost.

Net Profit = 1.80 * 100 = 180 BBs.

Now you raise:

.35 * 10 = 3.5 BBs won
.65 * 2 = 1.3 BBs lost.

Net Profit 2.20 * 100 = 220 BBs.

[/ QUOTE ]

Looks good... but... [img]/images/graemlins/confused.gif[/img] Why are you multiplying by 100?

[UtzChips]

[ QUOTE ]
[ QUOTE ]
.8039 * 2 = 1.6078
.1961 * 9.5 = 1.863

Net return: .2552 * 100 = 25.52 BB's long term,

.8039 * 1 = .8039 lost
.1961 * 8.5 = 1.6669 won

Net Profit = .8630 * 100 = 86.30 BB's long term.

[/ QUOTE ]

[ QUOTE ]
.35 * 7 = 2.45 BBs won long term
.65 * 1 = .65 lost.

Net Profit = 1.80 * 100 = 180 BBs.

Now you raise:

.35 * 10 = 3.5 BBs won
.65 * 2 = 1.3 BBs lost.

Net Profit 2.20 * 100 = 220 BBs.

[/ QUOTE ]

Looks good... but... [img]/images/graemlins/confused.gif[/img] Why are you multiplying by 100?

[/ QUOTE ]

That will be your net profit per 100 hands won, once the randomness of the cards evens out and you have won exactly 35% of the hands. Gives you an idea of your return long-term. The 2.2 BB return is a fraction of what you win each time that you make your hand.

Suppose it takes 380 hands before you have won your 35% share of them, which is 133 hands.

You could just multiply 133* 2.2 BB = $292.60

Or, 133 is 1.33 100's, so
1.33 * 220 BBs = $292.60