Did some math

[jackvance]

Ok, so two things I read on these forums were kinda guidelines I used in my game. Not sure where I read em orwho said it, but they are: "I don't see any reason why you would ever bet more than the pot" and "you should bet somewhere inbetween 1/2x and 1x the pot (to weed out the draws)".

Ok.. this wasn't really working out for me, and if I look at winning players, they don't seem to use the pot as an upper limit for their betting at all.

So I did some calculations.
- If I bet half the pot, my opp needs to invest 1/4 of the pot to call it.
- If I bet the pot, my opp needs to invest 1/3 of the pot to call it.
- If I bet twice the pot, my opp needs to invest 2/5 of the pot to call it.

A few conclusions, if the math is correct, which I think it is:

1. So.. if I bet half the pot, anything that has more than a 25% to drop and kill my hand is profitable.
2. If your stack is smaller than the pot and you have a flush draw.. push all your chips in the middle asap. You'll have the better odds. (chance for flush on turn+river is 1/3)
3. If I want to chase off draw chasers, 2xpot bets should be in my repertoire. Also for bluffs. Because if I don't.. it might very well be in my opp's best interest to chase that flush.
4. Something similar for double-edged straight draws. The odds are a bit less than for a flush, but they're less detectable.
5. This one is weird.. but.. since your opp can never make you bet more than 50% of the pot, anything with >50% to win should be chased. This is pretty self-evident ofcourse, 33 vs AK has like 52% to win so ofcourse we'll rather go with 33 than AK in this match-up. Now then, a double edged straight flush draw.. 15 outs, or 56% to 'connect' on turn+river. So in theory.. you should ALWAYS pursue this one. Push all the chips if you have to, or just check, or call anything your opp throws at you. It's all good, since the odds are on your side here!

Now, these conclusions seem kinda weird.. really weird in fact.. so, eh, anyone can spot mistakes?

[jackvance]

Ok, mulled over it a bit more, and came to these conclusions:

These calculations are probably correct at any given time you are in this situation, but that doesn't imply it's a good thing to go for this as a strategy. To clarify:

Pot is $10. Opp goes AI for $10 with a hand that beats you but gets beaten by a flush. You have a flush draw and call it. So on average you make: (.37 x 30) - (.63 x 10)= +4.8 *
Even if your opponent bets twice the pot for $20 and you call, you are still up. (.37 x 40) - (.63 x 20)= +2.2
If your opp is more reserved and bets half the pot: (.37 x 20) - (.63 x 5)= +4.25

Flush draws seem profitable all of a sudden? The problem is twofold:

1. If you're holding something suited, your odds of getting a draw are 1 in 10. So 9 times out of 10 you waste money. This has to be calculated in.

2. A part of the $10 pot will be yours. If you want to talk strategy instead of 'what is best in this situation', you have to calculate this in too. In the worst case scenario, no dead money so you're actually in 50% for 37% odds.

So: It's really just as we all know.. only go for draws if enough people are in, and if you can look at the flop cheap.

But if at any time for whatever reason you find yourself chasing a draw.. don't be discouraged by even a pot-sized bet! You have the better odds there.

Another thing, specifically looking at the suited connector:
3 out of 4: you hit nothing (money lost)
1 out of 20: you hit something big: two pair, sets, flush, straight,..
1 out of 10: flush draw
1 out of 10: straight draw

* the odds are from two suited lower cards vs KK with flush draw on the flop.

[Fnord]

The answer is 2/3 to 3/4ish pot, unless the money is deep and/or there was no raise pre-flop.

The question is "How do I play a big pot when I want to?"

That being said, the full pot guys have some pretty strong merits.

[jackvance]

You speak in riddles..

[Fnord]

You speak in riddles..

Ten pounds of flax!

[jackvance]

But what is the difference between ten pounds of flax?

[chardrian]

Part of your problem is that you are forgetting that most of the time people aren't just going all-in on the flop.

So you really aren't getting 1/3 on the flop bets to call. Instead you are getting 1/6 to hit by the turn and then another 1/6 to hit the river if you don't hit the turn. But by the turn you are often going to have to pony up some more.

[Fnord]

I think a lot of newcommers (particularly the tighter ones) try to go to war against strong draws after getting donked-out on for some big pots.

Strong draws are strong strong draws, a pretty good hand when we often have to bet lots of money not really quite sure where we're at. When I'm drawing to the nuts, I know exactly where I'm at and can put the other guy to the test.

[benny999]

also, once in a while you find someone that always thinks you're bluffing and will call massive bets when the flush hits (this is implied odds). Also, if he has two pair or trips, you have to get rid of 1-2 of your flush outs (reverse implied odds). So yea, what you said about getting lots of ppl in the hand, knowing your odds of the turn AND turn/river, and in general having reads is very important.

[jackvance]

@chardrian
I know this.. that's why I circumvented this problem by going for all-ins.

If you want to be realistic, there are two uncertainties to add into the equation:
- if it doesn't hit on the river, you will face a raise. This adds to the cost.
- if it hits on either turn or river, the so-called implied odds will boost the pot in your favor. This adds to the benefits.

So one things adds to the cost, one things adds to the benefits. So if you auto-pay on the turn, 2/3 the turn raise bites you, 1/3 the turn+river raises add to your stack. So for easy calculating, I assumed both would cancel each-other out.


Side-note: just finished an MTT. The only times I won some money were 2/3 of my draws hitting home. (one straight, one flush) Then I took the pot once with AA and all folds, and got destacked with QQ vs AA. Place 200 of 700 people. Pretty horrible luck on getting dealt the 'power' cards. The only thing that kept me in there was playing those lower-odds-high-potential-payoff draws. That was pretty nice lol Knowing my odds really kept me calm and on the ball there.

[biondino]

One mistake above - if you bet twice the pot your opponent needs to invest 2/3 of the pot, not 2/5.

i.e. pot is $5, you bet $10, oppo is now having to bet $10 into a $15 pot.

[biondino]

One other thing here - you are ignoring the possibility that YOU will improve your hand. Clearly there is a difference between having AK on an A27 flop (5 outs to trips/two pair) and AK clubs on a AQJ 2-club flop (4 outs to straight and 9 outs to flush on top of trips/TP draw).

[jackvance]

One mistake above - if you bet twice the pot your opponent needs to invest 2/3 of the pot, not 2/5.

i.e. pot is $5, you bet $10, oppo is now having to bet $10 into a $15 pot.

Nope, he has to invest $10 into what will be a $25 pot, so 2/5.

One other thing here - you are ignoring the possibility that YOU will improve your hand. Clearly there is a difference between having AK on an A27 flop (5 outs to trips/two pair) and AK clubs on a AQJ 2-club flop (4 outs to straight and 9 outs to flush on top of trips/TP draw).

I let the odds that you or your opponent improve their hands cancel each-other out, for two reasons:
1- they should be roughly equal
2- we are using estimates anyway, with a variance of 1-2%, so decimal odds don't matter too much here.

[spot]

Jack- thats where your math error is coming into play. 5 dollar pot- I bet 10 dollars. That means that you have to bet 10 dollars to win 15 dollars. You can't count the 10 you put in as part of your winnings becuase you are giving that money up voluntarily.

[jackvance]

Jack- thats where your math error is coming into play. 5 dollar pot- I bet 10 dollars. That means that you have to bet 10 dollars to win 15 dollars. You can't count the 10 you put in as part of your winnings becuase you are giving that money up voluntarily.

This seems to be quite a common misunderstanding.

Quote from the strategy guide:
"The pot is current at $8.00, and Player1 bets $2.00. (...) I have to call a $2.00 bet to win what will be a $12.00 pot. Since my bet is only about 17% of the pot (...) Now let's say Player1 bets $12 instead of $2. I would have to call $12 to win what will be a $32 pot. My bet is 37.5% of the pot"

See? It should be more easily understable if I put it this way:

In the above example, betting 12$ for a $8+$12 pot is 60%. This would mean I need better than 60% odds to win to make this profitable according to pot odds theory. Now, obviously anything above 50% is bogus.. if my chances of winning are >50% then EVERY bet, no matter how big, is in my advantage!

So using the correct math of calculating your bet towards the pot which would include your bet (so $12 for a $8+$12 pot is 12/32 or 37.5%, not 12/20 or 60%!) then you can never get more than 50% here. This should be intuitively obvious. Having more than 50% to win is always favorable, so calculating a pot-addage over 50% is a clear indication of an error.

Example: Pot is 10$. opp goes all-in for $1000. If we don't include our own input in the calculation, we'd arrive at 99%. This would mean we'd even have to fold AA vs 27 unsuited! Because here we "only" have 88.8% chance to win, which is less than 99% we calculated.
(to be complete: the correct odds here are 1000/2010=49.75%)

Ofcourse this is preflop. If this doesn't convince you, postflop:
Example 2:
My hand: AA
Opp hand: 26 hearts
Flop: As Ts 9h

pot is $10. Opp raises $1000. I have a 95.6% to win.. my opp can only win if he hits his flush on turn+river, which would happen 4.4% of the time. But if we go 99% of pot-addage, I'd have to fold this, since I have "bad pot odds" as 95.6%<99%. This should be obviously bogus

Hope this clears things up.

[jackvance]

Btw, for the comprehensive math on suited connectors, scroll to the bottom of this post:
http://www.flopturnriver.com/phpBB2/...ic.php?t=31392

[midas06]

No, you don't count what you put into the pot as part of your pot odds calculation.

$5 into $10 is 50%, not 33% (5/15)

[chardrian]

No, you don't count what you put into the pot as part of your pot odds calculation.

$5 into $10 is 50%, not 33% (5/15)

Whoops - you are wrong midas.

$5 into $10 = $15 total pot. Pot odds ARE figured by dividing what your bet is into the total pot after your call.

5/15 = 1 in 3. If you have a 1 in 3 shot to win then you are exactly even money in the long run by calling.

1 time you call and win $10 in the pot= +10
1 time you call and lose $5 you just bet= -5
1 time you call and lose $5 you just bet = -5
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Total 1/3 shot = $0