Getting it all in with a draw on the flop (theory post)

[wtfsvi]

I'll go through the math more thorougly than needed in this thread, just because it's good for me to do some thorough poker math.

This post will deal with a statement I see around here that makes no sense to me: "We have to get it all in on the flop while we have correct odds, or else he can prize us out on the turn."

When we get it all in on the flop, we buy both the turn and the river card for one prize. When this prize gives us correct odds, that's fine. But it will always be better to buy the turn card for even more correct odds, and then get prized out before we see the river, than to get it all in on the flop. That should be obvious without doing lots of math imo, but here's an example anyway:

Decent LAG opens in the CO for 3bb. I (100BB) hold 7 [img]/images/graemlins/heart.gif[/img]8 [img]/images/graemlins/heart.gif[/img] on the button and raise it up to 10bb. Loose-passive villain (100BB) min-reraises in SB. BB and CO folds, I call.

Flop (43BB) comes 4 [img]/images/graemlins/club.gif[/img]5 [img]/images/graemlins/heart.gif[/img]J [img]/images/graemlins/heart.gif[/img]. Villain leads into me for 20BB. Now, tell me pushing isn't totally retarded? It seems to me it is.

EV of pushing:
This guy, as most LPs, can be put on an overpair with near 100% accuracy after this manuever, so I think it's safe to operate with no folding equity. According to twodimes, we have 45,3% equity against an overpair with half a heart.

EV push = (0.453 * 203BB)-80BB = 12BB

EV of calling:
Lets assume he will push any turn. That is the worst case scenario(, except if he check folds when I hit of course, but that isn't going to happen given his above mentioned characteristics).

I have 12 outs against an overpair. 9/12 = 3/4 of my outs are hearts. He'll have a heart 50% of the time, and that means 4.5 of the hearts will give him a flush redraw and 0.5 of them will give him a full house redraw. That means I'll own 83.4% of the pot 5/9 of the time and 100% of the pot 4/9 of the time when a heart hits. In conclusion, when my heart hits I have (5/9 * 0.834) + 4/9 = 90.8% pot equity. This is desregarding that the 4 [img]/images/graemlins/heart.gif[/img] gives him two outs to the boat, so lets say 90% for simplicity. Furthermore, when a non-heart 6 hits I have 100% equity, so that doesn't require much attention.

Now lets look at what happens when I don't hit my outs. Three different scenarios are possible: My hand improves without hitting an out (a seven, an eight, a nine or a ten), a brick falls, or he hits his set and I lose 1.25 outs (I lose the 4 [img]/images/graemlins/heart.gif[/img], and I lose the quad-making card the 1/4 times it's a heart). The latter will have fairly little impact, and I've conviently set up the math so I won't have to calculate it.

A seven or eight gives me 5 extra outs. A nine or ten gives me 3 extra outs. With a brick I still have my old 12 outs. The turn push is for 60BB to play a 203BB pot, so I need 30% equity to call. When the turn is a brick I have 9/46 + 3/44 = 26,4% equity, so I fold. (And when the turn is an A-Q it is a tiny bit worse since there's a chance he hit a set, so I obviously fold then as well.) When the turn is a seven or eight I have 26,4% + 5/44 = 37,7%. Great, I call. When the turn is a nine or ten I have 26,4% + 3/44 = 33,2%. I call.

The turn will be a heart 9/47 times, a six 3/45 times, a seven or eight 6/45 times and a nine or ten 6/45 times. The rest of the time it will be a brick or an overcard, both which I fold to.

EV call = (1-9/47-15/45)*(-20BB) + 9/47((0.9*203BB)-80BB) + 3/45(203BB-80BB) + 6/45((0.332*203BB)-80BB) + 6/45((0.377*103BB)-80BB) = 14BB

This doesn't seem like a huge difference, but remember I'm using the worst case scenario as to his play. He will probably be scared of not get payed off on his aces and bet 30BB or something like that on the turn. It will at least happen some of the time, enough to make quite the difference.

Now if you add in some folding equity (in this scenario the only folding equity we have is misclick equity [img]/images/graemlins/smile.gif[/img]), it's a completely different story. But in conclusion: Villain leaving himself with enough behind to prize you out on the turn is a good thing for you, and when you're the one with the made hand, you should not worry about having enough left to prize his draw out on a later street.

[mason55]

I think your post is talking about a different type of game than some of the other "push big draws on the flop" posts.

The idea of pushing the big draw is exactly to push out those over pairs and so that if you get called and hit you still make money (we assume villain won't pay off if you call flop then come to life when the obvious flush completes). By taking away both of those points you change the situation severely.

However, on that note, I think what you're saying is more applicable to many of the posters in here who play in low limit, no-foldem no-limit holdem.

[wtfsvi]

Yes of course. Folding equity will change this up.

What I'm talking about though, is the statement "We want to get our money in on the flop while it's +EV so we can't be prized out on the turn." I'm just trying to show that that doesn't make any sense.

[stu-unger]

[ QUOTE ]
Yes of course. Folding equity will change this up.

What I'm talking about though, is the statement "We want to get our money in on the flop while it's +EV so we can't be prized out on the turn." I'm just trying to show that that doesn't make any sense.

[/ QUOTE ]

i agree that this statement is thrown around too much lately. obviously u r not going to call a 3 bet OOP pre-flop but i think another variable that really changes this situation is position. i would be much more inclined to 3-bet this flop all in OOP. but being priced in in position there is no way im trying to get in knowing that im behind.

[mason55]

[ QUOTE ]
Yes of course. Folding equity will change this up.

What I'm talking about though, is the statement "We want to get our money in on the flop while it's +EV so we can't be prized out on the turn." I'm just trying to show that that doesn't make any sense.

[/ QUOTE ]

I'm getting ready to leave and don't have time for the math, but I'm think that if the opponent folds when the heart hits it would change the math to a push on the flop.

I'm also thinking that by adjusting stack sizes and bets you could get the exact opposite result. I'll play with the math if I don't get home too late tonight.

[wtfsvi]

</font><blockquote><font class="small">Svar på:</font><hr />
</font><blockquote><font class="small">Svar på:</font><hr />
Yes of course. Folding equity will change this up.

What I'm talking about though, is the statement "We want to get our money in on the flop while it's +EV so we can't be prized out on the turn." I'm just trying to show that that doesn't make any sense.

[/ QUOTE ]

I'm getting ready to leave and don't have time for the math, but I'm think that if the opponent folds when the heart hits it would change the math to a push on the flop.

[/ QUOTE ] Yes it would, but you're missing the point.

</font><blockquote><font class="small">Svar på:</font><hr />
I'm also thinking that by adjusting stack sizes and bets you could get the exact opposite result. I'll play with the math if I don't get home too late tonight.

[/ QUOTE ] This is partially correct, but the results will never back the statement I was targeting, because it's a faulty statement.

EDIT: Now I don't want to come off as cocky, I do look forward to see your math play if you get to do it.

[mason55]

I guess I don't get it. Yes in this specific situation it's better to call because you can't get priced out on the turn. I'm saying that there are some situations where the opposite is true.

Edit: Intuitively I think there are at least.

[Malachii]

Good post. I think, in general, draws should be played aggressively against players that are either weak or capable of folding big hands. Against most players, they should be played passively. Given how well disguised your hand is here, I think calling here is the only way to play this.

Edit: This is a minor violation of the 5/10 rule though [img]/images/graemlins/grin.gif[/img]

[wtfsvi]

</font><blockquote><font class="small">Svar på:</font><hr />
Good post. I think, in general, draws should be played aggressively against players that are either weak or capable of folding big hands. Against most players, they should be played passively.

[/ QUOTE ] Against most small stakes players at least. I'm however not question the value of playing draws aggressively, I'm questioning the value of getting money in on the flop rather than the turn, just because your draw has better equity there. It was to isolate that factor I chose a scenario with 0 folding equity and certainty villain would push any turn. If villain wouldn't push the turn 100% of the time (but still call if we pushed) that would greatly favor calling and if villain would sometimes lay down his overpair on the flop or turn (or sometimes have AK), that would greatly favor pushing. The choice between calling and folding would mostly come down to those two factors weighed against each other (How often will he not push the turn, what will he do in stead, how often will he lay down an overpair on the flop, how often will he lay it down when these and these cards hit the turn, and so on.) I deliberatly left those conciderations out of the scenario though (along with meta-game conciderations) because I wanted to isolate a point: We'll have the benefit of being able to fold some turns, that I showed in the OP, on the call-side of the scale, not the push-side (where I see some people putting it when they give advice).

</font><blockquote><font class="small">Svar på:</font><hr />
Edit: This is a minor violation of the 5/10 rule though [img]/images/graemlins/grin.gif[/img]

[/ QUOTE ]Not really [img]/images/graemlins/smile.gif[/img]

EDIT: Small error in the OP. He'll have three outs to the boat when the 4 [img]/images/graemlins/heart.gif[/img] hits. The impact of this is probably close to none-existant though.
EDIT again: Oh yes, that's right, I didn't bother to calculate the 4 [img]/images/graemlins/heart.gif[/img] thing anyway, so the error didn't make my math more right or wrong [img]/images/graemlins/smile.gif[/img]

[fuzzbox]

The only reason you perceive yourself to have close to zero fold equity is because you reraised preflop, and then called the subsequent 3-bet. You got 20% of your stack in preflop, and that was a big mistake.

Pushing here is good because even if he folds even a small amount, you are +EV at this point (you already made a 20BB mistake earlier in the hand).

You push for 80, and there is 63 in the middle. You guestimate that you win 45% of the times that he calls, then you are betting 80 to win 123 if he calls, which is 1.5/1 (aka 60/40) on a 55/45 shot (good odds for you), and if he folds then you win 63 right now, which is clearly +EV.

Any folding equity at all is quite big for you.

If you call then you are committed to calling the turn (pot will be 83 and you will have 60 left, and you will have at least 13 outs, so you will have odds, when he pushes.

Sooooo you are going to see the hand out regardless of what happens, and even if you have 1% fold-equity, you gain by pushing. And every % you gain in fold-equity is big (but it doesnt matter because you already profit by 5% by pushing and having him call).