How aggressive can you afford to be as the big stack?

My friend Mike and I were having a discussion about this last night as we battled heads up at the end of a single table tournament in my home. We had two contrasting schools of thought. I won't say what I think because I am really interested in an honest answer from the rest of you.

Assume for starters that we are talking about a situation where, at the end of a tournament, you have at least twice as many chips as the other guy. Let's say there are 30,000 chips in play so you have 20,000 (at least) and he has 10,000 (at most). How aggressive can you afford to be about putting him all in? How much does that change as he becomes more and more short-stacked?

Let's actually look at two somewhat different situations. In situation 1, you have 20,000 and he has 10,000. In situation 2, you have 25,000 and he has 5,000. So obviously if the other player doubles up once in situation 1, he moves ahead of you; in situation 2 he would have to double up twice to move ahead, and a single double up still gives him only half your chips.

Does this affect the kind of percentages you need to make a call? If he goes all in, or for you to put him all in? For argument's sake let's say you know for sure you're about 40% likely to win the hand - either you have a decent draw on the flop, or it's pre-flop and you hold a slight dog like K9 vs. his AT. With a 40% chance of winning, would you call his all in if you had twice his chips? If you had five times his chips?

Assuming neither player is much better than the other...

You 2:1
40% win outright + 0.6 x 0.33 chance of winning if you lose (now you are outstacked 2:1)= 60% chance which is worse than if you fold.

You 5:1
40% win outright + 0.6 x .67 chance (now you are down to 2:1) = 80% chance of winning
which is worse than the 83.3% (5 in 6) you would have if you fold.

So, 40% is not enough. I am pretty sure (without doing math) that 50% is exactly even with zero blinds.

If the blinds are 10% of the total chips (so 3000), then it becomes much closer (because, for example, in the 5:1 case, his chance of future winnings goes up 60% if you just fold!)

It's all about the blinds. Say the blinds were like $1/$2 and the stack sized are like 20K to 10K. If the short stack pushes every hand, just fold until you get a good hand. You'll get one long before he catches up to you. Obviously, if he's not pushing every hand then you actually have to play poker instead of algebra.

Originally Posted by zenbitz

Assuming neither player is much better than the other...

You 2:1
40% win outright + 0.6 x 0.33 chance of winning if you lose (now you are outstacked 2:1)= 60% chance which is worse than if you fold.

You 5:1
40% win outright + 0.6 x .67 chance (now you are down to 2:1) = 80% chance of winning
which is worse than the 83.3% (5 in 6) you would have if you fold.

So, 40% is not enough. I am pretty sure (without doing math) that 50% is exactly even with zero blinds.

If the blinds are 10% of the total chips (so 3000), then it becomes much closer (because, for example, in the 5:1 case, his chance of future winnings goes up 60% if you just fold!)

It's all about the blinds. Say the blinds were like $1/$2 and the stack sized are like 20K to 10K. If the short stack pushes every hand, just fold until you get a good hand. You'll get one long before he catches up to you. Obviously, if he's not pushing every hand then you actually have to play poker instead of algebra.

What?? Maff makes me head hurty

Thanks for the breakdown, zenbitz. Your approach seems obvious but I hadn't thought of it before. So basically to call an all in with the worst hand, assuming the blinds are fairly low, you'd have to have a significantly larger stack than him - and even then it's just because it wouldn't significantly alter your chances of winning if you fold OR if you call.

There's also another variable of skill. Your assumption here is that a 2:1 chip advantage means you're 66% likely to win the game, but if there's any kind of a skill gap (for example, he's much better but you've been lucky and built up a big stack) it might change your decision. If it was me vs. Daniel Negreanu, for example, I might be happy with a 40% shot to take him down rather than let him hang around and outplay me. Of course, if you are more skilled than your opponent AND have him outstacked, I'd say there's no merit at all in calling his all in with a worse hand; you are only decreasing your chances of winning, which are quite high before the hand starts, since you have more chips and a higher skill level.

This by the way was basically my position: that there was almost never a good reason to call with a worse hand if you KNEW it was a worse hand. Mike looked at it another way, which is that being the big stack (4:1 or more) meant you could call with a worse hand a couple times just because it was "worth it to try to put them out." Personally when I have a bigger stack, I wait for the best possible opportunities... I don't just call because I can, unless the short stack is really REALLY short.

Note that this is assuming you are calling not pushing. If you push, you have folding equity (although this is very close to zero heads up if the blinds are big).

So, at some level, you can say it's proper (+EV) to push every hand. The problem is, after the first couple of pushes (that are folded), you opponent will figure out that you are pushing with any two. This makes it trivial for him to figure out if he should call or not (i.e, he should call with anything >50% equity against a random hand,

Q2/J6/T7/98s,
Q6/J8/T9o

If it's 25,000 to 5,000 I call with just about anything for a chance to get rid of my opponent. This weekend I called with 72 suited and won. I was at like 13,000 and my opponent 2,000. If I lost the hand, I was still outstacking him 3:1. It basically comes down to the elimination attempt outweighing the consequence of losing the race. The bigger your chip domination, the weaker you're willing to race with.

You basically want your opponent running into a brick wall when they get desperate. You should not lay down any hand whatsoever when you have 85-90% of the chips. I mean call with ANYTHING.

Unless you have a gross chip lead like 6-1 I am not inclided to "push w/ anything." This is assuming the blinds are not outrageous and you are of equal or greater skill than your opponent.

The chip lead lets you poke and prod preflop with some raises and re-raises. You can set some better traps that way. I prefer to play post-flop in heads up situations so you can see if you pair up, bluff etc...

When you get up to 8-1 or more than you can just push AI blind and take a shot or two and ending the thing with any 2 cards.

The risk of doubling someone up when you are only at 4-1 or less is a problem for me. Say you have 20K v. 5K it only takes 2 double ups on the part of your opponent and the tables are turned. On the other hand, if you have a relatively weak opponent you can pound them into submision with that type of chip lead.

In any case, the cards have far more to do with the outcome than any "moves" you make. For instance, I lost AA v. A2 in heads up confrontation, everything went in pre-flop. So, this might be an argument for puhing with any 2.

Doyle brunson had David Sklansky outchipped 10:1
He got 89o and went all in
Sklansky picked up something like AT and won
Doyle went all in next hand
Sklansky picked up Ace high again
Doubled up
Doyle went all in next hand
Sklansky picked up K high and doubled up
Sklansky now had Doyle outchipped 10:1
Sklansky goes all in
Doyle picks up king high (better hand) calls and loses

Sklansky comes back from 10:1 chip disadvantage to win it

I'm not sure calling with any 2 is the proper move even at 8:1 stack advantage IF the blinds are small (relative to the small stack). The only way he can come back is if he doubles up 3 times - by calling with crap, you make that much more likely.

I'mnot saying you should wait for an ace... but may as well wait until you have an above average hand (like Q7o or something). I think the break even point is when the SB+BB = remainder of small stack - then you should call with any 2.

So, like 500/1000 blinds short stack has 2000 you have 16000 before posting.
After posting: SS 1500 Pot 1500 You 15000 - trivial call with any 2.
But if it's like 50/100,
SS 1950 Pot 150 You 15900 - this is a bad call (with like 2/3o) if SS/SB pushes.

Unless you have a hot date or something - then just try to end it quickly

When you have more than 85% of the chips, you race as soon as possible with just about ANY cards. I will do ANY cards, but I don't want to condone ANY for everyone. It's just my style. I don't care how bad the cards are. If you were good enough to get such a dominant chips lead in the first place, then it shouldn't be a problem when he doubles up to 20-25% of the chips. Just crush him again.

Originally Posted by Rondavu

When you have more than 85% of the chips, you race as soon as possible with just about ANY cards. I will do ANY cards, but I don't want to condone ANY for everyone. It's just my style. I don't care how bad the cards are. If you were good enough to get such a dominant chips lead in the first place, then it shouldn't be a problem when he doubles up to 20-25% of the chips. Just crush him again.

I don't see the point though, Rondavu. If you're that much better than him, why give him opportunities when you can outplay him to death? If you have a big chip lead and more skill, his best chance of winning (or even hanging around a while) is doubling through when you call his all ins with bad hands. I could see the logic if the blinds were big relative to his stack, but if the blinds are small you have all the time in the world to outplay him - why make it harder on yourself?

If i have that sort of chip lead its simple.
If i have Ax i put him all in.
If i have two face cards i put him all in (probably, but not always)
any pp >55 i put him all in
and with AA i DEFINATLY put him all in
If i hit tpgk or two pair or better on the flop i put him all in (where there are no obvious made hands that can beat mine) If hes drawing to the better hand i still put him all in. preflop, play the same. Raise anything better than Q7 (the computerized average heads up hand i think)
If you have a draw and hes all in dont call imo. Dont give him free chips wait till u have the hand then put him all in n the draw.
Works for me and i like to play heads up stuff. But then i play my cards a bit more rather than the situation heads up.
Personally i do not put him all in on suited conenctors (unless both face cards) or connectors like 87. You are not guarenteed to win the hand if you catch top pair, whereas your chances are better with a kq or qj etc)
If your going to make him coin flip, take the advantage into it preflop or make it count if you have it post flop. Dont be on the opposite end of the flip so to speak with 87 or suited conenctors imo.
EG.
Game #924930895 (Level I, Game #4) - 5/10 No Limit Texas Hold'em (1-on-1) - 2005/08/08-08:18:29.9 (CST)
Table "Kauehi" ($5 tournament) -- Seat 4 is the button
Seat 4: Miffed22001 (1,960.00 in chips)
Seat 7: tredogrex (40.00 in chips)
Miffed22001: Post Small Blind (5)
tredogrex: Post Big Blind (10)
Dealing...
Dealt to Miffed22001 [ 6c ]
Dealt to Miffed22001 [ Jh ]
Miffed22001: Call (5)
tredogrex: Check
*** FLOP *** : [ Jd 7s 9h ]
tredogrex: Bet (30)
Miffed22001: Call (30)
*** TURN *** : [ Jd 7s 9h ] [ 8d ]
*** RIVER *** : [ Jd 7s 9h 8d ] [ Tc ]
*** SUMMARY ***
Pot: 80 | Board: [ Jd 7s 9h 8d Tc ]
Miffed22001 bet 40, collected 40, net +0 (showed hand) [ 6c Jh ] (a straight, seven to jack)
tredogrex bet 40, collected 40, net +0 (showed hand) [ 6d 8h ] (a straight, seven to jack)
-----------------------------------------------------
Game #924931502 (Level I, Game #8) - 5/10 No Limit Texas Hold'em (1-on-1) - 2005/08/08-08:19:42.3 (CST)
Table "Kauehi" ($5 tournament) -- Seat 4 is the button
Seat 4: Miffed22001 (1,935.00 in chips)
Seat 7: tredogrex (65.00 in chips)
Miffed22001: Post Small Blind (5)
tredogrex: Post Big Blind (10)
Dealing...
Dealt to Miffed22001 [ Td ]
Dealt to Miffed22001 [ Ac ]
Miffed22001: Call (5)
tredogrex: Raise (55)
Miffed22001: Call (55)
*** FLOP *** : [ 7s 5h Th ]
*** TURN *** : [ 7s 5h Th ] [ 5s ]
*** RIVER *** : [ 7s 5h Th 5s ] [ Jc ]
Miffed22001 said, "lol"
*** SUMMARY ***
Pot: 130 | Board: [ 7s 5h Th 5s Jc ]
Miffed22001 lost 65 (showed hand) [ Td Ac ] (two pair, tens and fives)
tredogrex bet 65, collected 130, net +65 (showed hand) [ Kd Jd ] (two pair, jacks and fives)
-----------------------------------------------------
Game #924932156 (Level II, Game #4) - 10/20 No Limit Texas Hold'em (1-on-1) - 2005/08/08-08:21:00.3 (CST)
Table "Kauehi" ($5 tournament) -- Seat 4 is the button
Seat 4: Miffed22001 (1,865.00 in chips)
Seat 7: tredogrex (135.00 in chips)
Miffed22001: Post Small Blind (10)
tredogrex: Post Big Blind (20)
Dealing...
Dealt to Miffed22001 [ 8s ]
Dealt to Miffed22001 [ 7c ]
Miffed22001: Call (10)
tredogrex: Check
*** FLOP *** : [ 5s 3c 7s ]
tredogrex: Bet (115)
Miffed22001: Call (115)
*** TURN *** : [ 5s 3c 7s ] [ Js ]
*** RIVER *** : [ 5s 3c 7s Js ] [ 2c ]
*** SUMMARY ***
Pot: 270 | Board: [ 5s 3c 7s Js 2c ]
Miffed22001 lost 135 (showed hand) [ 8s 7c ] (a pair of sevens)
tredogrex bet 135, collected 270, net +135 (showed hand) [ 6s 4d ] (a straight, three to seven)
(dumb call but he could have had anything!!)
-----------------------------------------------------
Game #924933239 (Level III, Game #3) - 15/30 No Limit Texas Hold'em (1-on-1) - 2005/08/08-08:22:57.9 (CST)
Table "Kauehi" ($5 tournament) -- Seat 7 is the button
Seat 4: Miffed22001 (1,800.00 in chips)
Seat 7: tredogrex (200.00 in chips)
tredogrex: Post Small Blind (15)
Miffed22001: Post Big Blind (30)
Dealt to Miffed22001 [ As ]
Dealt to Miffed22001 [ 7c ]
tredogrex: Raise (185)
Miffed22001: Call (170)
*** FLOP *** : [ Kh 9d 2h ]
tredogrex said, "gg"
*** TURN *** : [ Kh 9d 2h ] [ 5h ]
*** RIVER *** : [ Kh 9d 2h 5h ] [ 4c ]
tredogrex said, "lol"
*** SUMMARY ***
Pot: 400 | Board: [ Kh 9d 2h 5h 4c ]
Miffed22001 lost 200 (showed hand) [ As 7c ] (high card ace)
tredogrex bet 200, collected 400, net +200 (showed hand) [ Ad 3d ] (a straight, ace to five).