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View Full Version : Calling all-in early on in a tourney


pergesu
09-06-2005, 09:16 PM
"Someone pushes and turns up their hand on level 1. What's the minimum advantage you need to call?"

This is a question that Bones just posed to me, and we've been discussing a bit for the past few minutes. My initial idea is pretty simple - the probability of you losing can be no more than your over all probability of making the money. For example, if I've played 10k SNGs and find that I have an ITM of 40%, I'd be a fool to take any bet that has me losing more than 40% of the time.

You have to determine how the extra chips affect your chances of making the money. I think the effect is inversely related to your skill edge over the field. If you're significantly better than the field, then having twice the chips early on doesn't help you nearly as much as if you're only marginally better than the field.

Continuing with the example of a 40% ITM player who plays low stakes SNGs, the minimum edge he should be willing to take is probably around 57/43. I don't know exact numbers (and I'm very interested in studying this further), but I'd say that if I double up on the first hand I probably increase my chances of making ITM by around 10% (10% of 40 is 4...40+4...my chances are a tad less than that). So if my opponent shows a hand where I'll lose 43% or more of the time, I should fold. As an example, if he has AKo I should call with TT+, but fold anything else.

If your edge over the field is smaller, it's correct to take greater risks if that will significantly increase your edge. Some of you may groan at this, but I think Gigabet's infamous Q3o hand is an extreme example that illustrates this point well. Though he's a great player, every other player at the $15k buyin knows what they're doing, and he probably doesn't have that much of an edge over them. This changes entirely when he gets twice the chips. His general skill + big stack skill + the fact that he can't bust on a single hand allows him to pick up more pots, and over all have a significant advantage over the field.

Keep in mind that this is all relative to the rest of the players at your table. Of course Gigabet is a better player than me...but I probably have a greater edge over the table at low limit SNGs than he does at the ultra high stakes games. Fortunately if you're playing on Party, you have a good idea of where you stand compared to the general population at your limit.

The basic idea to take away from this is that when you're faced with an early all-in decision, you need to estimate your edge should you win the hand, and take the bet only if that figure is greater than your probability of losing the hand.

This would be interesting to study because it's not a simple matter of finishing in the money, because of the different weights of finishing 1/2/3. ITM is simply a benchmark to use as the starting point for this idea, and hopefully I can expand on it.

Jman28
09-06-2005, 09:20 PM
[ QUOTE ]

This is a question that Bones just posed to me, and we've been discussing a bit for the past few minutes. My initial idea is pretty simple - the probability of you losing can be no more than your over all probability of making the money. For example, if I've played 10k SNGs and find that I have an ITM of 40%, I'd be a fool to take any bet that has me losing more than 40% of the time.

[/ QUOTE ]

This is incorrect. Without going into why it is, here's an exaggerated example:

you have AA. KK, QQ, and JJ all push in front of you.

Calling will put you out of the tourney ~46% of the time.

pergesu
09-06-2005, 09:23 PM
[ QUOTE ]
This is incorrect. Without going into why it is, here's an exaggerated example:

you have AA. KK, QQ, and JJ all push in front of you.

Calling will put you out of the tourney ~46% of the time.

[/ QUOTE ]
Doesn't really disprove my point. What is my edge relative to the field when I hold 40% of the chips in play, 7-handed with plenty of time to go? Significantly better than 46%, I would imagine.

Jman28
09-06-2005, 09:27 PM
[ QUOTE ]
[ QUOTE ]
This is incorrect. Without going into why it is, here's an exaggerated example:

you have AA. KK, QQ, and JJ all push in front of you.

Calling will put you out of the tourney ~46% of the time.

[/ QUOTE ]
Doesn't really disprove my point. What is my edge relative to the field when I hold 40% of the chips in play, 7-handed with plenty of time to go? Significantly better than 46%, I would imagine.

[/ QUOTE ]

Okay. Too strong of an example.

The point is, you have to take into account the higher probability of 1st you get from doubling up, which goes up much more than your chance of making it ITM.

pergesu
09-06-2005, 10:04 PM
[ QUOTE ]
The point is, you have to take into account the higher probability of 1st you get from doubling up, which goes up much more than your chance of making it ITM.

[/ QUOTE ]

That would make this seem even more applicable then. It skews the numbers, but as I said at the end of the post, I'm just using ITM as a starting point. I'd like to dig deeper.

I just don't really see what you're disagreeing with here. Care to explain?

benkahuna
09-06-2005, 11:57 PM
I think while you're correctly considering the downside here that you're not accurately considering the upside.

This is actually a simple mathematics problem for the most part. There are a few pieces of data you need to know:

1. Your hourly rate.
2. How long the tourney will take if you win.
3. What change in winning chances will you have if you win?

Obviously, you need to estimate these.
Let's say you do the 10 dollar SNGs to make things easy.
Let's say you place in the money 40 percent of the time with an equal proportion of 1st, 2nd and 3rd. With prize pool of 100, the average win you'd have is 25. Let's say it takes an hour to get ITM on average.
That puts you at 25-11 for 14 per hour, 40 percent of the time, or let's say 6 bucks per hour (rounding).

Let's say if you win the hand, you'll finish people off in 45 minutes.

Let's say winning the hand doubles your winning chances (Harrington's statistics).

So, the times you win, you have an 80 percent chance of winning 25 or 14 net. For 40 minutes that's 3/2*14 per hour or 21 per hour. If you lose, you lose 11 instantly.

So your EV is a certain percentage for -11 in 10 minutes and a certain percentage to win 14 in 45 minutes. If you bust and play another tournament, you'll get your average for the remaining time you would have been in the tournament.


I'm going to play with the numbers here even though I have no idea what I'm doing. I'm just relying on my mathematical and logical intuition. If I make a mistake, please fix it!!! I know I said it's a simple math problem (and it is), it's just that I haven't done this sort of problem before.

So, for 45 minutes, you'll get -11 + 6*(3/4) or -6.5 for the ITM time. If you win, you'll get +14 80 percent of the time so about 11.

I think your ability to make 11 in the same period of time where you could make -6.5 is worth a risk of that proportion, 11:6.5. I think you can actually take the worst of it here and make more money. I find this result surprising. Because you're a profitable player, getting out a tournament or doubling up quickly would be a risk worth taking. A problem arises in how consistently making plays of this sort would affect your winrate.

You'll notice that by playing with the numbers such as decreasing your ITM chances or increase the time already invested in the tournament, you'll get closer to only being profitable making
calls when you're getting the best of it. Time spent in a tournament is an opportunity cost against playing in another tournament where you're making your average winrate.



I'm unsure about a few things here. One I'm not sure how to mathematically include skill advantage. I guess you would include that in ITM chances. You'd obviously want to incorporate the other players' chipstacks as well. Another issue is that consistently making plays like this in the long term will cause you to bust out of tournaments and lose money. So, consistently making this play should have a negative EV. At the same time, it's clearly worth taking the worst of it at some points in tournaments to increase your winning chances significantly. I'm also not sure how to deal with time and the buy in here. In some ways, it almost seems like the time and buy in should be discounted because they are past events, not unlike posting a blind or putting money in a pot are not considerations in pot odds, only the pot size is. I know the proscribed tournament strategy is as follows:

1. Don't risk your entire stack early in close to even money situations.
2. If you can outplay your competition, take fewer even money risks.
3. Shoot for 3rd (single table tournaments).
4 (poker generally) don't call all ins unless you're quite sure that you're ahead.

The problem is that I can't reconcile these ideas (which have worked for me and I believe to be true) with the math I've just done (which seems intuitively correct).

pergesu
09-07-2005, 12:30 AM
Wow...that's definitely some cool stuff upon reading it. This is already getting rather complex though. I'd like to focus on maximizing EV in the tourney now. Then when that's kind of figured out move on to hourly rate considerations.

Freudian
09-07-2005, 12:47 AM
[ QUOTE ]

The problem is that I can't reconcile these ideas (which have worked for me and I believe to be true) with the math I've just done (which seems intuitively correct).

[/ QUOTE ]

I think for me at least, doubling my stack in hand 1 doesn't double my $EV.

That of course doesn't mean I wouldn't be able to increase my $/h by taking coinflips early on. And if there is dead money in the pot or I get the 53-55% end of the coinflip most of the time, it will definately help quite a bit.