Aiming for first or second

[Wynton]

Pure math question here. Playing pokerstars $20+2 sitngo. First pays $90, second $54, third $36. Here's my question.

Sometimes when I have survived to third (not terribly short-stacked, but second still has clear lead), I decide I would rather be very aggressive, go for first, rather than just try to maneuver into second place. Presumably this strategy will increase my third and first place finishes, and decrease my second place finishes.

What I'm wondering is whether there is a formula for figuring out whether my increased number of third and first place finishes justifies the fewer number of second place finishes. Can any of you math geniuses out there figure this out for me?

[Daxonovitch]

You'll need to figure out some percentages to dictate how you should play.

Let's say you decide to play for 1st (strategy A). You're currently in third chip position with first and second (in terms of % total chips) have 80 and 12. You've got 8.

Your odds of making first are very small, and so by "playing for first" here (and not simply outlasting 2nd for a 2nd place finish) you are hurting your overall finish.

On the other extreme, let's say everyone has 33 chips and you decide to play for second (strategy B), not getting into big confrontations with marginal hands. The odds of you making 1st-3rd are all about the same.

The easy way to figure this out, mathematically, is take the odds of you making a given finish, and multiply times the payout. That will be your average return. So:

Situation 1 (80-12-8):
Normal Strategy: odds of 1st: 8%, odds of 2nd: 50%, odds of 3rd: 42%. (purely by chip equity)
Strategy A, odds of 1st: 15%, odds of 2nd: 35%, odds of 3rd: 50%. (guesstimating values)
Strategy B, odds of 1st: 5%, odds of 2nd: 75%, odds of 3rd: 20%. (again, guesstimating)

Payouts:
Normal: .08*90 + .50*54 + .42*36 = $49.32
Strategy A: .15*90 + .35*54 + .50*36 = $50.40
Strategy B: .05*90 + .75*54 + .20*36 = $52.20

So as you can see, in the first situation, the best strategy is to do your best to outlast 2nd place. Playing a bit more tighter here nets you an average of 2 or 3 dollars more than "normal". Interestingly, playing reckless and aggressive (strategy A) also nets you another dollar on normal. While my estimations of how much strategy A or B may affect your outcome are totally open to debate, the principle remains that strategy B is the best here when WAY outchipped (and unlikely to make 1st place regardless of how you play).

Let's look at the other situation.

Situation 2 (33-33-33):
Normal Strategy: odds of 1st: 33%, 2nd: 33%, 3rd: 33% (chip equity)
Strategy A: odds of 1st: 40%, 2nd: 20%, 3rd: 40% (guesstimate)
Strategy B: odds of 1st: 30%, 2nd: 50%, 3rd: 20% (guesstimate)

This assumes that playing Strategy A gets you more 1sts and 3rds, less 2nds, and playing Strategy B gets you less 3rds, more 2nds, and about the same 1sts.

Payouts:
Normal: .33*90 + .33*54 + .33*36 = $63.00
Strategy A: .40*90 + .20*54 + .40*36 = $61.20
Strategy B: .30*90 + .50*54 + .20*36 = $64.20


Interestingly, doing the math indicates playing safe and getting more 2nd place finishes will raise your net return. Interestingly (and contrary to what I had previously believed), playing aggressive seems to hurt your net return compared to playing it safe.

I may have the odds of getting 1st/2nd/3rd off, obviously that's open to debate since there are a number of factors involved. How much does playing aggressive really help? If the players are simply rolling over for you and the blinds are large, you should CERTAINLY be playing aggressive as the odds of you getting 1st go up dramatically (even the odds of you getting 2nd go up some). Hopefully, you'll be able to do your own calculations as far as your equity for a given situation, as you can see it's not too bad.

As you play more and more, you'll start to get a better feel for the math and how it should dictate your play relative to the payout structure. For example, in the 3-table party SNGs, the payout in the money is completely flat, indicating you should play strategy B or "normal". In a multi-table tournament at the final table, you should almost always play the other extreme, as aggressive as possible since the money lies in the top three spots.

Hope this helped.

[Wynton]

Very interesting. I am surprised that playing it safe, and going for second, in the scenario where you have an equal number of chips, is the most profitable. What about the situation where chip leader has 60%, other guy has 25%, and you have 15%? This is the situation where I find myself debating whether it makes sense to go for first.

[RPatterson]

If there are 3 people left and your in 3rd place you are going to have to make plays anyways. It doesn't really matter if you think you are going for 1st or 2nd.

[slogger]

Take this FWIW, but I think this is wrong. I play on Party (not Stars - though I'm assuming the payouts are roughly 50-30-20%) and I don't have the time to draw out the math, but the projections (probabilities of 1st, 2nd, 3rd) you're using are arbitrary and likely do not coincide with how the game will actually play out.

If you are even-stacked in these tourneys, I'm fairly certain that a very aggressive strategy will pay out better over time than a strategy in which you simply wait until someone else busts. The SNG experiences of just about every winning player on this forum bare this out.

In the 50-30-20 payout structure, two things matter:

1. Making the money.
2. Winning the tourney.

Even sacrificing a few points off your ITM finish percentage in order to position yourself favorably for a win is generally correct.

When shorthanded in SnGs, aggression is king.

[Daxonovitch]

Right, I think I made my estimates of the odds fairly conservatively. Aggression IS king as even one extra round of blinds picked up at the right time is a sizable portion of your stack. As I said, the odds are open to debate, the math was the original point of the post.