Taking coinflips early

[AtticusFinch]

This is from another thread, but it's a new topic, so I thought I'd start a new thread.

In the earlier thread, Psyduck said that you should consider taking a coinflip early in a tourney with AK if your only concern is hourly rate, not ROI:

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I don't have the exact math behind it, but if you're playing a set # of hours a day, taking coinflips early should theoretically increase your hourly rate but decrease your overall ROI. Maybe we should ask Lorinda to re-post it.

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Interesting notion. It seems possible conceptually, but I'm not sure if the math plays out.

Let's make a few assumptions and try a test case:

1) It's the first hand
2) The hand takes essentially 0 time
3) A full SNG takes one hour on average
4) Your normal EV for a SNG is 1.2 buyins.
5) Your EV for a SNG after doubling on the first hand is X

If you fold the flip, it's essentially the same as playing a SNG from the start, so your EV is 1.2 buyins or .2 buyins net.

If you take the flip, your possible outcomes are:

1) Lose and start another: Pay 2 buyins, get 1.2 back => -.8 net buyins.
2) Win: Pay 1 buyin, get X back => X - 1 net buyins

In either case, you're playing for one hour on average, so your effective hourly rate will be your average EV for the various possible outcomes.

Assuming the two outcomes are equally likely (a true coinflip) your overall EV is:

(-1.8 + X)/2

Meaning that in order to break even for your one hour under these somewhat idealized conditions, your EV after an early double must be greater than 1.8 buyins. In order for you to tie the EV of folding, your EV for doubling must be 2.4, or precisely double the EV for a normal sng.

I don't know about you, but I doubt my EV doubles from a first hand double-up. Furthermore, with AK, you're going to be on the 45% end of a flip, so in truth, you have to MORE than double your ev.

Still looks like a fold to me, if you KNOW you're in a flip. But you won't know that for sure. Perhaps the times when you're up against a dominated hand like AQ make up for all this.

[psyduck]

No replies yet? I thought that this was a pretty interesting topic that might (possibly) change how we look at coinflips during the early game. I was hoping that Lorinda specifically would post a response.

Anyway, I do think that this idea takes into account you getting involved with dominated aces (AQ, AJ, maybe lower) when you have AK. You're not looking specifically to get into a coinflip with AK (i.e. you might run into a worse ace, which becomes more common as you go down in levels, $30+3s, $20+2s), but you don't MIND a coinflip because of the reasons stated above.

I didn't take a close look at Atticus' math, but it seems sound from an initial glance. So unless you play very good bigstack poker, I don't think many of us would be able to double our EV from our early double-up.

[psyduck]

Damn! Bump muthafockas.

ok iwould like to add a little twist to this becuase this situatiobn came up 2 days ago and i felt i was justified in my call. 2nd level sng you have AKS with 2300 in chips raise to 90 from UNG 2 looooose players call BB goes all in for 1000 im pretty positve he has eithe QQ or JJ now what do you do??? auto call?? still fold?? hmmm still have 1200 chips if you lose startingg stack is 1500 so not far behind. also assuming you feel your a better player then most at table.....

[axeshigh]

Even with a lot of rationalization, it will be hard to make those AK calls early seem correct. Starting lvl3 I think pushing AK over a raise is fine though. Pushbotting seems less and less effective as the fish 'learn' to call with queen-high, so taking some gambles with AK, 99, that sort of hand doesn't seem so bad anymore.

I have no idea if this even makes sense but whatever, I feel better busting calling someone's 44 with AK then having someone call my T8o push with Q3.

According to ICM, your EV increases by only 84.4%.
You would need to be significantly better at playing a larger stack than you are at playing an average stack to make up for this.
I don't like early coin flips, personally.

[Ixnert]

I made some scribbles on the back of an envelope pondering the same question the other day, making essentially the same simplifying assumptions you made, and came to the same conclusion -- even from an hourly rate perspective, calling a push before you with no other money in the pot with AK when you know you're in a coinflip is still bad.

What I think is more interesting to consider is the situation where you acted first, raised, and then got re-raised all-in, and again know that you're in a coinflip. Is there some range of original raises you could make where it is -$EV/tournament but +$EV/hour to call?

The problem here is that we've never really formalized the assumption that we're better than the competition, beyond the assumption that we have a certain magnitude of +$EV at the beginning of the tournament, and I think answering this question demands some concept of how much more a small/large stack is worth to us than the average player.

[pooh74]

I dont like quantifying this. I dont see how its possible to have a "normal EV" for an SNG where you "don't take a coinflip" early. How are you seperating this? I think the variables are so hypothetical that they don't carry over to real life.

i.e.

How often are you sure you are in a coinflip?

How often in your "normal SNG" do you win a coinflip early-mid game?

What size stack are you 50/50 against?

[fnord_too]

I will work on some math in a little while if I have time. In STT's, I don't have an answer. In MTT's, I'll take all the coin flips I can get early.

[psyduck]

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In MTT's, I'll take all the coin flips I can get early.

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Do most people agree with this?