Hand 1 from Stars 11+R

[TheTimeIsUp]

On a side note, Tso has been playing very tight and rarely opening any pots.

[Lloyd]

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On a side note, Tso has been playing very tight and rarely opening any pots.

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So would you say a range of any Ace, any pair, any 2 broadway is about right?

What do you think the other guy is pushing with? I'm thinking AA-88, AK-AQ since tsop hasn't been playing too aggressively.

[Drizztdj]

Smells too much like a coin-flip to me rather then a possible dominated hand either way (AA,KK or AQ,AJ).

But I don't know if I'm good enough to fold after 5 or 6 hours of play.

[Lloyd]

HAND ASSUMPTIONS

UTG+1 (tsoprano) is raising with any Ace, any pair, any 2 broadway. That's tighter than it should be at this stage but according to TTIU he's playing particularly tight. This represents 298 of the possible 1,326 hands (taking into account the fact that our hero has AK).

UTG+2 is re-raising with AA-88, AK-AQ. Again, if UTG+1 was playing more aggressively than this should be a greater range .

If our hero folds, UTG+1 is getting 2 to 1 odds and will call with AA-77, AK-AT, KQ-KT, QJ. This range is about 1.5 to 1 against AA-88, AK-AQ making the call pretty favorable. This is a total of 139 hands so UTG+1 will call in this situation 47% of the time.

If our hero calls, UTG+1 will only call if he has AA-KK. There are only 6 possible combinations for him to have AA-KK so he would only call in this situation 2% of the time.

PRIZE MONEY

I don't have the actual numbers from this tourney but we can use the numbers from tonight's event as an approximation. All players are guaranteed 10th place money of $412. They are playing for the remaining pool of $31,562. Once the next person is eliminated all remaining players are guaranteed $772 ($360 more than they are guaranteed now) and are playing for an additional pool of $28,322.

CHIPS IN PLAY

Again, I don't have the actual numbers and this could make a slight difference but I don't think it will be too significant. Tonight there are 6,596,000 total chips in play. Tonight's prize pool is almost identical to the tournament we're looking at so I'm comfortable using this number.

IF HERO FOLDS

His Stack: 1,016,946 (15.4% of total chips)

UTG+1 Calls 47% of the time. He will win 40% of the time. If UTG+1 wins, UTG+2 is eliminated. All players are now guaranteed 9th place money. Our hero's equity is .154*28,322+360=$4,722. If UTG+1 loses, our hero's equity is .154*31,562=$4,861. The total equity for our hero if UTG+1 calls is $4,805 (4722*.40 + 4861*.60).

UTG+1 Folds 53% of the time. Our hero's equity is $4,861 (it makes no difference if UTG+1 calls and loses or just folds, only whether or not UTG+2 is still in the game).

The total equity of folding is $4,835 (4805*.47 + 4861*.53).

IF HERO CALLS

UTG+1 will fold 98% of the time. Hero will win against UTG+2 50% of the time. If Hero wins, UTG+2 is eliminated and the Hero wins 851,726 and has a stack of 1,958,672 (29.7%). If Hero loses, his stack is reduced to 474,220 (7.2%).

Hero's equity if he wins is .297*28,322 + 360 = $8,772. Hero's equity if he loses is .072*31,562 = $2,272. Total equity when Hero calls and UTG+1 folds is $5,522 (8772*.5 + 2272*.5).

For the 2% of the time that UTG+1 has AA-KK, I'm going to ignore since it 2AM. But I did want to crunch these numbers since it's a good example.

In summary:

$EV of Folding = $4,835
$EV of Calling = $5,522

Calling is clearly superior to folding based on the assumptions above.

[Lloyd]

Here's the important lesson from my analysis at least in terms of what I take from it in a practical sense. If we're sitting at a table (online or live) and get into a tough situation, there's no way we can do this detailed of an analysis in the short amount of time we have to decide. We have to draw on our experiences and trust our intuition.

So if I'm on a table facing this type of a decision hopefully I can remember this hand and the conclusion and act accordingly. I'm not going to remember all of the details but here are the important facts the way I see them:

1) We're at a final table bubble where the prize money will be going up substantially from here on out;
2) We have a hand that looks to be about 50/50 versus the range we put our primary villain on;
3) There is a fair amount of dead money in the pot;
4) Even if we lose, we still have enough chips to take a few stabs at the pot and get right back into the game.

Now we gave our opponents a pretty tight range and opening it up will no doubt benefit us even further. So in some respect this is almost a worse case scenario and against normal standards this is even a more favorable situation.

[Che]

...you insult our intelligence with such surface-level analysis? [img]/images/graemlins/laugh.gif[/img]

I do have a serious question, actually.

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If UTG+1 wins, UTG+2 is eliminated. All players are now guaranteed 9th place money. Our hero's equity is .154*28,322+360=$4,722. If UTG+1 loses, our hero's equity is .154*31,562=$4,861.

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Are you sure hero's equity *decreases* when a player is eliminated? This result flies in the face of the "survival has value" theory which assumes your chips increase in value when players are eliminated (especially deep in the money).

On another topic, I would estimate our hero's EV would drop by ~$90 if we include the times that UTG+1 calls, which still leaves this as a clear push. Throw in that we're using a worst case scenario for the opponents' ranges (as you mentioned) and it's too bad TTIU didn't have any time bank left. [img]/images/graemlins/frown.gif[/img]

Very nice work, Lloyd!

Che

[schwza]

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Are you sure hero's equity *decreases* when a player is eliminated?

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in real life, no, of course not. this is another place where chip count gives you bad results. suppose you have 99% of the chips left with 3 people in a 5/3/2 sit n go, so 4 units still up grabs, 2 locked up. chip count estimates you get .99*4+2 ~= 6. when you knock one guy out, you have 3+.99*2 ~=5. the same thing is happening here.

we're giving 9 of the 10 players left $360 (and one goes home). so of the prize pool that's being distributed right now, hero gets 11.1%. but chip count was assuming before he'd get 15% of the remaining prize pool in play, so knocking someone out and getting "just" 11.1% hurts hero's EV, according to the math.

nice analysis, lloyd.

[SossMan]

[ QUOTE ]
HAND ASSUMPTIONS

UTG+1 (tsoprano) is raising with any Ace, any pair, any 2 broadway. That's tighter than it should be at this stage but according to TTIU he's playing particularly tight. This represents 298 of the possible 1,326 hands (taking into account the fact that our hero has AK).

UTG+2 is re-raising with AA-88, AK-AQ. Again, if UTG+1 was playing more aggressively than this should be a greater range .

If our hero folds, UTG+1 is getting 2 to 1 odds and will call with AA-77, AK-AT, KQ-KT, QJ. This range is about 1.5 to 1 against AA-88, AK-AQ making the call pretty favorable. This is a total of 139 hands so UTG+1 will call in this situation 47% of the time.

If our hero calls, UTG+1 will only call if he has AA-KK. There are only 6 possible combinations for him to have AA-KK so he would only call in this situation 2% of the time.

PRIZE MONEY

I don't have the actual numbers from this tourney but we can use the numbers from tonight's event as an approximation. All players are guaranteed 10th place money of $412. They are playing for the remaining pool of $31,562. Once the next person is eliminated all remaining players are guaranteed $772 ($360 more than they are guaranteed now) and are playing for an additional pool of $28,322.

CHIPS IN PLAY

Again, I don't have the actual numbers and this could make a slight difference but I don't think it will be too significant. Tonight there are 6,596,000 total chips in play. Tonight's prize pool is almost identical to the tournament we're looking at so I'm comfortable using this number.

IF HERO FOLDS

His Stack: 1,016,946 (15.4% of total chips)

UTG+1 Calls 47% of the time. He will win 40% of the time. If UTG+1 wins, UTG+2 is eliminated. All players are now guaranteed 9th place money. Our hero's equity is .154*28,322+360=$4,722. If UTG+1 loses, our hero's equity is .154*31,562=$4,861. The total equity for our hero if UTG+1 calls is $4,805 (4722*.40 + 4861*.60).

UTG+1 Folds 53% of the time. Our hero's equity is $4,861 (it makes no difference if UTG+1 calls and loses or just folds, only whether or not UTG+2 is still in the game).

The total equity of folding is $4,835 (4805*.47 + 4861*.53).

IF HERO CALLS

UTG+1 will fold 98% of the time. Hero will win against UTG+2 50% of the time. If Hero wins, UTG+2 is eliminated and the Hero wins 851,726 and has a stack of 1,958,672 (29.7%). If Hero loses, his stack is reduced to 474,220 (7.2%).

Hero's equity if he wins is .297*28,322 + 360 = $8,772. Hero's equity if he loses is .072*31,562 = $2,272. Total equity when Hero calls and UTG+1 folds is $5,522 (8772*.5 + 2272*.5).

For the 2% of the time that UTG+1 has AA-KK, I'm going to ignore since it 2AM. But I did want to crunch these numbers since it's a good example.

In summary:

$EV of Folding = $4,835
$EV of Calling = $5,522

Calling is clearly superior to folding based on the assumptions above.

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Very nice work.

[Lloyd]

[ QUOTE ]
Are you sure hero's equity *decreases* when a player is eliminated? This result flies in the face of the "survival has value" theory which assumes your chips increase in value when players are eliminated (especially deep in the money).

[/ QUOTE ]
You know that baffled me as well, of course. But I remember a thread that Adanthar posted a couple of weeks ago that had a similar conclusion. In that example, the hero's $EV decreased after the ITM bubble just like in this one.

To come up with the prize money for the calculation:

1) With UTG+2 still in:

I took the total prize money for 1-9 and subtracted out 9 times the 10th place money since all 9 of those people are guaranteed at least that much.

2) With UTG+2 out:

I took the total prize money for 1-8 and subtracted out 8 times the 9th place money, since all 8 people now are guaranteed that much. Once that number is multiplied by the appropriate chip count percentage, I added back the difference between 9th and 10th place (the $360 figure) to account for the increase in what everyone is guaranteed.

I'm pretty sure this is correct but I'm open for another suggestion.

$EV isn't perfect, of course. But there are very few ways we can analyze a situation like this and I don't if any other way is any better.

[DonT77]

Nice work Lloyd. As you pointed out, the chances of running into AA/KK are slim because of you holding AK (leaving only 3 ways each to make AA & KK). Thus we are likely either an 11:9 dog against a PP or a 3:1 favorite against a dominated hand like AQ. Math suggests that whenever you can include AQ in your opponent's ROH (range of hands) then playing AK is profitable whenever you are getting close to even money or better.

I agree with your analyis and other posts (e.g. good god people) that say this is a clear push because of the dead money in the pot and the fairly wide ROHs that we can assign to our 2 opponents. In this case, even if we could rule out AQ from the reraiser's ROH (and I don't know how we could possibly do that given his stack size) we should still be willing to get all-in as an 11:9 dog against a short stack given the > 11:9 pot odds we are getting.

Yes, the fact that another larger stack is yet to act is scary - but if he calls with anything less than AA/KK (e.g. JJ/QQ) he is just increasing our pot odds.