Further hypothetical - but now we involve gameplay and maths

[Garth Kay]

Middle of the tournament - Full ring - 500/1000 blinds no antes.

Position/Stack/Stats (VPIP/PFR/3b)

UTG - 16,000 - 22/18/4.6 - is now playing standard push fold poker with a 16BB stack

MP - 56,000 - 22/17/4.5 - very solid player, understands position/starting hand ranges and is a level 2 thinker.

DB - 160,000 - 12/10/2.6 - super tight player, has only showed down big hands, will flat for set mine value with pockets below TT but plays JJ+ very aggressively. Is a ROCK!

BB - 240,000 (HERO) - irrelevant.

UTG open shoves for 16K
MP three bets to 56K all in
DB snap shoves his whole stack in for 160K
POT now equals = 232K

Two scenarios:

1.) You look down at Ah, As.
2.) You look down at Kh, Ks.

Questions:

1.) Do you call in each scenario; elaborate on why you take your action?
2.) What hand ranges do you assign to each player?
3.) If we reverse chip stacks between DB and HERO does it change our actions as previously stated in 1?

[Garth Kay]

Noone wants to have a stab at this yet? What's the go? Paging Bennymacca!

[bennymacca]

Lol Garth u posted at 4am

I just woke up, I'll have a crack at it today some time

[bennymacca]

Disclaimer: all of the decisions below are made on maths and maths alone. this is completely ok in a hypothetical situation as this is. but in general, there are other things to consider, such as the stage in a tournament, how big a stack we have compared with everyone else, and our general edge over the field, if any. these things are not part of this discussion, and i dont think they should be - we can debate about that in another thread

for example, the fact that we are so deep might lean us towards the conservative side, because it means that we are likely to be one of the bigger chip stacks. if we win our tournament equity doesn't increase by a huge amount, but it drops by a huge amount if we lose.

i have not considered this in the current situation, but that is something that we could debate - whether it is correct to call with ANY cards.


i am going to answer the second question first, as it forms the basis for answering whether we call or not.

Question 2

UTG
if UTG is solid, shoving 16bb from UTG should be pretty tight. 16bb is in the push/fold range, but it is not desperation stakes just yet - if he let the blinds pass, then he would still have 13.5bb, and basically in the same position with regards to the amount of fold equity he has. so in this case, i expect his range to be pretty tight.

i think a range like 88+, AJo+, ATs+, KQs is a pretty decent range.

MP
MP's shove is clearly for isolation against the UTG shove. since he is a level 2 thinker, this means that he could have a fairly wide range, especially with hands like pocket pairs. BUT, he would flat call with his really strong hands, because he wouldn't want to isolate with these. so i would have basically the same range, but add pocket pairs 77-55, suited aces down to A8s, add KQo and KJs, and drop AA and KK, becasue these hands would flat.

this gives an overall range of 55-QQ, AJo+, A8s+, KJs+

DB
now this is where it gets interesting. this player is a rock at the best of times, and now he is shoving over 2 allins!
this is a super tight range most of the time. i doubt this is ever AK. since the other two players are relatively shorter than us, i think QQ is there still.

i give an overall range of QQ+ and thats it

Question 1

now we can use pokerstove to work out our equity against these ranges with AA and KK


anyway, the pot equals 232k, and we need to put 160k at risk here.

our pot odds are (232)/160 = 1.45:1
this equates to a pot equity of 1/(1+1.45) = 1/2.45 = 40.8%


now we can use pokerstove to plug in aces or kings for us and see what we get out.

Scenario 1 - AA
11,569,195 games 20.304 secs 569,798 games/sec

Board:
Dead:

equity win tie pots won pots tied
UTG: 12.302% 11.61% 00.69% 1343729 79740.67 { 88+, ATs+, KQs, AJo+ }
MP: 12.300% 12.04% 00.26% 1392974 30252.17 { QQ-55, A8s+, KJs+, AJo+, KQo }
DB: 16.391% 14.81% 01.58% 1713415 183228.00 { QQ+ }
Hero: 59.006% 56.88% 02.13% 6581078 246600.17 { AA }


as you can see from the above pokerstove output, we are 59% equity in this situation. only 59%! that might be surprising to some people. (compare this with QQ vs AK, which is 57/43 in favour of the QQ)

in any case, our pot equity required is 40.8%. because 59% is significantly higher than 40.8%, it is a clear call.


Scenario 2 - KK

no we can use pokerstove to determine our equity when we have kings

14,239,244 games 21.915 secs 649,748 games/sec

Board:
Dead:

equity win tie pots won pots tied
UTG: 17.532% 16.67% 00.86% 2374107 122575.83 { 88+, ATs+, KQs, AJo+ }
MP: 14.677% 14.20% 00.48% 2021590 68550.58 { QQ-55, A8s+, KJs+, AJo+, KQo }
DB: 33.559% 30.98% 02.59% 4410640 368498.42 { QQ+ }
Hero: 34.233% 31.70% 02.53% 4514365 360853.92 { KK }


now, you can see that our equity has dropped significantly, down to 34%. as this is less than the required equity of 40.8%, this is a clear fold.
thats right folks, the only hand that we can be justified in calling here is with aces.

as an experiment, i added AKs to the DB's range. this only increases our equity by 2%.

so in either case its a fold.


Question 3

can you elaborate on this garth?

who is DN? is that supposed to be DB?

the effective stacks are 160k with this person regardless of if we swap.

warning: spoiler will make you nerdier just for reading, and is an extension to the above question

Spoiler:

in a slight extension, i can do something else.
what we can do however is work out the stack size that we need to make Kings a call. as we can see, with effective stacks at 160k, it is not correct to call with Kings, but the shorter stacked we get, it will be correct to call with a wider range.

stack size to call with kings = x/(2x + 16+56) = 0.342

x = 0.342(2x + 16+ 56)

x = 0.684x + 24.62

0.316x = 24.62

x = 24.63/0.316

x = 77.9k


therefore if we have less than about 78k, it becomes correct to call with Kings as well, not just aces.

great question garth

[Garth Kay]

Excellent answers benny the cunt.

I thought you might enjoy this exercise and seeing as Pundies wanted to start learning about the Maths of the game I would throw out the above questions.

Question 3 was in regards to "increasing the stakes" because now you have to put your tournament on the line, and we step into the realms of tournament equity; exactly what you posted in the disclaimer but now I will flesh it out.

Mid stages of tournament, money starts from 40th.
200 players in tournament left out of 450 starters.
Average stack is 62,000
DB is chip leader of the tourney, Hero is 22/200

Remember that DB now has 240K and Hero has 160K

(Haven't worked it out properly, but this should do it)

[pundies]

1.) Do you call in each scenario; elaborate on why you take your action?

AA - Yes I call
KK - Fold


2.) What hand ranges do you assign to each player?

UTG - 77, A 10 s, A J off and above
MP - QQ, KK, AA. Maybe AQs or AKs or off.
DB - KK or AA. Maybe QQ but probably not

3.) If we reverse chip stacks between DB and HERO does it change our actions as previously stated in 1?

AA for me is an easy call. I have the best possible starting hand and the opportunity to eliminate 3 players. If I loose I am still left with $80k, plenty to play with. With a swapped stack with DB, I still call at this stage of the tournament. If we were approaching the money, I think I fold. There are too many players in the hand, too many possible scenarios. I am positive DB has the best hand next to myself, so I leave it for them to eliminate 2 players and I move closer to the money.

KK with the action before & many possbile scenarios makes the fold easy.

[bennymacca]

in the case where we have to put our tournament life on the line, i think that it is 100% correct to fold aces.

60% is just nowhere near enough equity to be tangling with the chip leader when we have such a big stack ourselves. i would want to be 80+ at a minimum in this spot to be able to call, which obviously can never happen preflop here.

this is a definite fold


in the case where we have 220 and the other guy has 160, then i think we can still call.

if we lose, its not the end of the world. we still have an above average stack.
just depends on whether we will be tilting at losing such a big pot

i really do think that folding aces is ok in this scenario as well. especially if we think we are better than the field.

i.e if this is in the world series, and we are sitting with a bunch of pros, then i think its a call, because in general we are not good enough to get into better spots often enough.

however if it is a tourney where we like our chances, i think it is ok to fold and keep the chip lead, and use our edge in later situations.

I have the best possible starting hand and the opportunity to eliminate 3 players

with 200 players left and the money starting at 40th, knocking out 3 players doens't really do anything for us in terms of the tournament equity, but dropping from the chip leader down to just above average has a HUGE effect at this stage.

[trishan]

Hey Ben,

There would three pots if Hero calls.

Pot 1: 3 players for a total of 48K
Pot 2: 2 players for a total of 80K
Pot 3: 1 player for a total of 104K

You need to calculate equity only against the players in each pot and then average EV to see if it is +EV or not.

EV = Equity (Pot 1) * 48K + Equity (Pot 2) * 80K + Equity (Pot 3) * 104K - 160K

[bennymacca]

Hey Ben,

There would three pots if Hero calls.

Pot 1: 3 players for a total of 48K
Pot 2: 2 players for a total of 80K
Pot 3: 1 player for a total of 104K

You need to calculate equity only against the players in each pot and then average EV to see if it is +EV or not.

EV = Equity (Pot 1) * 48K + Equity (Pot 2) * 80K + Equity (Pot 3) * 104K - 160K

good point trishan. this is getting pretty advanced though. probably beyond the scope of the question. i think the above will still hold true as an approximation but you are definitely correct.

i wonder how this will change things.
standby, i will work it out

[trishan]

I think it makes a huge difference benny the cunt because you are getting most of your money in against the rock!