Hand 1:
This situation arose when Sandra Naujoks “missclicked” to 5k instead of 500 utg, 8 handed at blinds of 100/200 with an effective stack size of around 12k. A middle aged guy next to act after Sandra flatted her raise. This guy had just been moved to our table and was covering everyone at the table, he had roughly 50k. My impression of him was that he was likely a soft spot in the field. It was then folded around to me in the big blind. I had 30k and looked down at AQo. If the big stack hadn’t flated it would have been an easy shove in my opinon given Sandra’s missclick, but now stack dynamics made the situation slightly awkward.
At this point with the little information I had on the big stack I was trying to figure out his range for flatting here. I think it’s fair to say that he can flat strong here for sure, though I would expect him to raise his strong hands more often than not. I also expect him to be more likely to flat KK-AA than when he has QQ and AK due to playability reasons. I’d say he is also capable of flatting hands like KQ, AJ, 77-88 occasionally. The majority of the time when he flats, I would expect him to show up with 99-JJ, AQ.
So let me think about the rough mathematics of the situation. At this point there are 10,300 chips in the pot. If I jam then I am risking 30,000 to win that. I will assume that the big stack will call with QQ+, AK. Against this range our equity with AQo is 24%:
Hand 0: 24.420% 23.05% 01.37% 113673216 6751686.00 { AQo }
Hand 1: 75.580% 74.21% 01.37% 365966964 6751686.00 { QQ+, AKs, AKo }
Sandra will be likely to call well against my shove here as she is comfortable with the tourney buy-in and realizes that a small stack will not be worth much at this stage in the tournament. However the player left to act behind might affect her decision. Nonetheless she will be getting 3.5-1 immediate odds to my shove. I’m not entirely sure on her range for calling to be honest, but I think she will be atleast calling with 88+, AQ here.
Against that range of hands I have 40% equity:
equity win tie pots won pots tied
Hand 0: 39.878% 30.85% 09.63% 34861061 10888158.00 { AQo }
Hand 1: 60.122% 51.40% 09.63% 58086991 10888158.00 { 88+, AQs, AQo }
I think if Sandra calls the bigstacks range will remain unaffected more or less. Against the combined range I have an equity of 17%:
Hand 0: 16.767% 14.81% 01.96% 2139301071 283659049.83 { AQo }
Hand 1: 33.308% 31.46% 01.85% 4545162393 267969978.33 { 88+, AQs, AQo }
Hand 2: 49.925% 49.13% 00.80% 7099440611 114955564.83 { QQ+, AKs, AKo }
So let me try and formulate some sort of rough equation for this problem:
First I will estimate how many hands I think Sandra is raising here in general. I don’t really know much about her game, but I know she is a lead instructor of some coaching site, so I’ll assume her approach to the game will be tight by default. I’d say a somewhat “normal-tight” range for raising here first to act would be : 22+,A2s+,KTs+,QTs+,JTs,T9s,98s,87s,AJo+,KQo, this consitutes 15.6% of hands. 88+, AQ make up 5.6% of hands. Ergo I estimate she folds 1-5.6/15.6=64% of the time.
The overcaller is slightly trickier to analyze, because I have more uncertainty when it comes to his range. KQ, AJ, 77-88 make up for 4.5% of hands. If I assume he has this range 25% of the time when he calls, it means on average this range is representative to 4.5*0.25=1.125% of hands or 1.125% of the total combinations of preflop hands possible in Holdem. I’ll assume he can have 99-JJ, AQ everytime he flats (simplified) which represent 2.6% of hands. And QQ-AA, AK 25% of the time, for a total of 2.6*0.25=0.65%. So based off of my assumptions villain will be calling 0.65/(0.65+2.6+1.125)=14.9% of the time.
At this point I would like to point out that we are assuming that the big stack will make mathematically incorrect folds if we shove AQ here, because we think he is a below average player. I think it is reasonable to assume that a weak player may look at how much we put in the pot and just fold JJ, despite getting very good odds. In the defence of my opponent, I think hardly anybody in this field would expect me to jam AQ or worse here, because they all value tourney life so highly. Coming from a cash game background I sometimes have to remind myself that +ev plays are not allways that good if they are high variance in a tournament with players against whom you don’t play with on a regular basis.
We now have enough information to estimate the ev of shoving here:
Both players fold:
0.64*0.85=54.4%
Sandra calls, big stack folds:
0.36*0.85=30.6%
Sandra calls, big stack calls:
0.36*0.149=5.4%
Sandra folds, big stack calls:
0.64*0.149=9.536%
Number check: 54.4+30.6+5.4+9.536=99,9% (error is due to rounding off of numbers)
0,544*10300+0,456*(0,31*(0,4*(10300+7000)+0,69*(-11800))+0,054*(0,17*(10300+7000+25000)+0,83*(-29800))+0,095*(0,24*(10300+25000)+0,905*(-29800)))=-3083
Note there is a small error in the equation, because sometimes I will beat the bigstack, but lose to Sandra and vice versa. I have neglected this to simplify the calculation. However this should not make up for the negitive ev, as the entire play yields an ev of minus 15 big blinds and this specific scenario only occurs 5.4% of the time. I also feel as though I set the paramaters as such that they would be favourable to shoving in general.
For what it’s worth, it was interesting to see some numbers on this scenario. I’ve also learnt that I should restrain myself from doing these calculations per hand, as they are too tedious. I can probably do this in half the time with the right tools. “Per hand” calculations are fine with only one opponent involved, but as soon as things start to get multiway it get’s complicated.
I’m still in Valencia right now. Busted the tournament at the end of day one. It was a questionable bustout, as I had a reasonable stack, but I went with a read and happened to be wrong. I expect my play to be +ev on average in the long run as I usually trust my reads, but it’s one of those high variance/slightly +ev spots I mentioned above. Got to play with Dal, a Dutch player who won the Sunday Million. He was very loose in the early stages, but was able to make some pretty good valuebets with pretty weak preflop holdings so it probably worked out for him. He tightened up a lot when the table got deeper and the stacks shallower.
Had a video of my room in Valencia, but I’m unable to upload it right now as the internet is messing about. Will hopefully be able to upload It later. It’s really annoying when you’re in a hotel and the internet isn’t working due to internal problems. The internet isn’t working in the whole hotel, so imagine the opportunity costs to a hotel full of internet poker players :S. Anyhow, all the best for now.

Daniell

edit:

The internet is back up again so I was able to upload the tour of my room: