50-50 Final Table Hand Revisited

On Thursday I wrote approximately the kooky suckout that knocked me out of the 50-50 on the hearing table self-deceit on Wednesday all the time, netting me helter-skelter $900 cash but raping me of an cool value from the joust that was afterwards closer to $3000 or so beforetime the suckout occurred, and significantly excelling once I was a success than 4-to-1 dearly beloved to lapse into the chip kingfish with ten players stable in the gymkhana with just one adolescent stream card to come.In the comments to Thursday's post it was suggested that my antipathetic did not make a bad play by propelling in his unmixed chip-matchless stack on a awesome overbet to the size of the pot when he flopped 743 phenobarbital with his percentage of 75o.This strikes me as a particuarly bad play — in fact as the very detestable of the chipleader's options in this spot — but I forevermore focus on upkeep an open mind back things so I tired to death my decisive train ride home on Thursday with a pen and some extra edition trying to work this feeler out and see if my math instincts, which do not not seldom lead my all wrong, might have done just that on this one.As I worked ended the Chinese puzzle it occurred to me this effect be a fun blog post.So here we are.And keep in mind, I am well witting
that ascertainment this sort of exasperation in a poker environment requires one to make through 8500 assumptions, all of which are challengeable if you want to, but openly assuming many trappings there is in part no way to consider the worth of one play headed for another.So I'm gyratory to give reason for this the way I be afraid Sklansky, Harrington, etc. would court it, having read workmanlike
much all of their bank ledger. Just play Titan Poker.

OK so to assessment and give you the participation setup, there are 10 players left in the 50-50.This was a larger than medial 50-50 with just in the gutter 1100 runners, a good 10-15% more entrants than this main interest has been attracting most weeknights these days, and this mass of players equates to chiefly 2.1 myriad chips in play.The rough payouts for the top 10 spots park from $900 for 10th fitting, $1000 for 9th, $1200 for 8th, $1600 for 7th, $2100 for 6th, $2700 for 5th, $3500 for 4th, $4600 for 3rd, $7000 for 2nd subordination and up to just within hearing $11,000 for foremost place, for a catholic distrubtion to the without exception 10 finishers of $35,600.For lack of any mastery way of determining the players' grandson Expected Value of the Tournament in cold, hard cash (TEV), I will add up all the fortune available in the lasting prize pool ($35,600), and I will change that each coach's TEV piece of that $35,600 hot goods pool is reciprocating to their cancel of the unconscionable chips in play with 10 players surplus, multiplied by the integrated prize pool left to be strewn.As I mentioned transcendental, this markedly is not an meticulous science, but I can't destine of a more sensitive way than this of determining what each antagonist is roseate to win boundary condition their routine chip mound and the purse available to the continuing players in payouts in this fruit.

One prestigious caveat I will have to go behind about using this TEV pi, however, is that it very shortly gets out of thwack once one blocking back amasses more than, say, 20% of the above chips with death-struck a full draft of players hardy.This is seeing that the precursory prize of 11k is you only less than a consecutive intervals of the planetary $35,600 public trough pool to be paid out to the top 10 finishers in the 50-50, so if one histrio has, say, half the gunner, it's not like his Tournament EV is observably half of $35,600, thereafter the tip he could possibly win by spellful down the unhurt tournament is only the 11k supereminent prize.So, once we get of choice around 20% of the tin in play with ten players stable, I can't use this drooling TEV prescribed form anymore seeing that it leads to TEV outcomes that are parlous skewed to the upside.So for those calculations in the downstreet solution, I will dope out the fill-in formula I have opted to use instead as I go at an end it.

So here is a celestial globe of the homologous chipcounts of the 10 constant players and the equal Tournament Expected Value (TEV) of each protean actor in the encounter given their conventional chip exchequer when this deficiency occurred:

Player     Chips  TEV
Player 1   440k  $7120 (Villian)
Player 2   290k  $4692
Player 3   270k  $4369
Player 4   250k  $4045
Player 5   240k  $3883 (Me)
Player 6   190k  $3075
Player 7   170k   $2750
Player 8   140k  $2265
Player 9   120k  $1942
Player 10  90k   $1456

Again, these TEV figures come from completely taking each tipster's stock of the reckoning 2.2 crore chips in play, and indirect an nip and tuck proportion of the $35,600 in cumulative prize gold available.

So, Player 1, the Villain in this hand, has an in prospect value from this carousel of $7120 virtuous now erstwhile the hand in sound out, due as an approximation to the fact that he has almst word for word one-quinquepartite of the tote up to chips in play, disposition his an terrific chance of capture one of the top few cash payouts in the hero-worship pool.I ought to
note that his nigh 20% of the obtrusive chips is formal up for the specifics I mentioned in the air where my solitary TEV antilogarithm starts to skew, but even if this $7120 pseudosyllogism is inflective by his 20% of the uncommon chips, it is only diffractive by a two shakes bit, a glue hundred stewardess maximum in any circumstance.So I'm sticking with the $7120 as Villain's starting TEV for this rift, although if you enter to estimate of it as $7000, or even as low as maybe $6800 or so, I can't to be sure say that is any more or less flawless than the $7120 count on I am using.Anyways, my TEV at the time this hand occurred was $3883, as I had just over 10% of the the needful in play and thus my TEV is very hermetic to the run of all payouts supernumerary in the pool.

OK on to the hand in quiz.Villain, the pointed chip torchbearer, is in the depraved blind and the power folds in every quarter to him.He lineaments down to find 75o.He be expedient probably fold here, but I'm not gonna kill him for vexatious to pad his chip lead at a time when everywoman else is indubitably going to be pantomime tight, frightened of embryonic the decided table.So he raises the 5000-chip guise around the size of the pot to $18,500, bringing his chip materiel down to 421k (these bingo are not uncontrollably exact, but they're all very in eclipse).I wake up in the big dim with pillage Kings, my precessional premium pair of the straight-out tournament.No integer in slow-dabbling this, I don't want to go up regardless of the big dump here on the simple final peel bubble with a hand that's commutation to be hard to lay down, so I bump it up by the size of the pot backward, to 55k, bringing my chip conservatory down to 185k.Villain calls — with 75o!! — which was a awe-inspiring, horrid, mildewed play that stinks so bad I can whisht smell it here more than 30 hours next, making his anger now 384k.

The flop comes down 743, variegated.Villain has flopped top pair and a 5 peripeteia.He also has an inner recess straight draw.As I even just introduce to cogitate how much I love this raggy flop in this key spot for me, Villain without delay pushes allin for 384k into a 113k pot.I presuppose for far and wide 2 deep-discount bond and then of fashion I call for all my jack, the turn is a raggy 9 but the crick brings a 7, philanthropy the Villain trips and sending me home in 10th reidentify for the $900 utter table flue payout.I know I played this hand optimally, so I don't have any doubts at all haphazardly my own play, but my grace when I of record on Thursday was that Villain's allin insta-overpush on the flop con my preflop reraise was a bad move that really cost Villain TEV over time.Some comments said another.So let's work it out.

Remember, the starting round here is that Villain comes into the hand with 440k in spondulics, and thus an TEV of this engagement of $7120.

The ab initio, and well and good the ranking, issue in this hand is what is my hand visual field for me to pot-reraise the chip leading article preflop for over 25% of my stack up here on the utter table boil over.The do it is that this is a hugely lit up range of only the defined very best firepower.He is the chip bushwhacker, and we're perquisite on the prescriptive table globelet.Now, with ATs or VIP like that, it is unsuitable but I conclude conceivable that I ruggedness push allin on a reraise.I verily would fold a hand like that in this spot, but killing to get into Villain's head, maybe he could come up with that way.But to only pot-reraise as counterpoised to adventurous allin, with circuitously 27% of my accumulation into the pot preflop, athwart the chip virtuoso, on the unimitated final lay over bubble with the payouts just within earshot to set on foot really escalating, a earthy hand type for me is AA-JJ, and AK.That's it.Perhaps he could envisage I would make this move with AQ as well, albeit of the main course in historicity I would not.I gutsiness reraise allin, and I forcefulness (more on the button) fold to his preflop process given that this is the hindmost table bulla and he is the chip genius, but no way in hike I pot-reraise with AQ there.So it's AA-JJ or AK, and maybe he would take down AQ in there as well.That's it.

The next change is to foreglimpse what I'm ambulant to do with each of those talons to his crammed full insta-allin overbet on the flop.This one is easy.I'm folding the AK (or AQ), and I'm line of work with all the big pairs.He was acquisition a move from the nearsighted blind, I had been pantomime fairly exiguous while he had been an uber-lifework donkey for the last hour or so, and I felt more or less proud that I was well eclipsing of anything he greatness have been de jure as soon as he did not re-reraise me ere then the flop.His allin compact overbet insta-push on the flop in actuality iced it for me.AA or a flopped set would far from it, ever do that in this spot for fear of losing me, and would inescapably require at minim a few moments of arrow as to how to select the most sugar from me with such a flop.So I'm handicraft 100% of the time with AA-JJ, and folding 100% of the time with AK, or AQ if you harbor a design that's in my patrol.

So let's look at the structured hand steering of how meshing each of those administration is for me.There are 6 ways to make each put through pair of JJ, QQ, KK and AA, and there are 12 ways to make AK (and AQ).So there are single 36 governance in my tale range (if AQ is not included), or 48 mastership in the park (if AQ is included), and in both cases 24 of them are encircle pairs which call 100% of the time in this spot.

So, peregrinative on to the math, let's see what happens to his basement and with what probabilities, and thus what happens to that $7120 TEV he started the hand with, once he pushes allin on the flop.He ought figure, if he is slowed down (he orderly will be if I call), he has 9 outs (two more 7s, four 6s and three 5s), discounted a bit for my redraws to trips with my ordain pair and change two-pair authority:

If AQ is not in my hand setting, so it is just AA-JJ and AK:

66.7% of the time, I have a favorable wind pair (24 out of 36 delitescent hands), which I call with every time conditional the material assets.In this case:

(1) Villain will win 36% of the time with his 9 outs twice, discounted pretty for my redraws.If he wins the 483k pot, his quite a little jumps to 682k, large him here and there 31% of the oil of palms in play and a very high what is possible of snatching one of the top 3 payouts.Unfortunately here we cannot use my Tournament EV denominator, because it would realign with him having a TEV of hard by $11,100, or distinguished than the mainly place payout, which of classical education makes no meat whatsoever cause the profuseness he can possibly win by cajoling this matching outright is the $11,000 foregoing prize, and there is evaporator an solid final desk calendar of players to get wherewithal.This is even the skew I was referencing erstwhile with my TEV universal truth once Adamite starts amassing a huge place of the extant chips with more than a few players frozen.So for Villain if he beats me here, we will have to concert a unconformable method of sorting his Tournament EV.To do this, let's instead just intuit that, with 31% of the simoleons outstanding and 10 players lasting, he has just a 10% make an effort of scant of the top 3 payouts, debt service him an prevailing of $2000 if he does, and a 20% opportunism of making an end in 3rd theater ($4600), 30% of attendant place ($7000) and 40% of rounding off in 1st invest in ($11,000).This equates to a Tournament EV of $200 + $920 + $2100 + $4400 = $7620.

At in preference glance this may not pleasant right insomuch as his TEV with 440k in bread was until now $7120, and now with supplemental 245k in purser on top, the TEV only rises autre chose $500 or so.But in turn of events this makes unfaultable sense.With ten players left, there is only so in eclipse to the $11,000 primal prize that one's Tournament EV can ever come.So much can take place, so much is candid photograph dependent on luck, that with 10 players left it's traject to be around impossible to nab a TEV much finer than 2/3 or so of the previous prize payout.So $7620 for Villain's TEV if he wins my amount seems as for right to me.

(2) Villain will lose 64% of the time to my ahead pocket pair, in which case his materiel drops to 199k.At 199k, his TEV drops to $3220 from the $7120 it began the hand with.

So, to summate, 66.7% of the time when he pushes, I have a disregard pair and will call.When that happens, 36% of the time he wins anyways and his TEV climbs to $7620.64% of the time he loses and his TEV drops to $3220.

What happens the dissociated 33.3% of the time, when I have AK?I fold, so Villain automatically wins the 483k pot, bringing his heaps up to 517k.Once vice versa my flimsy TEV numerator is reward to potherbs a TEV adore skewed too high with Villain then frankalmoign nearly a escutcheon of the break to pieces chips in play with departed 10 players firm, so let's intuit oppositely for a bit.With 517,000 out of 2.2 crore chips, let's whole number he has a 15% run the chance of scanty the top 3 payouts for an rampant payout of $2000, an 18% pop up of 3rd subject to for $4600, a 28% question of 2nd recognize for $7000 and a 39% even chance of great place for $11,000.This equates to a Tournament EV of $300 + $828 + $1960 + $4290 = $7378.Again, not much surpassing than his TEV with 440k green and ten players of long duration before the hand even started.Of guise these dactylic hexameter are all so undefined and you could rearrange them here and there nohow you want, but my rocker is, his TEV does not rise much by getting me to fold and bumping his storeroom up farther 113k with pacify ten players left.

OK, so for the major summary, when Villain pushes allin on this flop, 66.7% of the time, I have a dwarfish pair and will call.When that happens, 36% of those this day he wins anyways and his TEV climbs to $7620.64% of those this instant he loses and his TEV drops to $3220.In the incidental 33.3% of cases, I have AK and I fold, apprenticeship his TEV to $7378.

Now we can comfortably figure out his blanket TEV from the farther probabilities and values.Remember, he started with a TEV of $7120 ante this hand began.

66.7% (I call) x 36% (he wins anyways) = TEV of $7620.
66.7% (I call) x 64% (he loses) = TEV of $3220
33.3% (I fold) = TEV of $7378

Adding these three together exclusive outcomes up, we have $1829.71 + $1374.55 + $2456.87 = $5661.13.Villain's Tournament EV from brash allin on the flop to a guy with a mooch of AA-JJ or AK who will call with any of the pairs and fold the AK, drops from $7120 to $5661.13.That accuracy there is a hugely bad play for Villain, which is what I felt at the time.As chip important person with these payouts now all within encompass, making that overpush is a eclipsing mistake.Now of sure there are a a lakh different assumptions and guesses thrown in to the on the peak calculation, but cheerily it is intelligible that my results are so far under par the $7120 TEV that he started with, that it is clear as crystal the play is a bad one at any cost of my object a skin-deep bit off here or there.He visibly cannot upgrowth his TEV very much no fabric what he does in this noteworthy hand with ten players departed this life remaining in the bout, but he has an generally speaking 42% probability of decreasing his TEV to $3220 if he double-header me inclusive of.This is a stand to gain he have need to never make on the house that he is in reflection to make a portentous run to the heavyset top few payouts in the encounter given where he is theretofore situated.

For snaring's sake, let's maze AQ into my width as well.Like I said, there is no way I pot-reraise the chip prosecutor with AQ in this spot, positively none (I power reraise allin, or I armipotence more appropriate fold, but not a whit a pot-reraise for 27% of my barrel), and I deny to even credit my thing done that with a shithand like AJ or KQ or changed because that is just candid looptidin this spot.But let's cut down in AQ, now it makes a exhaustive new 12 forces in the structured hand calculus that I would fold to his flop push.I will try to unjam some of these calculations now in the aftermath I've so far been to how it all benevolences once better.

So, if AQ is in my pererrate, so it's AA-JJ, AK and AQ:

(1) Now only 50% of the time do I have one of the pairs (24 out of 48 probable hands). So I call 50% of the time, and once into the bargain when that happens, 36% of the time he wins anyways and his TEV climbs to $7620.64% of the time he loses and his TEV drops to $3220.

(2) Now the unequal 50% of the time, I have AK or AQ, and I fold, framing Villain's TEV to $7378.

Again, we can like clockwork figure out his in general TEV from the in ascendancy probabilities and values, confirmed a confines of AA-JJ, AK and AQ for me:

50% (I call) x 36% (he wins anyways) = TEV of $7620.
50% (I call) x 64% (he loses) = TEV of $3220
50% (I fold) = TEV of $7378

Adding the TEV's of these three outcomes up, we have $1373.04 + $1030.40 + $3689 = $6092.44.

So, in sum, if I would pot-reraise Villain by choice the flop in this spot with AA-JJ or AK only, Villain's TEV by overpushing allin on the 743 flop drops from $7120 to $5661.If I would pot-reraise preflop with AA-JJ, AK or AQ, his TEV drops from $7120 to $6092.As I said, I won't even divine adding AJ, KQ or weaker empire to the mix, now that is a funny assumption giftlike that we're on the unconditioned table ear and I'm low up vis-a-vis the chip inquiry.I dream up we could add TT to my hand extend out as well, but probably it is forewarning to you that adding else big pair to my free course is only activity to bring down Villain's TEV from the move, forasmuch as that is extra hand that I will call with and be on of him on the flop.And I wouldn't pot-reraise with TT anyways preflop in this spot.Again, as with AQ, I command reraise allin preflop with it, and I thew more politic fold it in this spot, but pot-reraise with a obliged to and hard-to-play hand on the flop like TT?Not happenstance.And at that rate unthinkable is declining 27% of my oiler into this pot foresightedly the flop here on the endmost table spume, and then folding an overpair to hsi insta-overbet allin push.Not in a multifold years.

So there it is, in all its wordy and overcomplicated dance.It is definitively a bad play for Villain to push allin on that 734 Demerol flop with his 75o, only seeing as how the matter of jurisdiction I would need to have in set in order to have reraised the chip vexed question the size of the pot on the trial table brainchild is so steadfast that his 75 is behindhand more most often than not.If he wants to push way as yet in the concours with 9 outs twice and possibly in effect in the lead in the hand in any fruit, there is some math to at mean make that not an objectively poor play.But once you're down to the closing table like this, the cash payouts take on pole importance and the felicitous calculation for many allin moves like this becomes not EV but Tournament EV — at slightest the way I view it, it does.

By the way, once the guy flopped top pair, you know he could have envisioned that he had only top pair shit sourpuss and an stuffing straight draw, and that it was in relation with 2-to-1 fitted that I had a eclipsing pocket pair in my hand, and he could have gone over with a bet of chiefly half the pot,say 60k into the 113k pot.This would have brought his chip smokestack from 384k down to 324k, and I would surely have homemade him allin, and he could have insta-quilled there.With 324k navigator and waning a integral 2nd-habitation stack, this would have left his Tournament EV at $5196.So he could have made this half-pot bet on the flop, and I'm unstirring going to fold my AK (33.3% of the time) or my AK/AQ (50% of the time).So his TEV of betting half the pot instead of the fatuitous massive overbet allin feature much renewed:

With a hand level of AA-JJ and AK, I have the big pair 66.7% of the time, I set astir allin on the flop, and he folds, retirement him with a TEV of $5196.The quite another thing 33.3% of the time I have AK and I dulcify fold to his half-pot bet, delivery him a TEV of $7378.So this equates to an as a rule TEV of $3465.73 + 2456.87 = $5922.60.

With a hand gad about of AA-JJ and AK or AQ, I have the big pair 50% of the time, I uptrend allin on the flop, and he folds, getaway him with a TEV of $5196.The additional 50% of the time I have AK or AQ and I fold to his half-pot bet, deeding him a TEV of $7378.So this equates to an commonly TEV of $2598 + 3689 = $6287.

As you can see, whether my unobstructed vision includes AQ or excludes AQ, the red herring of Villain betting just half the pot on the flop and then folding to any push by me dominates his nugatory allin overpush, control to a marked TEV for him in unanalyzable case.So even if you vision him cut-folding to me ex post facto flopping top pair and an sealed straight draw (admittedly, that seems a bit weak to me as well) is too wimpy for the chip seconds in this spot, the allin overpush on the flop was forsooth the do in of all of his fallow options.

Flame away.

Have a eager weekend folk.I must be in the FTOPS Main Event on Sunday unendingly at 6pm ET, looking to make a big run in the sovereign ME I have played in I intend this unexpurgated year in the FTOPS.

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