In the situation I gave earlier this was a no-limit ring game where house was taking 5% of pot – probably you would fold unless you have better odds. After the 5% house cut calling would only be worth 1470 or so (less than 1500 you would have if you folded).
It would take a few bizzare factors like needing the win to enable you to buy into a tourney starting in 3 min with say 10 players paying 1-10 and say 500$ added – and not being able to just add money to your account to make this pay in a percentage way.
The decision to call would also be justified if you read your opponent as having a lesser holding but if you knew he had at least a pair of K then you would have to be confident that you could use it to exploit your table image.
OK that is ring games. I would beware of justifying decisions on the basis of table image, it is most often used as a way of justifying a bad decision than a justification in itself. It is very hard to put a money value on image, so focus on putting it on mathematical odds.
What about tourneys though? I have taken the view that whilst in tourneys you have to adapt in your willingness to call these sort of things dependant on quality of opponents at the table, general quality of opponents in the tourney, blinds, payouts, etc. All of these factors are hard to put accurate numbers.
If we assume you are in a 5$+1 three table tourney, first gets all in if all you do is risk 50/50′s with people with the same chip stack and your chips dont alter otherwise (impossible I know but useful for the mathamatical model) if you play 900 tourneys you will win 30 (4500) and it will cost you 4500 in stake and 900 in rake. Not very good, most people think a 50/50 is an ok call in this sort of tourney. But it is clearly not.
Assuming that you are not able to exploit a chip stack into being worth more chips from bullying then you want 6/5=1.2, so if it is a 50/50 you need 200 in the pot already if you have 1000 chips or calling is clearly bad. This 1.2 is the expected value of calling / chips left if fold = Z (I will call this Z value here on). It only applies if calling will knock you out if you lose (but crippling your stack amounts to almost the same thing). If you are a good player in a tourney full of fish you may feel that even 1.2 is too low.
Note this only applies when 1) you cant exploit a larger chip stack to a significant degree either to get more chips or in tourneys with wider ranges of payout – get you in the money, 2) if the way players are playing you can envisage getting into either an all in with a higher Z value. In a 10+1 tourney the Z value needed is only a 1.1 or greater, whilst everyone plays much tighter in this sort of tourney stake actually they could legitimately play slightly looser.
I feel I can legitimately take 50/50s early on in 2-3 table tourneys because getting to the final table with a moderate amount of chips will normally see me into the money. I also focus a bit more on $ per hour profit than $ per tourney. My best game is short stack after I have got reads on players and I am a good heads up player. Also most of the players who reach the last 5 or so are normally unable to adapt to the different style of play required. But it is interesting to know the general position that in a 5+1 you want a Z value of greater than 1.2 or subject to superior play later on you are playing in a way that will lose you money.
People often avoid calling 30%ers say calling on the turn with 13 outs, but if the pot is big you will often have a Z value that makes calling clearly justifyable. Whilst you may get a better chance later on or be able to pick up small pots if you fold and save yourself for later, it would be hard to present factors worth folding as far as I am concerned if there was enough in the pot to give you a 1.5 or higher Z value. Also if it gives a 1.2 rate then your call cannot really be legitimately critisized.
One of the key things that should be gained from my Z value concept is that you really dont want to be getting in a lot of these sort of situations. So trying to win small pots and chose opponents with lesser stacks is exceedingly important if you want to make a profit. Adapting this formula for larger tourneys is a bit tricky as so many other factors come in to play but if you were playing in a system style of heavy preflop play you may make it hard for pros to beat you but you would need to steal a lot of pots to even cover the tourney rake, if you were trying to make a profit in the long run.
No one I play against seems to have a mathematical way of adjusting pot odds in all in situations in tourneys. They generally seem to feel a 50/50 is ok even without a pot to give 1.2 Z value is ok but are skeptical about a 1 in three that will knock you out the rest of the time but have a 1.2 Z value and they play tighter in a higher money tourney with only a 1.1 Z value needed to justify a call.
As I play for time and try to keep my stakes well within my bankroll I reckon I can legitimately call on almost even .9 (call EV/ fold EV) early in a tourney but after 40 minutes it would be foolish to do so without a 1.2 (in a 5+1 or a 1.1 if it is a 10+1). My calling on a .9 could be critisised but my calling on a 1.2 mid way through even if I am only .3 to win is sound as far as I am concerned.
What do you folks think? How would you adapt this to larger tourneys? My own feeling is that with solid play in 5$ large tourneys is that terrible play by other players gives more to the prizes than the rake takes out so that I would avoid many 50/50s because I would hope for either small gains or a 60% + double through but that generally speaking I would feel I would need a small +1 to call on a EV call/ EV fold or I am just not taking advantage of the fact that there are poor players there.
After the first hour I would feel I would need a small +1 to call and it would depend on what was happening at my table and after that I would consider calling if I had not over average chip stake anything with +EV pot odds unless there looked safe money on my table to be got in later hands.