I have some online friends I play with on PokerStars' "Home Game" deal (a great feature--too bad you can't use it on mobile). We usually get four or five playing; only once did we get six, and that was the only time PokerStars allowed us to "pay" (we are Americans so we are just playing for fun and bragging rights) second place.

Most of them have much less poker experience than I do, but they are all sharp customers, as we know each other from a high-IQ society. So I was chatting with them about how cash games are different because (at least in theory) if you played the cards face up and you knew you had a 35% chance to triple up, you would take it every time (as long as you have the bankroll to handle the variance). Whereas in tournament play, you can't handle the variance that comes with very thin EV edges as a dog.

But then one of them asked a very good question: doesn't that go out the window for us most weeks, since tonight for instance we had five players (and a rebuy period as well, with one person doing so--not sure if that affects my question) and the winner gets all the chips AND all the "cash"? (For the purposes of the standings we are keeping track of and posting on the Facebook group, we just use net chips won or lost without counting the silly "rake" Stars charges even in play money.)

That question really stumped me. On the one hand, it is certainly different from a structure that pays second place, allowing you to win money just by losing all your chips more slowly than the other losers. But what about the fact that in a cash game, you can decide to fold to preserve some chips and then stand up and cash those in for real money? Or what about the fact that late in a tourney, letting yourself get too shortstacked means you get buffeted around by the blinds and have no fold equity for preflop raises?

I'm sure some poker theory minds sharper than mine will see this and be able to set me straight.

A little wordy, but in essence I think your question is "if you are inclined to take a 35% equity hand in a 3-way all-in in a cash game (I which I agree is +EV), shouldn't you want to do it more so in a winner take all scenario tournament. The 4:1 "cash" odds leverage up the +EV.

Why do you say “more so”?

Because neither you nor the opponents can escape a tourney as long as they have chips left, unlike in cash games where they can quit at any time, theoretically, you should take opportunities to gamble with a neutral or slightly negative chip EV if you think the opponents are stronger than you, because you'll benefit from playing fewer hands vs the sharks and spending the saved time on playing in a soft game instead, but you should pass up on high-variance moves whose EV is slightly positive and 'wait for a better spot' if you believe the opponents are weaker than you and will give you chances to gain more EV later in the tournament.

Afaik, this consideration came up in the 'Kill Phil' book; for a much more scientific discussion of this so-called 'winrate-maximising play' in tourneys (a strategy that maximises the expected winnings from a WTA STT as a whole, instead of maximising the EV of each hand in isolation), see volume 2 of Will Tipton's 'Expert Heads Up No Limit Hold'Em' where the concept is explained for HU SNGs, one of the greatest poker books ever written that benefits non-HU players too.

One of the toy examples there is the situation where you're sitting in a 100 bb HUSNG vs a maniac who shoves every hand preflop; in this case, your range for limp/calling all-in should be very tight despite the top 50% of hands giving a positive chip EV on the call (as commemorated in the 'just wait for QQ or better' meme (read the initial thread first!) about a reg of the $11 no-blind-increase HUSNGs that used to be offered at Stars whose strategy was to stall at every opportunity, put the opponent on massive tilt and make them shove every hand) because it costs relatively little to wait to be dealt a monster when you know the opponent will surely pay you off.

I used to love those NBI HU SNGs! I was not playing them with that degree of gamesmanship, timing down and all that; but I did definitely play them “smallball” style, and most of the time my opponents would get frustrated and start shoving every hand, at which point I would just wait for a premium hand as you describe. However, sometimes I’d run into another patient and thinking player, and we’d have a long duel. I actually enjoyed that more than getting easy money from the impatient.

The main difference between cash and tourney play comes indeed from the payout-structure.

There is a formula called ICM which tournament players use to calculate the difference. However this formula merely considers stack-sizes, as such it is incomplete, however the best guestimate we got so far.

If you only go by this formula a WTA-tournament plays exactly the same as a cash-game.
Because mathematically each cash-game hand you play follows a WTA structure.

However there are factors, as pointed out by coon74, which arent considered by ICM. So you can say it is very very similiar, yet a little different. Using cash game maths would deffinitely be the best approach to solving hands, then you can assume some edge or -edge if some of the rather subtle tournament factors come into play.

“Very very similar, but a little different” was my intuition as well. But I’d love to have some kind of solid theoretical or empirical foundation for that intuition to take back to these guys.

In a freezeout format, busting means you forfeit future opportunities to make good bets.

When playing better opposition = take smaller edges because you're less likely to get bigger ones in the future.

When playing worse opposition = pass smaller edges because you're more likely to get bigger ones in the future.

It's up to you to figure out where a league of geniuses fits on that scale.

As the tourney progresses, you begin to run out of time for these future edges to show themselves.

200bb deep = pass smaller edges for your stack because you have plenty of time.

8bb deep= take any edge you can, because you're not far from having to take the least negative option.

Thank you! That makes total sense, because you can’t just chip up like you can in a cash game.

We do allow up to two rebuys, no add-on. How would you factor that in? It won’t allow us to rebuy unless we get completely felted.