Effect of high ROI on decisions early in a tournament

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Effect of high ROI on decisions early in a tournament

Suppose you're one of the best players in level 1 of a long structure MTT with a soft field. For instance, the WSOP main event.

From looking at marketplace markups and consulting a couple of friends who are knowledgeable on the subject, I think the best (maybe top 5%) of players in a tournament like this are achieving 50-100% ROIs.

There are two effects on $EV vs. cEV that I can think of when facing high variance spots early in tournaments:

Effect 1: Diminishing marginal value of chips (i.e. you wouldn't voluntarily take a flip for your stack level one, all other things equal, because chips 0-30,000 are worth more than chips 30,000-60,000)

There are points in a tournament where the marginal value of chips can change, like if you have a chance to accumulate a big stack approaching the bubble, but I'm only talking about early on.

Effect 2: ROI / skill level

Here's a completely different reason you wouldn't take a flip the first hand of the tournament if you have a positive ROI. I will illustrate with a hypothetical situation:

2 handed $1000 SNG, winner take all, no rake
Blinds are 5/10 and never change, stacks are 100,000,000
player a +20% ROI ($EV = $1200)
player b -20% ROI ($EV = $800)

On the first hand player b goes all in in the small blind and shows AsKs
Player a is in the big blind with JJ. Even though JJ has 54%, player a should still fold because .54*2000 = $1080, less than his $EV if he folds down to 99,999,990 chips.

My point in making this post is to ask how can we quantify the ROI effect early in big MTTs for allin decisions? As a player with a 50% ROI, you really don't want to be in spots where you risk all of your chips even if you have the best of it, but where do you draw the line?

The most I can conclude from this right now is that it is extremely beneficial to avoid huge pots early unless your cEV on the play is ridiculously high.

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