so anyways, i decided to expand my repertoire of games online and decided to start playing some heads-up matches. i particularly like them for when i don't have the time to sit down and devote myself to a full session of ring play (four-tabling to usually around 500 hands, taking about 2 hours). i then one time decided that i was going to try one of the multi-table "shootout" style heads-up matches, specifically the four-perosn, two-level ones. i fell in love! read on to discover why.
the simple reason is the +EV edge that this tournament style gives over its non-shootout counterparts. how is that you ask? well, to start with is has to do with the fees involved in entering these events.
i assume that you can play two heads-up contests back to back. that is one regular HU contest followed by another regular HU contest, or a single two-tier "shootout" HU match. if you cannot, then quit reading
also, i assume you know what win rate means, and know what your win rate is in this type of contest. i'm going to use the numbers from the PokerStars tournaments, because that's what i'm familiar with, but any site that has a constant 5% fee structure will have similar results.
WinRate% = WR = the win rate of the concerned player
BuyIn = 100%
Fees = 5%
Expenses = E = -1 * (BuyIn + Fees) = -105%
PrizePoolNormal = 200%
PotentialProfitNormal = PPN = PrizePoolNormal + Expenses = 95%
PrizePoolShootOut = 400%
PotentialProfitShootOut = PPSO = PrizePoolShootout + Expenses = 295%
so first we start with the EV of a normal HU tournament:
EVNHU = WR * PPN + (1 - WR) * E
= WR * (PPN - E) + E
= WR * 200% - 105%
= 2 * WR - 105%
we learn from this that break-even (EV=0) is a win rate at 52.5%. anything better is gravy
next is the EV of a two-tier shootout HU tournament:
well, there's three distinct cases here...
1). you loose in the first tier
2). you win in the first tier, but lose in the second tier.
3). you win in the first tier, and win in the second tier.
note the conditional probability that exists here. to win in the second tier you must have won in the first tier.
so the EV is:
EVSO = (1 - WR) * E + WR * (1 - WR) * E + WR * WR * PPSO
= E - E * WR + E * WR - WR * WR * E + WR * WR * PPSO
= E - WR * WR * E + WR * WR * PPSO
= -105% + 105% * WR * WR + 295% * WR * WR
= 4 * WR * WR - 105%
which means to break even, (EV=0) you must win just shy of 51.25% of your matches.
you're basically paying the same expenses to play two matches most of the time (proportional to your win rate of course), versus the same expenses every time (if you just played normal HU matches). does anyone else think this is a great idea? if you don't believe me, set the two EV equations equal and solve for WinRate%. you'll discover that in order to have better EV playing in shootout style HU matches over normal HU matches, your win rate simply has to be better than 50%. that's quite a boon isn't it? now you might tell me that winning two normal contests back to back is difficult because the opponent you run into in the second tier is likely to be a tougher opponent than the one you faced in the first tier. you may be right, but considering how the second tier is structured (on PokerStars at least) the second tier is a carbon copy of the first with everything doubled (starting chips, blinds, etc.). so it's almost identical to registering in another separate HU match against a tougher opponent, except you don't have to pay the expenses again. you never know, that "tough opponent" just might be a lucky donk who you can easily put out of their misery
. you'll also likely say that since a shootout match is two contests, you're taking twice the time to win twice the prize, therefore its a wash. if you really do think that, you need to go back and read this post more carefully.
the moral of the story folks: twice the time, twice the play, same expenses = +EV
