In SNG Hero, 1st place gets 75% of the prize pool, while the other 25% is asigned randomly to a bounty.

In this case, btn is the bounty. Im not sure how to approach this mathematically. Whats the minimum equity I need to call here? (I guess I have 2, since there are 2 pots?)


partypoker - $20+$0|15/30 NL (4 max) - Holdem - 4 players
Hand converted by PokerTracker 4

SB: 30.67 BB (VPIP: 39.42, PFR: 30.90, 3Bet Preflop: 16.25, Hands: 329)
Hero (BB): 11 BB
CO: 20.33 BB (VPIP: 77.78, PFR: 66.00, 3Bet Preflop: 55.56, Hands: 57)
BTN: 4.67 BB (VPIP: 48.89, PFR: 42.86, 3Bet Preflop: 21.43, Hands: 47)

SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has Q T

fold, BTN raises to 4.67 BB and is all-in, SB raises to 30.67 BB and is all-in, Hero ??

Just set the payment structure to wta, bounty should not change it. Then use some SNG soft there are many of them.

In general, I suggest that you search for Collin Moshman's videos about knockouts (direct links would be against the 2+2 rules) - he explains math adjustments in KO tourneys very well.

If there are $20 regs who use the chip EV mode Nash equilibrium in spots where the bounty player has gone all-in, they'll become $10 regs soon

In this spot, I think the GTO isoshoving range for SB is as wide as 70-80%, down to rags like 74s, because the other big stack has already folded and so the potential side pot doesn't deter SB from contesting the main one with the bounty added, and surely he'd love to remain in a HU pot with BTN.

As the bounty is worth 1/3 as much as the regular prize pool, 667 chips (2000 chips in play, divided by 3) should be added mentally to the main pot (whenever the bounty player is in and Hero is covering him) to represent the bounty. So it becomes t420 + t667 = t1087 here. The side pot is t380.

However, if Hero folds, then he doesn't totally lose the chance to take the bounty - if BTN wins the current hand, then, in the few next hands, Hero's chance of winning the bounty will be even slightly higher than 1/4 imo because the big stacks will make each other fold from time to time when the bounty player shoves again. I'd say it will be 30% or so.

BTN will win the current hand in 55-60% of cases if Hero folds because BTN's shoving range is stronger than chip EV Nash (consists of value hands only; the bounty player is inclined to wait for a better spot to get his chips in with a big equity and has an orbit or two to do so, as if he were surrounded by loose fish), I'd say it's top 20-25%.

Hence Hero's chance of taking the bounty later if he folds now is something like 60% * 30% = 18%, and we should add that to Hero's stack if he folds, i.e. assume that he'll have (t330 - t30) + 18% * t667 ~ t420 if he folds now.

If Hero calls all-in now and fails to win the main pot, his chance of winning the bounty later becomes negligible in any case.

So the problem is reduced to whether to call all-in to contest the main pot of t1087 and the side pot of t380 vs a top 25% (BTN) and a top 70% (SB) range or to fold and retain t420.

In this model, QTo becomes a snap call, and actually, Hero should call with a 50%-ish range imo, something like this:

Oops, pardon me, of course Hero's chance to take the bounty later if he folds and BTN doubles up will be very low because BTN will then get a t140 * 2 + t30 = t310 stack and Hero's actual stack will remain t300 after folding the bb and he'll also have to post t15 in the next hand. If he folds his sb too, then he won't be covering the bounty player until the latter posts and folds his bb or gives away some chips in some other fashion (which is unlikely because the bounty player with a ~10 bb stack will be very tight, looking for a value spot to put his chips in). So it will be advisable for Hero to steal a pot urgently to start covering the bounty player again, which he won't always succeed in.

So I'd say that Hero's chance of taking the bounty conditional on BTN doubling up is small, like 15%. The unconditional probability (after his fold) is 15% * 60% = 9%, where 60% is BTN's equity in the HU all-in race vs SB in the current hand.

So we need to add merely 9% * t667 = t60 mentally to Hero's stack if he folds, making it t360 (= t300 + t60).

The decision between contesting the virtual t1087 + t380 pots and retaining virtual t360 then becomes more conducive to overcalling.

Hero's overcalling range thus should be 90%-ish, incl. such total rags as 72s. That's because he won't have a good chance to knock BTN out later on.

Note that, if Hero had just 10 chips more (t340) in the stack, or even better, 25 chips more (t365) his calling range would be much narrower, as described in the previous post. That's because he'd be covering BTN in the next few hands.

What a difference do 10 chips make in KO tourneys sometimes! That's their beauty and horror - the value of a stack is a discontinuous function unlike an ICM value - it can sometimes make a significant jump if one adds or subtracts a few chips from the player's stack.

Hey co on!

In your calcs, bounty should be t500, because it represents 1/4 of the prize pool. Right?

Thanks a lot, great response.

No. The first place prize in low multiplier tourneys (corresponding to the total number of chips in play - t2000) is 3/4 of the total prize pool and the bounty is 1/4 of the total prize pool, so the bounty is 1/3 of the first place prize and it corresponds to t2000/3 ~ t667.

Great, thanks! Its a lot of math I have to assimilate