A note about the probability calculations for quarters, chops and losses.

In all-in preflop situations, preflop or post flop, the author started with the prediction models of propokertools.com to determine the percentage of time that a hand will win or chop the high, win or chop the low, and scoop the pot. The author then used the formulas below to derive the remaining possibilities.

Three-quarters wins = (th% * wl %) + (wh% * th %)
One-quarter wins = (th% * (1-wl% -tl%)) + ((1-wh% - th%) * tl%)
Losses = (1- wh% - th%) * (1-wl% -tl%)
Chops = 1 – all other possibilities (scoops, quarters, losses)

In English:

Three-quarters wins occur when we tie for high (th%) and win the low (wl%), they also occur when we win the high (wh%) and tie for low (th%).

One-quarter wins occur when we tie for high (th%) and lose the low (1-wl% - tl%) and they also occur when we tie for low (tl%) and lose the high (1-hl% - th%) We calculate the times we lose the low as the inverse of the times we win or tie low (1-wl% - tl%), and we calculate the times we lose the high as the inverse of the times we win the high (1-wh% - th%).

Losses, or the Risk of Ruin is calculated as the instances where we lose the high (1-lh% - th%) multiplied by the instances where we lose the low (1-wl% - tl%).

It is the author’s unproven hypothesis that the Risk-of-Ruin will be the best shortcut number for determining the appropriate pushing range in push-or-fold ICM decisions, and that the DQ will lead to a somewhat counter-intuitive hand selection that will appear to the untrained eye to be ‘donk plays’ when they are often mathematically correct.

Hi Dan - I don't think you define DQ (death quotient) in the article. Interesting concept. How do you find DQ?

Buzz

Hi Buzz,

I kind of liked 'Death Quotient' for a catch-phrase, but in the end I decided that 'risk-of-ruin' was more self-explanatory, and does double duty to describe the overall options throughout the hand.

In an all-in situation, Risk-of-Ruin is the probability that we will not survive the hand. In a non-all in line conjecture, risk of ruin is the possibility that we will somehow end up with all of our chips in the middle and be eliminated by the river.

These split pot tourneys add an extra level of possibility since we are often just as happy to put our chips in the middle and split a pot, since our cEV will not be any worse.

Regards,
Dan

What do you guys think on PLO 8/b? I feel that is it probably the best cash game to play even know its hard to find any action of it any more. What I'm trying to say is that PLO 8/b is more profitable against poor players than NL Hold'em...anyone agree?

Usually is PLO 8/b is a bad player got lucky its usually for half the pot, but in NL Hold'em they get lucky they scoop =).

Oh and nice post Daniel J.

Thats the reason you can't get a game.

I play live limit O8 and I beat it, but its a huge grind and extremely slow. I do it mostly for entertainment (I can get completely hammered and still beat it) but I still stick to 3-5NL to make the majority of my money because there are plenty of bad players who keep coming back because they can win when they get lucky.