Hi Matthew: I couldn’t figure out how to post this directly to Sklansky – nobody seems to use the Discuss the Magazine Forum anymore. However, given that I wanted to discuss this issue with you anyway, the timing is propitious. In any event, if you agree with my analysis, hopefully there’s still time to pass this info along in time to do some good.
Please note that I spent a year consulting on the HM2 stats, wrote most of the current HM2 stat definitions, and I’m probably the only person alive who has written more algorithms and calculated EV more times than you have …
The problem is that Sklansky’s EV calculations in his December article are incorrect. He is calculating EWin rather than EV - a very common mistake. See Sklansky’s current article, Norman Zadeh’s Simple GTO Game, Part One (December 2013); contrast to EV calculated correctly - See
http://www.twoplustwo.com/magazine/i...ploitation.php
In this current hypothetical “There is one round of betting, each player has contributed $1 to the pot and the bet is now $2, which is the remaining stack of at least one of the players. In other words, if there is a bet, it is the size of the pot and there’ll be no raise. If it goes check-check, there is a show down.” This is analogous to River Jam situations that you analyzed in Part Eleven: River Play.
I’m just going to look at the River Jam decision, beginning with the following basic algorithms:
Decn EV (River Top 14% Jam OOP HU) = (OppFold%)(RiverPotsize) + (OppCallWin%)( RiverPotsize + Betsize) - (OppCallLose%)( Betsize), p. 332, and
Decn EV (River Bottom 7% Bluff Jam OOP HU) = (OppFold%)(RiverPotsize) – (OppCall%) (Betsize). p. 353.
Note: Because of the way River Jams are calculated, it doesn’t make any difference to the EV calculation whether the dead money in the beginning River Pot comes from the players or from Santa. On the other hand, the amount of player’s dead money is required information to calculate EWin in this hypothetical.
Assumptions: RiverPotsize = $2; RiverBetAmount = $2 and RiverCallAmount = $2; FinalPotsize when called = $6.
Player A Bets and
wins when OppFolds: Player
wins $1 on the hand, but Player’s
profit on the bet is $2.
Player A Bets and
wins when OppCalls: Player
wins $2 on the hand, but Player’s
profit on the bet is $6 - $2 = $4.
Player A Bets and
loses when OppCalls: Player
loses $4 on the hand, but Player’s
loss is limited to ($2).
Player A bluffs and
wins $1 on the hand: but Player’s
profit on the bet is $2.
Player A bluffs and
loses $3 on the hand: but Player A’s
loss on the bet is limited to ($2).
Summary of EV of Jamming (First 3 and last 2 calculations, Bet is $2 (Pot Bet):
....Jam ($2)............Freq%...Profit...EV
Top 14 v Top 14 Win... .0098..... 4.... .0392
Top 14 v Top 14 Lose.. .0098.... (2). (.0196)
Top 14 v 14 - 50 Win.. .0504...... 4... .2016
Top 14 v 50-100 Win... .0700..... 2... .1400
Bluff v Top 50... Lose.. .0350.... (2). (.0700)
Bluff v Top 50... Win... .0350..... 2.... .0700
...............................
21.00% ....... .3612
Total Bet = $0.42 EV $0.3612 ROI = 86% Total Final Pot = $1.12
Sklansky’s EWin calculations:
....Jam ($2)............Freq%...Win...EWin
Top 14 v Top 14 Split .0196...... 0 ... .0000
Top 14 v 14 - 50 Win .0504...... 3 ... .1512
Top 14 v 14 - 50 Win .0700...... 1 ... .0700
Bluff .. v Top 50 Lose .0350..... (3). (.1050)
Bluff ...v Top 50 Win. .0350...... 1.... .0350
.............................
21.00% ......... .1512
Total Bet = $0.42 EWin $.1512 ROI = 36% Total Final Pot = $1.12
AT LAST! Irrefutable proof that it happens to everybody. ☺
Larger issues: Sklansky concludes that “In other words, the first position player loses an average of a bit more than $.08 per hand”. This is EWin, not EV. We know that EV (Player) <> -EV (Opponent) and that EV (Player) + EV (Opponent) = $2 for this hypothetical River Jam OOP HU decision. Without making the rest of the calculations, we also know that the EV River Jam OOP HU decision in this hypothetical is at least $.13 per decision (-.08 + (.3612 - .1512)).
These are both great examples of how to calculate EV as a discrete random variable in a hypothetical. Once the EV calculations are fixed, Part II of the current hypothetical should be a great example of one way to use and apply decision theory for exploitative purposes to maximize the expected value of a discrete random variable. I call this methodology paragraph C of the Optimal Corollary to the Fundamental Theory of Poker.
Matthew: Note the subtle distinction between “
bet, wager, play, decision or situation can be expected to win or lose on average” and “
hand can be expected to win or lose on average.” The first is profit and EV. The second is EWin.
p.s. There a number of valid reasons why default EV stats don’t, and never will, calculate profit – they define and calculate EWin. You got blindsided – big-time. My apologies. Glad to share this very long and complicated story with you, just not in the forums. ☺
You might find these “unified” theoretically consistent definitions helpful:
Expected Win is NetAmountWon adjusted for Pot Equity (Total Adjusted Winnings).
Expected Value (
decision or situation faced) tells us how much we expect to
profit (adjusted for Pot Equity) on average and considers all money previously invested in the pot as dead money. This means folding at the point of calculation always has an expectation of zero (EV) regardless of whether we lose money overall on the hand (EWin).
Expected Value (decision or situation faced) is the weighted average profit (adjusted for Pot Equity) of making a decision to act (or not to act).
Expected Value (decision or situation faced) is the weighted average value of making a decision to act (or not to act).
Looking forward to your response …. PM would be terrific.
Last edited by TheZepper; 12-28-2013 at 10:07 PM.