more on calculating tournament ev...

[NYIsles 0]

In an earlier post, I posed a general question as to whether or not it would make sense to call an all-in turn bet while assuming 14 outs with one card to come during the late stages of a tournament. The particular scenario was as follows:3 table sit 'n' go; 4 players left, all in the money.Subject is sitting with Ad 7d; board is Jc 6d Td 7h. He is faced with an all-in turn bet against one opponent. The chip counts following the all-in bet are as follows:Subject: 5,745Opponent: 1,867 (remaining if Subject calls)P3: 14,090P4: 8,753Pot: 10,045The payouts are as follows:1st: $502nd: $363rd: $244th: $14Most of the responses I had gotten focused exclusively on pot odds – i.e., it wouldn’t make sense to call the bet, because the Subject was getting less than 2:1 on his money. (This was also the rationale I used when folding the actual hand.) Upon reflection, however, it occurred to me that focusing exclusively on pot odds only makes sense if your tournament chips are magically converted to cash at the end of the day, on a dollar for dollar basis. This clearly isn't the case. The question is, how much of an edge should you be willing to lay (insofar as pot odds are concerned) if winning the bet will put you in great position to win the whole thing? And how do you make those kinds of calculations on the fly?I didn’t get any responses to these questions, so I decided to develop a spreadsheet to calculate tournament EV when faced with a post-flop all-in decision (either yours or an opponent’s) at a final table with up to 4 people remaining. Getting into the mechanics of the spreadsheet is a bit beyond the scope of the post – but suffice it to say that Paul Phillips goes into some details on his website, and also lists a link to further discussion that can be found on RGP. If anyone is interested in looking at the spreadsheet (or would like to confirm its accuracy, which I would welcome), PM me and I’ll send it to you. (Please note: I am not stating that I used Paul Phillips’ methodology. The methodology I used appears – on a very general level – to be similar, but I can’t confirm that it is or isn’t the same.) Here is a synopsis of the results for the given hand:Call and win: 1st place: 38.99% 2nd place: 33.43% 3rd place: 22.78% 4th place: 4.80% Call and lose: 1st place: 0.00% 2nd place: 0.00% 3rd place: 0.00% 4th place: 100.00% Fold: 1st place: 14.19% 2nd place: 17.39% 3rd place: 23.79% 4th place: 44.63% 2 cards to come: EV: Call: $28.25 Fold: $25.31 1 card to come: EV: Call: $21.20 Fold: $25.31 In summary, according to the above chart, the EV for a fold ($25.31) exceeded that of a call ($21.20). So, in this case, a fold was the right play.In experimenting with this a bit, I tried to find a similar situation where a call would be in order from a tournament EV perspective, nothwithstanding the fact that the pot odds themselves would not justify a call. Perhaps unsurprisingly, the EV for a call did not approach the EV for a fold until the Subject’s current chip position approached a level far in excess of his opponents’.However, and perhaps this is a bit surprising, it was easier to find a scenario where a call would be incorrect from a tournament EV perspective, notwithstanding the fact that the pot odds themselves justified a call. Consider the following:Subject: 6,045Opponent: 1,867 (remaining if Subject calls)P3: 6,790P4: 4,753Pot: 21,045Results: Call and win: 1st place: 66.89% 2nd place: 25.60% 3rd place: 6.72% 4th place: 0.79% Call and lose: 1st place: 0.00% 2nd place: 0.00%3rd place: 0.00% 4th place: 100.00% Fold: 1st place: 14.93% 2nd place: 24.44% 3rd place: 30.31%4th place: 30.33% 2 cards to come: EV: Call: $32.30 Fold: $27.78 1 card to come: EV: Call: $23.25 Fold: $27.78 In this case, although calling and winning gets the Subject first place almost 67% of the time vs. 15% of the time when folding, the tournament EV for calling is only $23.27 vs. $27.78 for a fold. This, keep in mind, is with adequate pot odds for a call.Developing the spreadsheet is a bit time consuming, but I’m going to eventually build a model that would be applicable for up to a full 9 player final table – and also something that would evaluate more than one player going all-in at a time. The only required inputs are the current chip positions, the prize structure, the number of outs, and the current bet.Perhaps these results are self-evident to a great many of you, but I, for one, like to see calculations in support of theory. Again, if any of you are interested in verifying the validity of the methodology (or checking for mistakes, which I acknowledge I may have easily made in constructing this), I would welcome your input.Thanks…

[MrNiceGuy 0]

However, and perhaps this is a bit surprising, it was easier to find a scenario where a call would be incorrect from a tournament EV perspective, notwithstanding the fact that the pot odds themselves justified a call.

Actually, this isn't really that surprising ... reasoning that if you call and lose, you finish 4th no matter what, whereas if you call and win, you still might only finish 4th, while if you fold, you might do better than 4th. (Basically, in a spread payout structure, survival matters.)

[NYIsles 0]

Actually, this isn't really that surprising ... reasoning that if you call and lose, you finish 4th no matter what, whereas if you call and win, you still might only finish 4th, while if you fold, you might do better than 4th. (Basically, in a spread payout structure, survival matters.)Very true. I imagine the lines become a bit greyer when your opponent is the one who is all-in...