### 11-30-05 [poker]

This is the hand I went out on, and I'm going to analyze it in a fancy way. I'm going to look at chip EV vs. actual tournament money EV, because I think this is one of those cases where it may matter. This is a 3-table $30 entry tournament, the top 5 places pay $270,225,180,135,90. There are 7 players at this point and I'm the short stack.Before the hand starts, the stacks and expectations are :

stacks : Seat 1: pokrprofesr ( $3460 ) - Seat 2: HARLEYGUY814 ( $5535 ) Seat 3: Gatormancc ( $3090 ) Seat 4: baystar ( $2525 ) Seat 6: chukb ( $2250 ) Seat 7: euming ( $6400 ) Seat 9: bobsway ( $6740 ) dollar expectations : pokrprofesr : 117.846351 HARLEYGUY814 : 155.915487 Gatormancc : 108.856359 baystar : 93.473993 chukb : 85.243610 euming : 167.340767 bobsway : 171.323433

First, I'm surprised how high my dollar expectation here was. It's only slightly under the $90 for last place, so certainly I should not give up easily just because I'm short stack.

Now, here's the action :

Blinds (100/200) ** Dealing down cards ** Dealt to chukb [ 5h Ad ] bobsway calls [200]. pokrprofesr folds. HARLEYGUY814 calls [200]. Gatormancc folds. baystar folds. chukb is all-In [2150] I'm in the small blind, there are two limpers before me, and the big blind behind. I figure I need to take a shot and they probably have weak hands, so I'll push my A5. euming folds. bobsway calls [2050]. HARLEYGUY814 folds. bobsway shows [ Jc, Js ] a pair of jacks.As it turned out, bobsway limped jacks, and busts me. But what was my actual EV ? First of all, let me say I think this was a marginal move by me, just because my stack was actually big enough I could have just limped or folded here. My M was 7, which is not terrible. If my M was 4, I should have definitely pushed here, with M = 3 or 5, it's borderline. M = 2 is actually too low, you can't make anyone fold. M of 6 or 7 is high enough that this is not necessary.

So, let's look at the EV. First of all, I'm going to assume that the 3 guys in the hand will call with AT or better and 66 or better. We'll ignore AA and say that in all those cases I'm 30% to win. That's roughly the top 10% of hands they're calling with, and they limped maybe the top 50%, so they're calling with 20%. The chance that noone calls is 0.9*0.8*0.8 = about 60%. We'll ignore multiple calls. (actually I'm assuming here that they always limped their good hands, which is not true at all, so really the chance of them calling should be even lower).

So, in terms of EV, if I fold, I have 2150. When I push, 60% of the time, noone calls and I get 2150+700. 40% of the time when someone calls, I will win 30%, and wind up with 2250*2 + 400 = 4900, and lose 70% and wind up with 0. The overall EV in terms of chips for pushing in is : 0.6 * 2850 + 0.4 * 0.3 * 4900 = 2298. Slightly +EV.

What about in terms of actual money EV ? I'll assume that the caller is bobsway. If I just fold and bobsway wins what's in the pot, my EV goes to $82.33 . If I push and noone calls, I'd be up to $101. If I push and win, I'd be up to $142.83 . If I push and lose, obviously I'm down to $0. So my money EV overall is : 0.6 * 101 + 0.4 * 0.3 * 142.83 = 77.739 . Clearly minus EV !!

So, that's very interesting. This is one of those clear cases where tournament EV is different from just chip EV. In this case, if I fold the negative EV is not very bad, I still have a good shot at last place money. Also, the positive EV of the double up is not worth that much. You see when I more than double up in chips - from 2250 to 4900 - my money EV only goes from $85 to $143 , not nearly a double up.

So, clearly I should have folded and made a big mistake here. In bubble situations, it's not worth taking gambles, because the value of having any chips at all is so great, and the value of doubling up is not that great.

(btw the money EV's here were computed with GoldBullion using the correct tournament equity algorithm I described earlier).

Also note that this tournament payout structure is really exceptional for this type of hand. There's a big jump from $0 to $90 on the bubble, and then the payouts above that just increase linearly, not exponentially like they usually do. In more typical multi-table tournament payouts, you don't see nearly such a big affect, because the large prize for first place makes money EV much closer to chip EV. Also, the jump from bubble to cash is not usually so big, here it's 3x the buy in, more typically it's just 1x the buy in. If you ever need to play cautious on the bubble, it's in this type of payout structure which doesn't reward gambling late.

The basic key principle here is that larger stacks are worth less in terms of dollar EV. When you double your stack in chips, you much less than double your dollar EV. If everyone else's stack is the same, when my chips go from 2000 to 4000 to 8000, my dollar EV only goes from $83 to $128.50 to $176. You can see that getting allin, even as a 60/40 favorite, is a major disaster, and the bigger your stack the worse it is.