| the arithmetic of jackpots |
[Jul. 8th, 2009|09:09 pm] |
| [ | Tags | | | poker | ] |
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As a general rule, at the level of poker I'm playing at, I'm very mildly in favor of jackpots. It's zero-sum, and keeps poorer players in hands that they shouldn't be in, so it ends up being a plus for me. Hitting it didn't hurt either. :)
As I mentioned in the comments earlier, the possibility of hitting the jackpot actually affected the play of the hand I won it in. Here's what happened:
I was in a $1/$2 NL game with $200 on the button with AK of spades. There were 2 limpers in front of me, I raised it to
$10, everybody called ($46 in the pot).
Flop was Qs Js 8d. The blinds checked, next player bet $25, I called, everyone else folded. ($96 in the pot.)
Turn was the 3s. My opponent bets $50. I call. ($196 in the pot.)
The point is that here I would normally have raised him all in, for two reasons: first, if he has trips or two pair, I want him to pay to get there. Second, if a spade comes on the river, it might kill all the action. The problem here is that if I raise him all in and he folds, I lose any chance at the jackpot.
The jackpot normally comes in somewhere between $1500 and $2000. There was a big guaranteed tourney that was going to suck out a bunch of players, so this was going to be at the lower end. For our purposes, let's call it $1600. (It actually was $1574.) My chances of spiking the Ts on the river is a bit better than 1 in 46. I say a bit better because there are some implications. The folks who folded certainly didn't have the T9 of spades, and probably didn't have 98 or Tx of spades, or they would have hung around. Similarly, the remaining opponent doesn't have those holdings, or he would have been afraid to bet. So guessing my actual chances are about 1 in 45, the E.V. from the jackpot is going to be about $35, with very high variance. :)
If my opponent has 2 pair or a set, the chance of the board pairing is 10/44. Another 7/44 times a spade will come that kills the action. For what it's worth, what I actually think is going on, given my opponent, is that he's representing an A high flush. So basically a quarter of the time a scare card will come, and I'll only be behind some variable amount of the time when it does (he might be on a bluff, or now have three pair - I'll certainly call any bet he makes.) My guess is that a scare card will on par, cost me $25. The other thing to consider is that if I put him all in now, he can't bluff the river, which he might well do. (I'd seen him make fire three bullets often enough that I was a certainly not in a believing mood.)
So I guesstimated that a check was about $25 worse than a raise all-in. So on par, that meant playing for the jackpot was right, I did so, the T of spades came in, and my opponent put me all in for another $115 on a total bluff.
You can see if I was playing in even a $2/$5, raising all-in on the turn would have been a better play, I guess sort of depending on how likely I valued the chance of my opponent being on the big bluff. |
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| Comments: |
For what it's worth, what I actually think is going on, given my opponent, is that he's representing an A high flush.
...And, obviously, he doesn't realize that you already HAVE the A high flush! Which is, I must say, a sweet, sweet position to be in... I just love being that guy, in my heart of hearts thinking, "Muthafuggah, you tryin' to bluff me when I got the nuts!"
The thing is, if he has trips, it's 88. Remember that he didn't raise or re-raise preflop. so it is less likely he has QQ or JJ. Plus for it to be 88 he has to have decided not to go for the check-raise on the flop.
This makes the real danger cards on the river a Q or J, since if he started with 88 or QJ he's home, whereas an 8 only helps him if he had 88 to begin with.
Sure, there were a few outs (hell, he could have had QQ or JJ and been slow-betting, though your limited characterization of him makes that sound pretty unlikely). But as you say, you put him on representing A high flush, which is what you actually HAD...
... so maybe not "I got the nuts!", but at least "I got you." Still a good feeling, and an excellent example of how poker isn't just knowing the outs and the odds, but also reading the story that the other guy is telling.
So this bit is instructive. If you are going to slow-play a big pair pre-flop in early position, the normal idea is to reraise pre-flop when you get raised downstream. So it can't just be the case that the guy was slowplaying, he had to be slow-slowplaying. Not impossible, of course, particularly in a $1/$2 game, but it is certainly going to be out of the ordinary.
This is why I don't gamble; doing such calculations off the top of head is something I can't so.
Also, it reminds me; I really need to get a simple book on statistics.
This stuff is hardly statistics - it's just a bit of arithmetic. It seems hard, but once you do it a hundred times or so, it becomes second nature.
Are jackpots really zero sum? My impression is that they get dipped into by the house a lot, either via fees or outright fraud.
I can't speak to fraud, but Mohegan Sun claims that they hand out all the jackpot money to the winner; and the floor boss invited me to be there for the count if I wanted to. | |
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