MASON MALMUTH

A mistaken check can be expensive. Not only does it cost you the equity you would have accumulated from worse hands that would have called, but it sometimes costs you a much larger third value bet that you could have made on the river had you built the pot on the turn. Checking can also cost you a bet from hands that would have paid off on the turn but not on the river, and in worst case scenarios it can cost you the pot when a hand that would have folded gets to see the river for free.

The May issue of the magazine is just now being published, ten days into the month, because of the hacking and subsequent forum downtime at Two Plus Two. I know that a lot of people are frustrated by this, particularly those with SCOOP and/or WSOP packages to sell on the marketplace, but I actually think that Mason Malmuth et al deserve considerable praise for the decision to shut down the forums rather than put sensitive user information at further risk.

I don’t know enough about such things to estimate how much this downtime is costing them, so let’s just agree that it’s a lot. Two Plus Two gets boatloads of traffic that’s targeted and extremely desirable to a number of companies with big advertising budgets. They voluntarily shut down that money machine to protect our personal information. Yes, it’s the right thing to do and I’d expect nothing less, but it deserves a hat tip all the same.

There are two seminal books that address the value of tournament chips: David Sklansky’s Tournament Poker for Advanced Players and Mason Malmuth’s Gambling Theory and Other Topics. I haven’t read Malmuth’s book, but my understanding is that both make a similar argument that this value is non-linear. Another words, your last chip is worth more than your second to last chip is worth more than your third to last chip etc. Each chip you add to your stack increases the value of your stack, but by less than the preceeding chip did. So if you have on chip worth x, and you double up, your stack is worth marginally less than 2x. And if you double again, your stack will not be worth 4x. This is because survival has value in a tournament where all of the prize pool is not paid to the winner.

The countervailing principle is that chips are worth more in the hands of a skilled player than an unskilled player. This is because better players will have the opportunity to use those chips to win more chips. They contain within them the player’s expected value for the tournament. In FTOPS Event 4, the first 2000 chips, which cost $300, were probably worth $750 or so to the best player in the field. Conversely, they were probably worth about $50 to the worst player.

You can see that at this rate, it is clearly correct for the best players to rebuy immediately in a tournament that allows unlimited rebuys. Even though his second $300 buys him less than his first expenditure, it still buys him more than $300 worth of value. Conversely, it is incorrect for the worst players to rebuy. In fact, it is incorrect for them to play at all.

When only a single rebuy is permitted, this could at least theoretically change. If a skilled player uses his rebuy immediately to double his starting stack, he risks losing all 4000 of his chips at once. Although his rebuy was a good investment, he missed out on the opportunity to make an even better investment in a second tournament life. Remember, going from 0 to 2000 is worth more than going from 2000 to 4000. By opting for the latter, the player cost himself the chance to do the former a second time.

However, this must be balanced against the risk of immediately getting over 2000 chips, remaining there for the entire rebuy period, and thus losing the opportunity, to invest that second $300 at all.

The one other thing I haven’t mentioned yet is that it matters how many chips the other players at your table have and how good they are. A player cannot realize the extra value that his skill imparts to his 4000 chip stack if no one else at the table has more than 2000. If several bad players to his right all rebought immediately, then the good player should do so as well, so that he will have the opportunity to invest his additional 2000 chips well against those weak players. If several very good players to his immediate left rebought to 4000, the same player might be better off saving his rebuy as an insurance policy against elimination. Otherwise, he risks playing larger pots out of position against very good players- a scenario where those additional chips would not be invested well. If the first hour is drawing to a close and his stack is below 2000, he can always take his second rebuy then.

Unlike an unlimited rebuy tournament, where it generally makes sense to push any edge during the rebuy period since survival is never at risk, this structure makes survival during the first hour particularly important. This is because the player will have the opportunity at the end of the first hour to buy chips at a discount. $300 will buy him, not 2000 chips, as with the rebuys, but 2500 chips for an add-on. It is pretty much always profitable for a good player to add-on, and if he is eliminated in the first hour, he won’t have a chance to take this good investment.

I include this exegesis on rebuy tournament theory because I have nothing interesting to say about the tournament itself. No one at my table rebought immediately, so I didn’t either. I lost my first 2000 chips with two pair in a limped pot at the 10/20 level. My opponent seemed like a fish, so I thought he would call me down with worse, but he ended up having a better two pair. Then I rebought, added on, lasted for about an hour more despite missing tons of flops, shoved over a very weak limper with K7s, and got called by one of the blinds who had AK.

I’m not all that good at PLO, but I do want to learn, and I’m sure it will be a weak field, so I’ll probably play today’s 2:00 $500 PLO 6-Max. I’ll be playing the Stars $300 anyway. Then at 4:30 there’s a $100 rebuy FTOPS that I’ll play if I’m not sick of poker by then.