I have been thinking if David Sklansky’s Fundamental Theorem of Casino Malaysia might not apply to tournament Casino Malaysia. My reasoning is that the theorem is based on poker as an infinite game, such that every loss where an opponent makes a mistake and calls with the wrong odds is paid back over a large number of hands where the odds will play out. In other words, say you make a pot size bet on the turn with top pair against someone on a straight draw, they call and hit their straight. You lose that money, but over many situations like that you will end up a net winner.
Another way to put it might be the common saying ‘all you can do is get your money in when you have the best of it’.
It comes back to the Law of large numbers. In a series of coin tosses, it is quite possible to get say five heads in a row. Over just ten tosses, you are going to lose money if you are betting tails. However over a million tosses, the lucky sequence of five heads it going to me meaningless, as there is likely to be just as many lucky runs with tails and the odds are going to smooth out.
So too poker can be viewed as just one long game with a few interruptions here and there. If you stop playing one session, have a break for ten years, the very next game you play will still have exactly the same chance of hitting or missing draws and miracle cards coming off on the river.
It also makes the very important assumption that, just as the game is, theoretically, infinite, so too is there an infinite supply of money to replenish losses to bad beats and allow enough hands to be played to even out the bad luck of the losses against the odds.
But now consider the special case of a single tournament. The game is not infinite; the increasing blinds will force it to end at some point. Nor can losses to bad beats be replenished from an external source. No poker player is going to pass up getting all their chips in the pot if they are a 10-1 favorite. Yet over a long tournament, it is quite possible to be beaten twice in such a situation (100-1, which we all know happens), and that will pretty much be the end.
In a cash game, an opponent who calls your all-in with only a 1 in 10 chance of winning is a blessing. As long as you can keep them at the table, and you can replenish the bad beat loss, your expectation is positive that the money will come back many times over. In a tournament, they are the total bane of the good player, because there may be no chance to get the money back in the limited time available. What if the all-in bad beat cost you 9,000 out of your 10,000 stack, and by some miracle you are able to play exactly the same hand against them a few hands later and win. Your pathetic 1,000 stack is now 2,000. Woo hoo.
In the special case where you only ever play one tournament in your life, it seems that it may be a mistake to commit chips to a pot in many cases where the odds are in your favour, because a bad beat will end your ‘life’.
Now let’s consider the general case of playing many tournaments – for theoretical purposes, let’s say we can play infinite tournaments with infinite money to buy into them. Assuming we played perfectly, I think the math of working out possible hands, bad beats etc etc becomes as complicated as the sum over path of quantum physics. But lets just make is simple enough that my weak math can cope.
Assume the top 20% of players cash, for an average cash out value of 5 x buy-in. Assume two bad beats ends a tournament. Assume a bad beat is losing a hand as the 2-1 favourite. In any one tournament, there are five bad beat risk hands. I am almost certainly wrong with the detail of the math, but the chances of getting beat twice as the 2-1 favourite over five hands is 5-6, or 1-6 of not being bad beat out of any one tournament.
But what poker play wouldn’t take even money as the 2-1 favorite?
For every six buy-ins of $1,000 we will win $5,000. $6k to get back $5k. Hmmm.
If we follow the maxim of ‘all chips in when you have the best of it’, over infinite tournaments we are going to be infinitely broke.
Ok, so my math is almost certainly wrong in detail. But it is going to be something like that.
This also breaks another convention of poker – not to upset the fish. In a cash game we want the runner, runner draw and the four outs on the river guy to call our pot sized bets. ‘Gutsy call mate’, ‘Nice hand, well done’, we try and say with a genuine smile. Anything to keep them in the game and making those donkey plays. But in tournaments they are death.
It becomes very clear why Phil Helmuth berates and humiliates such players. The cash game players call it bad form, but for Phil, it is his livelihood and long term success that is at stake.
I will have to think on this more and see what it really means in terms of my future tournament strategy.
ADJUSTING TOURNAMENT STRATEGY
If what I said before has some truth in it, then these are my thoughts for adjustments to play for tournaments:
- The nut hand is the only hand that warrants commitment of all chips
- There is a need to see many flops to give yourself the best chance of getting nut hands in the limited time available
- but you have to see the flops cheaply
- when the blinds are high relative to your chip stack, it may be worth chasing draws against the odds. An all in on the flop means your pot odds can’t get any worse on later streets
- With a large stack, it may be better to fold to a drawing hand to deny them the chance of sucking out, and waiting for the nut hand to crush them with
- If 2. is right, then one benefit is that when you do get the nut hand, it will likely be very well disguised. Also, you are going to have a fairly lose table image, increasing your chances of getting paid out.
I am going to try this out over the next few weeks at pub poker and see a) if it works at all and b) what refinements might be needed if it does work.
Writing this, it occurs to me that the strategy invoked is not unlike the styles of Daniel Negreanu or Gus Hansen. Though I notice both seem to have tightened up their play a lot recently, at least in the televised tournaments I have seen them in.