Bankroll

[J.R.]

I wouldn't be asking this if I knew my standard deviation in short-handed games. I want to learn to play shorthanded, and was wondering what a good bankroll might be. I am winning 2-4 to 3-6 online player, around 1.9 BB/hr. 300 big bets is the typical number I hear for full ring games, what goes for shorthanded?

Is there any rough, back of the hand measurement for estimating one's short-handed SD given a full ring games fluctuation?

[Mason Malmuth]

Hi J.R.:

There is no rule of thumb way to measure your stand deviation in a short handed game assuming you have an idea of what it is in a full ring game. However, be assured that it will be larger. And if you are playing against aggressive players, it will be much larger.

Best wishes,
Mason

[irchans]

Typical standard deviation for heads up is 3 BB *sqrt(hands per hour). Assuming 100 hands per hour, that gives 30 BB / sqrt(hr). For a 5% risk of ruin and a 2 BB/hr edge, the general formula is 3/2*sigma^2/edge = 3/2*900/2 = 675 BB.

[BruceZ]

For a 5% risk of ruin and a 2 BB/hr edge, the general formula is 3/2*sigma^2/edge = 3/2*900/2 = 675 BB.

This calculation is correct for a 2 bb/hr win rate, but that is really a 4 bb/hr "edge" over your opponent, since you win 2, and he loses 2. So win rate should be used in this formula instead of edge.

bankroll = 3/2*sigma^2/win_rate for 5% risk of ruin

or bankroll = ln(r)*sigma^2/(2*win_rate)
where r is risk of ruin.

[BruceZ]

I wasn't right about saying the edge is 4 bb/hr, but I was right in replacing edge with win rate. Apparently your "edge" must be expressed as a percentage of what you bet, so if I win 51% of the time and you win 49% of the time, I have a 2% edge. Win rate is that edge multiplied by the money I bet. If that comes out to 2 bb/hr, then I'm not sure it is correct terminology to say that is an edge of 2 bb/hr, but in any case it is certainly not an edge of 4 bb/hr, even though I win 2 and you lose 2. It would seem I have a 4 bb/hr edge "over you", but I'm not sure that's proper terminology. I would have a 2% edge, and a 2% edge "over you" as well.

In games where one player wagers a different amount than his opponent, the edge of one player is not the same as the disadvantage of the other player. For example, if I am getting 2-1 on an even money bet, I have a 100% edge, and my opponent has a 50% disadvantage. But I would win 67% of the money that goes in the middle, and he would win 33%. Is it correct to say I have a 33% edge "over him"? After all, this would be the case if the bet were even money. Mason, what say you? It's not a mathematical question, but a terminology question.

[BruceZ]

In games where one player wagers a different amount than his opponent, the edge of one player is not the same as the disadvantage of the other player. For example, if I am getting 2-1 on an even money bet, I have a 100% edge, and my opponent has a 50% disadvantage. But I would win 67% of the money that goes in the middle, and he would win 33%. Is it correct to say I have a 33% edge "over him"?

Make that a 50% edge for me, and a 25% disadvantage for my opponents, and I win 50% of the money that goes in the middle, so maybe it doesn't make sense to talk about "edge over opponents" as something separate from edge.