How does changing risk affect win rate?

Before we determine the amounts that we will bet, we have to decide the level of risk that we are willing to accept. Obviously the lower the risk, the lower our returns. This chart displays our win rate given four possible risks of ruin: 13.5%, 5%, 2%, and .025%. That is, we are setting bets such that our risk of losing our entire bankroll varies from 13.5% to .025%. All penetrations are displayed from 26 to 130 cards cut off. Win rate is calculated in dollars per hour with a $25,000 bankroll, a bet spread of 1-12, 100 hands per hour, and optimal betting. The jagged movement is caused by the fact that a minimum chip size of $5 is used and the increased penetration allows increases in the minimum bet in $5 increments.

The good news is that a dramatic decrease in our risk of ruin from 13.5% to 2% causes a much less dramatic loss in win rate. A drop in risk from 2% to .025% causes less than a 50% drop in win rate.

(For the mathematicians, these risk rates roughly correspond to full Kelly, two-thirds Kelly, one-half Kelly and one-quarter Kelly.)

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A single-deck chart along the same lines can be found at:

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 © 2009 Norman Wattenberger