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Last Updated: April 20, 2022

# Session Risk of Ruin Calculator

## Introduction

This purpose of this page is to calculate the session probability of ruin, given the bankroll, game, hours played, and hands per hour. The calculator assumes if the player ever goes negative before his session is over, then he must walk away broke. He may not ask for credit. In other words, the calculator is meant to advise how many betting units the player should bring to the table.

To use the calculator, select a game from the pulldown menu. That choice will propagate the hands per hour, house edge, and standard deviation fields. If you feel any of these are inaccurate, change them as you wish. You will have to put in the hours played yourself.

When the input looks correct, click calculate and the calculator will tell you:

• Total standard deviation = This is a measurement of the volatility you can expect. You can ignore this field if you don't understand it.
• Probability win: Probability of showing a profit over the session
• Probability of Ruin: Probability the player goes bust before his desired play is over.

## Assumptions

• Blackjack house edge assumes six decks, dealer hits soft 17, blackjack pays 3 to 2, double after split allowed, re-splitting aces allowed, surrender allowed, dealer peeks for blackjack.
• Roulette standard deviation figure assumes player makes even money bets only.
• Craps assumes player bets pass line and full 3-4-5x odds only.
• All house edge figures assume optimal strategy, except blackjack, which is based on basic strategy.
• The average bet for Ultimate Texas Hold 'em should be the bet on the Ante only (as opposed to sum of Ante and Blind bets).
• House edge for baccarat based on the Player bet.

The formula used for the probability of ruin can be found in Blackjack Attack, by Don Schlesinger, 2004 edition, page 132, under "The Short-Term, or Trip, Ruin Formula. Schlesinger says the risk of ruin from this formula is an overestimate and my own simulations agree with this.