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Thanks for the reply Bill
I saw the increase in my gammon chances, but as it was only a 1.8% increase, I didn't think it was a big factor
I can also see how the opponent would win now with the rolls you mentioned...something I hadn't considered.
I was just wary of the 11, 12, 13, 16 or a 6 on the opponent's following throw. It's definitely a new side of the game to me - taking risks like this for a slightly better chance at the gammon.
It’s not the increase in gammon chances in and of itself that matters, it’s that increase relative to the amount of increased winning chances you get by playing safe.
In a cash game, assuming you have a play that wins 100% but never wins gammon, you get 1 point by making that play. If another play increases gammon chances, but also creates losing chances you either win 2 points or lose 1. Losing therefore costs you 2 points (-1 instead of +1). Winning gammon gives you 1 extra point. Therefore to break even the risky play must increase your gammon chances by twice as much as it increases your chance of losing.
In your example, the gammon chance increased by 1.8%, losing chances by 0.6%. The increase in gammon chances is more than double the increase in losing chances, so it’s correct to take the risk to win more gammons.
Be careful with this in match play. The basic idea still applies, but the value of gammons is not constant like in a cash game. There are match scores where you need less than double gammon chances to take the risk and some where you need more than double. The relevant concept is called gammon price - for money games the gammon price always is 2. You need 2 gammons for each loss.
Just a simple example, consider a 5 point match where you trail 3-1 and you have doubled. Obviously you should be playing very aggressively for a gammon - you win the match if you gammon your opponent. A risk/reward calculation can tell you how aggressively you should play. If you could safely win the current game, you’d tie the match and therefore have a 50% chance of winning it. If you play risky you are risking that 50% chance (you have zero chance if you lose) to increase your MWC by 50%. You risk 50 to gain 50, so you should be willing to trade losses for gammons even up; the gammon price in this situation is 1.
Other scores will give other gammon prices, but unless gammons are meaningless (such as they would be to the leader in my above example), there will always be some ratio of increased gammons to increased losses that will make playing for gammon the correct play.